BASIC MATHEMATICS - XII SET - I

Size: px
Start display at page:

Download "BASIC MATHEMATICS - XII SET - I"

Transcription

1 BASIC MATHEMATICS - XII Grade: XII Subject: Basic Mathematics F.M.:00 Time: hrs. P.M.: 40 Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks. Attempt all the questions. SET - I Group A. a) A man has 5 friends of whom 0 are relatives. In how many ways can he invite 8 guests such that 5 of them may be relatives? [ 50! 4! 6 5! b) Prove that: toe c) If a binary operation * on Q the set of rational number is defined by a * b = a + b ab for every a, b Q. Show that * is commutative and associative. [. a) Determine the equation to the hyperbola in standard form with a verte at (0, 8) and passing through 4, 8. [ [ y b) Find the angle between two lines whose direction ratios are,, 4 and,,. [ 6 6 c) Find the distance between the parallel planes y z 0 and 4 4y z 0 [ 6. a) Find the value of m if the vectors i j k and i j mk are orthogonal. [ m = 4 b) Show that f is not differentiable at =. [

2 c) Evaluate: a d a 4. a) Solve: y yd dy 0 Sin log a y a [ C [ C b) Following are the information about the marks of two student A and B. A B Average Mark 84 9 Variance of Marks 6 5 Eamine who has get the uniform mark. [ A c) Find the probability of getting two heads twice in 5 tosses of two coins.[ 5 5. a) How many words can be formed from the letters of the word ENGLISH? [4 i) How many of these do not begin with E? ii) How many of these begin with E and do not end with H? 5040, 40, 600 b) Prove that the set G,, 5. Where is an imaginary cube root of unity is a group under the usual rules of multiplication. [4 4 y y y y Show that y...!!! 4 6. a) If... Prove that:...! 4! 6! e e...!! 5! [4 b) The projection of a line on the aes are 6,,. Find the length of the line and its direction cosines. [4 length 6 7; d.c' s,, 7 7 7

3 Find the ratio in which the line joining the points (, 4, 8) and (5, 6, 4) is divided by the y plane. Also, find the co-ordinates of the point of 7 8 inter-section of the line with the plane. :;,, 0 7. a) Find the derivative by using first principle of: tan [4 b) Evaluate: d 4 log [4 C 8. a) Marks of two students in si eaminations out of total score 00 were as follows. [4 Student A Student B Find which student may be considered to be more consistent. [4 Student A For the frequency distribution given below, calculate appropriate coefficient of skewness. Monthly income Below and (in Rs.) above No. of workers S k = 0.0 b) Suppose cards are drawn from a well shuffled deck of 5 cards. What is the probability of getting i) all three spades ii) two aces [4 7 i) ii) Define linearly dependent and independent vectors. Show that the three points whose position vectors are i j k, i j 5k i 5 j 4k form the sides of right angled triangle. [6 0. Define degree and order of a differential equation. Solve the dy y cos y differential equation d [6 and

4 y tan log c Define differential equation with eample. Also solve the given differential equation dy ytan sin d cos ycos c. Define focal chord and latus rectum of a parabola. Also prove that the latus rectum of a parabola bisects the angle between the tangent and normal at either etremity of the latus rectum. [6 Group C 6. a) Find the solution of the given equation by Gauss Seidel method after first iteration y 8, y 8, 9 b) Convert the given binary numerals into headecimal form [ BA c) Find all basic feasible solutions of the given system of equations +y =; - y+ z =. [ : =, z = (basic); y = 0 ; y =, z = (basic); = 0 7. a) Solve the given system of equation by using Gauss elimination method. y z ; y z ; y z [4 = k, y = 4k and z = 5k b) Write three methods for measuring error. Show that a root of the equation 5 0 lies in the open internal (, ). Find this root approimately by Newton-Raphson s method using two iterations only approimate, correct to two decimal. [6 Required root =.8 (Appro.) 8. Minimize P 0y Subject to: y 6; y 8, 0; y 0 [ Optimal Solutions P = 64 at (, 4) 9. Calculate the value of d taking 5 sub intervals by Trapezoidal 0 rule correct to four significant figures. Also estimate the error with its eact value , Error =

5 SET - II Group A. a) How many even numbers of digits can be formed if the repetition of digits is allowed? [ 450 b) Find the term independent of in the epansion of 5 5 [ t 7 = 00 G,, i, i and the operation be multiplication. Show that G is closed and associative under multiplication. [ c) Let. a) Find the equation of the parabola whose verte is at (, ) and the focus is at (5, ). [ y 4y b) Find the ratio in which the line joining the points (, 4, 7) and (, 5, 8) is divided by the y-plane. [ 7:8 c) Show that the given vectors are collinear i j 4k i 8 j 6k, i 5 j k,. a) A circular copper plate is heated so that its radius increases from 5 cm to 5.06 cm. Find the approimate increase in area and also the actual increase in area. [ 0.6 cm,0.606 cm b) Evaluate: lim 0 tan c) By using partial fraction; integrate d [ [. [ log 4 C log 4. a) Solve the given differential equation; y d dy 0 [ cy

6 b) A frequency distribution gives the following results (i) C.V = 5 (ii) (iii) Karl Pearson s coefficients of skewness = 0.5. Find the mean and mode of the distribution. [ 40; M 0 9 c) The chance that A can solve a certain problem is 4 and the chance that B can solve it is. Find the chance that the problem be solved if both try. [ 4 5. a) A committee of 5 is to be formed from 6 gentlemen and 4 ladies. In how many ways can it be done when i) At least two ladies are included? ii) At most two ladies are included? [4 86, 86 b) Define a group. Let G,* be a group then show that a* b b * a for a bg,. [4 6. a) If three successive coefficients in the epansion of n are 8, 56 and 70, find n. [4 n = Prove that:... b) Define parabola. Find the equation of Parabola in standard form. [4 y 4a Find eccentricity, the co-ordinates of the centre and the foci of the following ellipses. 9 5y 0y 0 7. a) Find, from first principles, the derivative of: sin a ; 0, ; 0,5 and 0, log [4 a cot a 6

7 Verify Rolle s theorem for f sin d b) Evaluate: cos 8. a) Solve: dy d y tan y in log 5, [4 5 tan C 5 tan [4 y sin C b) State and prove theorem of total probability. [4 9. Define dot product of a two vector, if be the angle between two vector. Interpret it geometrically. Also prove by using vector method that; b c a accosb. [6 Define cross product of a two vector, if be the angle between two vector. Interpret it geometrically. Also prove by using vector method that Sin A B SinA. CosB CosA. SinB. 0. Reduce the general equation of plane to the normal form. Also find the length of perpendicular from a given point on a given plane in normal form. [6. From the following data between the ages of husbands and wife s. Calculate the two regression equations and find the husband s age when wife s age is 0 and wife s age when husband s age is 0. [6 Wife s age (X) Husband s age (Y) b 0.95; b. 0 Group C 6. a) Convert the decimal numberals 86.5 into ocal form. [ 6. 8 b) Determine the feasible region of the following system of inequalities + y 8, + y 0,, y 0 [ y y 7

8 c) Use the Trapezoidal Rule to approimate the integral d. Find the error for the approimation. [ a) Using Newton - Raphon s method to find the positive root of 8 0 in (, ). [4.60 b) Solve the given equations by Gauss elimination method: [4 y z ; 5y z 6 ; y z 0 ; y 0; z 4 Use the Gauss-Siedel method to solve the system: y 5 y 5 ; y 8. Using simple method, maimize Z y. [6 Subject to y 0 y 4 0, y 0 Ma value Z=8 at (6, ) 9. Evaluate, using Simpson s rule the integral 0 using the approimation n 4. [ ; Error = d. Estimate the error in SET - III Group A. a) How many numbers between 000 and 6000 be formed with the integers,,, 5, 6, 7? [ 0 b) Find the middle term in the epansion of a a n [ 8

9 n 9 n n! ; n!! a n n! n! a n! c) Let G={0,, }, form a composition table for G under the multiplication modulo. Also, find the inverse of [. a) Prove that the line l + my + n = 0 touches the parabola y = 4a if ln = am. [ b) Find the projection of the join of the pair of points (,, ) and (5, 7, 4) on the given line joining the points (0,, 0) and (,, 7). [ 4 c) Find the area of a parallelogram whose adjacent side are determined by vectors i j k and i j k. [ 6 sq.units. a) Differentiate: tanh tan w. r. t.. [ Sec b) Prove that d log a a C [ c) Solve the differential equations: y y e d e dy 0. [ e y e C 4. a) Find the regression Coefficients b y and b y for the data given below X 4; Y ; X 74; Y 97; XY 57; n 7 [ b ; b b) If the mean and variance of a binomial distribution are 9 and 6 respectively. Find the distribution. [ y y 7 c) What is the probability of getting a black or ace from a pack of 5 cards. [

10 7 5. a) In how many ways can the letters of the word CALCULUS be arranged so that the two C s do not come together. [4 780 b) Let G Q the set of all rational numbers without. Suppose an operation * defined on G is given by a*b=a+b+ab. Show that the system is a group. [4 6. a) Prove that, by using vector method. [4 Cos A B CosACosB SinASinB Prove, in any triangle by vector method. SinA SinB SinC a b c b) Find the equation of the plane through the point (,, 4) and perpendicular to each of the planes 9 7y 6z 48 0 and y z 0. [4 y 6z 5 0 Find the direction cosines of two lines which satisfy the equations l m n 0 and l m n 0 7. a) Evaluate: dy d d b) Solve: y tan y sec dy y y d 0 0,, ;,0, Sin [4 C [4 C sin y cos y C log 8. a) Calculate the correlation coefficient from the following data: [4

11 X: Y: r b) The probability of a bomb hitting a target is 5. Two bombs are enough to destroy a bridge. If si bombs are aimed at the bridge, find the probability that the bridge is destroyed. [4 n C C C... C n 9. If C C 0 C C 0 n, prove that C C 7 th term in the epansion of 4... Cn C n y 0 n! n! n!. Also find the. [6!! Sum to infinity the given series y 4 6 e 0. Derive the equation of the tangent to the parabola y = 4a at a point (, y ) on it. Find the equation of the tangent at (, ) to the parabola y =? [6 a ; y yy. State Lagrange s mean value theorem. Interpret it geometrically. Verify Lagrange s mean value theorem for the given function log on e f, Group C 6. a) Determine graphically the solution set of the following system of inequalities y 5; y ; y 6 [ b) Find the inverse of the given matri by Gauss Jordan method. A e [6 [

12 A c) Given a tabulated values of the velocity of an object. Time (s) Velocity (m/s) obtain an estimate of the distance travelled in the interval [0,. [ 5 7. a) Use the Gauss-Siedel method to solve the systems 4 y z 8; 5y z ; y 4z [4 =, y =, z = b) Use the simple method to find the optimal solutions of the given L.P. problems Ma Subject to z 9 y y 8; 4 y 8; 0; y 0 Ma. Z = 6 at (4, 0) 8. Apply the method of successive bisection to find the root of the equation 4 0 lying between and correct to two places of decimal by successive bisection method. [ Find Newton s method to find the positive root of Sin 0 in (0, ) Determine using a) Trapezoidal rule b) Simpson s rule, the following d, n 4 integrals. Estimate the error in each case. Estimate the error in using the approimation n 4. [ ; ; Error:

13 SET - IV Group A. a) In an eamination, a candidate has to pass in all 5 subjects, In how many ways ca he fail? [ ways b) Epand upto four term: 5 [... c) Show that multiplication is binary operation on the set S {,, } where is an imaginary cube root of unity. [. a) Deduce the equation of the ellipse in the standard position whose focus is (0, 5) and eccentricity is/. [ 5 00y b) Prove that l m n where l, m, n are direction cosines of a line. [ c) Find a vector perpendicular to the plane of two vectors i j k and i j 5k. [ i j 0k. a) Find the points on the curve where the tangents are parallel to the - ais. y. [ b) Evaluate: d 4 c) Solve: dy y d; y0,,, 0 [ log C 6 y y [ 4. a) For a group of 0 items 45, 470and mode = 4.7. Find the Pearson s coefficients of skewness. [ S k =

14 b) Find the mean deviation from mean of the numbers:, 5, 9, 6, 55, 7, 7 [ 4.86 c) Given P A 0.4, PAUB 0.56, PB Are A and B independent? [ No 5. a) How many different permutations can be made with letters of the word RANDOM under the following conditions i) if permutations begin with D ii) if permutations end with N iii) if permutations begin with A and end with O iv) if vowels are never separated [4 i) 0 ii) 0 iii) 4 iv) 48 b) If a and b are the elements of a group (G, 0), then a0 = b and 0a = b have unique solution in (G, 0). [4 6. a) Show that the angle between the tangents to the parabolas y 4 and 4y 4 at their points of intersection other than the origin is tan [4 A double ordinate of the parabola y a is of length 4a. Prove that the lines joining the verte to its ends are at right angles. b) Define linear combination of vectors. Prove that the vectors a 4b c, a b 5c and a 7b c are coplanar, a, b, c are any vectors. [4 where Show that the vectors 5i 6 j 7k, 7i 8 j 9k and i 0 j 5k 7. a) Evaluate: are linearly dependent. d 4 9 Evaluate: a d tan 5 tan 5 [4 C a a log a C

15 b) Solve the differential equation dy yd y d [4 5 y y C 8. a) Find the line of regression of Y on X for the following data: [4 X Y Y = 9+X b) A class consists of 60 boys and 40 girls. If two students are chosen at random, what is the probability that i) Both are boys ii) Both are girls iii) One boy and one girl? [4 i) ii) iii) Define direction cosines of a line. Prove that the lines whose direction cosines are given by the relation al bm cn 0 and 59 f g h fmn gnl hlm are perpendicular if 0 a b c 6 6. [6 Define plane. A variable plane is at a constant distance p from the origin and meets the aes in the points A, B, C. Prove that the locus of the centroid of the triangle ABC is y z p. 0. If the r th term in the epansion of ( + ) 0 has its coefficient equal to that of (r + 4) th term, find r. Also epand upto four terms. [6. What do you mean by continuous function of f f for for 8 6 r 9;... f is continuous at =. If at = a? Given Show that f differentiable at =? How? [6 No Group C 6. a) A manufacturer uses two machines to produce two items A and B, the profit on each item A is Rs. 600 on each one sold and on each item B

16 Rs If and y denote the respective number of the articles A and B that should be produced each day, find the objective function. [ Ma. Z = y b) Determine the number of iterations required by bisection method necessary to solve f with accuracy 0 - using a a and b. [ Iterations = 0 c) Using Simpson's rule, evaluate 0 d, n = [ a) Use Newton-Raphson s method to approimate with an error less than [ ; Error = b) Solve the given system of linear equation by using inverse matri method. y z 5; y z ; 5y z 4 [4 (,, ) 8. Minimize W y Subject to 5 y 9; y 0; 0; y 0 Maimum value = 6 at (, 4) Evaluate an approimate area between the curve y,, and -ais taking 4 intervals by Simpson s rule. Also compare it with eact value. [ sq. unit; Error: = 0.0% Estimate the integrals d taking n = 6 sub intervals by Trapezoidal and 0 Simpson s rule and compare the result with eact value. 4.5 sq. unit; Error = 0 [6 6

17 SET - V Group A. a) In how many different ways can a garland of 9 flowers be made? [ 060 b) Prove that: n n n... n n n c) If a, b, c are the element of a groups (G, 0) and a0b = a0c, then prove that b = c. [. a) Prove that the line ty = + at touches the parabola y = 4a and find its point of contact. [ b) Find the length of the perpendicular from the point (, 5, 7) to the plane 6 + 6y + z =. [ [ 5 units c) If a and b are two vectors of unit length and is angle between them, show that a b sin. [. a) If a i j k and b i j 4k, find the projection of a onb. [ cosh 0 9 b) Find the derivative of a. [ a cosh c) Prove that: ecd log tan C dy y y d y 4. a) Solve: cosh log.sinh a a a cos [ [ y log y C 7

18 b) Find the correlation coefficient between the two variables from the given data n 0, X 8; Y 5; X 90; Y 0; XY 65 [ r c) If P A, and P B, A B 4 P ; find P(AB). [ y a) Prove that number of permutations of n objects taken r at a time is n! given by [4 ( n r)! b) Define a binary operation. Test the closure, associative and commutative properties for the given case, the operation defined by m* n m n m, n z [4 6. a) Find the sum of the infinite series. [ e!!! Prove that the middle term in the epansion of n is n! n n n. b) OB and OC are two straight lines and D is a point on BC such that BD : DC = m : n, show that n. OB m. OC OD m n 7. a) Find, from first principles, the derivative of: log [4 d b) Evaluate: 4 sinh log 5 [4 log tanh C 4 tanh 8. a) Solve the differential equation: [4 dy tan y e d y tan tan e Ce 8

19 b) State and prove theorem of compound probability. [4 In a binomial distribution consisting of 5 independent trials, the probability of and successes are and respecitively. Find the probability p of a success in a single trial. 9. Define conic section. If a normal chord (a chord which is normal to the parabola) of a parabola y = 4a subtends a right angle at the verte, show that it is inclined at an angle tan to the ais. [6 Define ellipse. Show that 6 5y 64 50y 0 represents the equation of an ellipse. Find its vertices, eccentricity, foci and length of latus rectum. 5, and 7, ; e ;, ; 5, ; 5 l, m n and 0. Derive the angle between two lines whose d.c s are,, m n l,. Also derive the condition of perpendicularity and parallism.[6. Find the mean, standard deviation and coefficient of variation of the following data: [6 Wages in (Rs.) No. of workers mean = 5.7; S.D. = 9.76; C.V.=7.4% Group C 6. a) Convert to decimal 000 [ 8 b) Test the consistency of the given system of equations: [ y z ; y 5z 4; 6 y 9z 4 inconsistant c) Evaluate the given integrals using Trapezoidal rule. Give your answer correct upto places of decimals. d, n a) A carpenter has 60, 40 and 5 metres of teak, plywood and rosewood respectively. The product A requires,, metres and the product B requires,, metres of teak, plywood and rosewood respectively. If A would sell for Rs. 560 and B would sell for Rs. 840 per unit. Give a mathematical formulation of the above LP problem for the maimum income. And find the maimum income of the objective function for a given feasible region with known vertices. [4 9 [

20 Z 6 9 6; 0; 0; Maimize Subject to By using simple method. Z = 8 at (, 0) b) Compute two approimate values for d using 4 0 h h with the composite Trapezoid rule. [ ) 8. Solve the given system of equations by Gauss-Seidel method. 5 y z 5; 4y z 4; y z [6, y, z 4 Solve the system of equations by using Gauss Jordan method y z ; y z 9; y z 9.005; y.998; z 5.00, y, z,,5 9. Find by Newton s method, the root of e 4 which approimately, correct to three places of decimals. [6.5 and 0

Basic Mathematics - XII (Mgmt.) SET 1

Basic Mathematics - XII (Mgmt.) SET 1 Basic Mathematics - XII (Mgmt.) SET Grade: XII Subject: Basic Mathematics F.M.:00 Time: hrs. P.M.: 40 Model Candidates are required to give their answers in their own words as far as practicable. The figures

More information

MULTIPLE CHOICE QUESTIONS SUBJECT : MATHEMATICS Duration : Two Hours Maximum Marks : 100. [ Q. 1 to 60 carry one mark each ] A. 0 B. 1 C. 2 D.

MULTIPLE CHOICE QUESTIONS SUBJECT : MATHEMATICS Duration : Two Hours Maximum Marks : 100. [ Q. 1 to 60 carry one mark each ] A. 0 B. 1 C. 2 D. M 68 MULTIPLE CHOICE QUESTIONS SUBJECT : MATHEMATICS Duration : Two Hours Maimum Marks : [ Q. to 6 carry one mark each ]. If sin sin sin y z, then the value of 9 y 9 z 9 9 y 9 z 9 A. B. C. D. is equal

More information

MockTime.com. NDA Mathematics Practice Set 1.

MockTime.com. NDA Mathematics Practice Set 1. 346 NDA Mathematics Practice Set 1. Let A = { 1, 2, 5, 8}, B = {0, 1, 3, 6, 7} and R be the relation is one less than from A to B, then how many elements will R contain? 2 3 5 9 7. 1 only 2 only 1 and

More information

MATHEMATICS. metres (D) metres (C)

MATHEMATICS. metres (D) metres (C) MATHEMATICS. If is the root of the equation + k = 0, then what is the value of k? 9. Two striaght lines y = 0 and 6y 6 = 0 never intersect intersect at a single point intersect at infinite number of points

More information

63487 [Q. Booklet Number]

63487 [Q. Booklet Number] WBJEE - 0 (Answers & Hints) 687 [Q. Booklet Number] Regd. Office : Aakash Tower, Plot No., Sector-, Dwarka, New Delhi-0075 Ph. : 0-7656 Fa : 0-767 ANSWERS & HINTS for WBJEE - 0 by & Aakash IIT-JEE MULTIPLE

More information

Time : 3 hours 02 - Mathematics - July 2006 Marks : 100 Pg - 1 Instructions : S E CT I O N - A

Time : 3 hours 02 - Mathematics - July 2006 Marks : 100 Pg - 1 Instructions : S E CT I O N - A Time : 3 hours 0 Mathematics July 006 Marks : 00 Pg Instructions :. Answer all questions.. Write your answers according to the instructions given below with the questions. 3. Begin each section on a new

More information

Complete Syllabus of Class XI & XII

Complete Syllabus of Class XI & XII Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-0005 Ph.: 0-7656 Fa : 0-767 MM : 0 Sample Paper : Campus Recruitment Test Time : ½ Hr. Mathematics (Engineering) Complete Syllabus of Class XI & XII

More information

CHAPTER-1. SETS. Q.4 Write down the proper subsets of { a, b, Q.5 Write down the power set of { 5,6,7 }? Verify the following result :

CHAPTER-1. SETS. Q.4 Write down the proper subsets of { a, b, Q.5 Write down the power set of { 5,6,7 }? Verify the following result : CHAPTER-. SETS Q. Write the following sets in roster form (i) A = { : is an integer and 5 5 } (ii) B = { : is a natural number and < < 4} (iii) C= { : is a two- digit natural number such that sum of digit

More information

DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO

DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO T.B.C. : P-AQNA-L-ZNGU Serial No.- TEST BOOKLET MATHEMATICS Test Booklet Series Time Allowed : Two Hours and Thirty Minutes Maximum Marks : 00

More information

WBJEEM Answer Keys by Aakash Institute, Kolkata Centre MATHEMATICS

WBJEEM Answer Keys by Aakash Institute, Kolkata Centre MATHEMATICS WBJEEM - 05 Answer Keys by, Kolkata Centre MATHEMATICS Q.No. μ β γ δ 0 B A A D 0 B A C A 0 B C A * 04 C B B C 05 D D B A 06 A A B C 07 A * C A 08 D C D A 09 C C A * 0 C B D D B C A A D A A B A C A B 4

More information

Grade XI Mathematics

Grade XI Mathematics Grade XI Mathematics Exam Preparation Booklet Chapter Wise - Important Questions and Solutions #GrowWithGreen Questions Sets Q1. For two disjoint sets A and B, if n [P ( A B )] = 32 and n [P ( A B )] =

More information

oo ks. co m w w w.s ur ab For Order : orders@surabooks.com Ph: 960075757 / 84000 http://www.trbtnpsc.com/07/08/th-eam-model-question-papers-download.html Model Question Papers Based on Scheme of Eamination

More information

02. If (x, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) x + y = 0 (B) bx ay = 0 (C) ax by = 0 (D) bx + ay = 0 (E) ax + by =

02. If (x, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) x + y = 0 (B) bx ay = 0 (C) ax by = 0 (D) bx + ay = 0 (E) ax + by = 0. π/ sin d 0 sin + cos (A) 0 (B) π (C) 3 π / (D) π / (E) π /4 0. If (, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) + y = 0 (B) b ay = 0 (C) a by = 0 (D) b + ay = 0 (E) a + by = 0 03.

More information

MINIMUM PROGRAMME FOR AISSCE

MINIMUM PROGRAMME FOR AISSCE KENDRIYA VIDYALAYA DANAPUR CANTT MINIMUM PROGRAMME FOR AISSCE 8 SUBJECT : MATHEMATICS (CLASS XII) Prepared By : K. N. P. Singh Vice-Principal K.V. Danapur Cantt () MATRIX. Find X and Y if 7 y & y 7 8 X,,

More information

KEAM (ENGINEERING) ANSWER KEY 2018

KEAM (ENGINEERING) ANSWER KEY 2018 MTHEMTIS KEM KEY 08 PGE: M.O: Kunnumpuram, yurveda ollege Jn., Trivandrum-, (: 047-57040, 47040 E-mail: info@zephyrentrance.in, Website: www.zephyrentrance.in KOHI KOLLM RNHES Puthussery uilding, Kaloor

More information

IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB

IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB ` KUKATPALLY CENTRE IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB 017-18 FIITJEE KUKATPALLY CENTRE: # -97, Plot No1, Opp Patel Kunta Huda Park, Vijaynagar Colony, Hyderabad - 500

More information

GOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD SCHEME OF VALUATION. Subject : MATHEMATICS Subject Code : 35

GOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD SCHEME OF VALUATION. Subject : MATHEMATICS Subject Code : 35 GOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD II YEAR PUC EXAMINATION MARCH APRIL 0 SCHEME OF VALUATION Subject : MATHEMATICS Subject Code : 5 PART A Write the prime

More information

Objective Mathematics

Objective Mathematics . A tangent to the ellipse is intersected by a b the tangents at the etremities of the major ais at 'P' and 'Q' circle on PQ as diameter always passes through : (a) one fied point two fied points (c) four

More information

DELHI PUBLIC SCHOOL BLUE PRINT WEEKLY TEST CLASS XI (MATHEMATICS)

DELHI PUBLIC SCHOOL BLUE PRINT WEEKLY TEST CLASS XI (MATHEMATICS) DELHI PUBLIC SCHOOL BLUE PRINT WEEKLY TEST CLASS XI (MATHEMATICS) S. N0. TYPES OF QUESTIONS NO. OF QUESTION MARKS TOTAL 1. VERY SHT ANSWER 6 1 6 2. SHT ANSWER 5 4 20 3. LONG ANSWER WITH ONE 4 6 24 VALUE

More information

CO-ORDINATE GEOMETRY

CO-ORDINATE GEOMETRY CO-ORDINATE GEOMETRY 1 To change from Cartesian coordinates to polar coordinates, for X write r cos θ and for y write r sin θ. 2 To change from polar coordinates to cartesian coordinates, for r 2 write

More information

TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad

TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad TARGT : J 01 SCOR J (Advanced) Home Assignment # 0 Kota Chandigarh Ahmedabad J-Mathematics HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP 1. If x + y = 0 is a tangent at the vertex of a parabola and x + y 7 =

More information

EINSTEIN CLASSES. C B S E XIIth Board PRACTICE ASSIGNMENT

EINSTEIN CLASSES. C B S E XIIth Board PRACTICE ASSIGNMENT EINSTEIN CLASSES P R E S E N T S C B S E XIIth Board PRACTICE ASSIGNMENT MATHEMATICS NOTE THE FOLLOWING POINTS : Einstein Classes is primarily concerned with the preparation of JEE-ADVANCE /JEE-MAIN/BITS/PMT/AIIMS

More information

Page 1 MATHEMATICS

Page 1 MATHEMATICS PREPARED BY :S.MANIKANDAN., VICE PRINCIPAL., JOTHI VIDHYALAYA MHSS., ELAMPILLAI., SALEM., 94798 Page + MATHEMATICS PREPARED BY :S.MANIKANDAN., VICE PRINCIPAL., JOTHI VIDHYALAYA MHSS., ELAMPILLAI., SALEM.,

More information

TS EAMCET 2016 SYLLABUS ENGINEERING STREAM

TS EAMCET 2016 SYLLABUS ENGINEERING STREAM TS EAMCET 2016 SYLLABUS ENGINEERING STREAM Subject: MATHEMATICS 1) ALGEBRA : a) Functions: Types of functions Definitions - Inverse functions and Theorems - Domain, Range, Inverse of real valued functions.

More information

Conic section. Ans: c. Ans: a. Ans: c. Episode:43 Faculty: Prof. A. NAGARAJ. 1. A circle

Conic section. Ans: c. Ans: a. Ans: c. Episode:43 Faculty: Prof. A. NAGARAJ. 1. A circle Episode:43 Faculty: Prof. A. NAGARAJ Conic section 1. A circle gx fy c 0 is said to be imaginary circle if a) g + f = c b) g + f > c c) g + f < c d) g = f. If (1,-3) is the centre of the circle x y ax

More information

12 th Class Mathematics Paper

12 th Class Mathematics Paper th Class Mathematics Paper Maimum Time: hours Maimum Marks: 00 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 9 questions divided into four sections A, B, C

More information

MockTime.com. (a) 36 (b) 33 (c) 20 (d) 6

MockTime.com. (a) 36 (b) 33 (c) 20 (d) 6 185 NDA Mathematics Practice Set 1. Which of the following statements is not correct for the relation R defined by arb if and only if b lives within one kilometer from a? R is reflexive R is symmetric

More information

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola) QUESTION BANK ON CONIC SECTION (Parabola, Ellipse & Hyperbola) Question bank on Parabola, Ellipse & Hyperbola Select the correct alternative : (Only one is correct) Q. Two mutually perpendicular tangents

More information

RAJASTHAN P.E.T. MATHS 1997

RAJASTHAN P.E.T. MATHS 1997 RAJASTHAN P.E.T. MATHS 1997 1. The value of k for which the points (0,0), (2,0), (0,1) and (0,k) lies on a circle is : (1) 1,2 (2) -1,2 (3) 0,2 (4) 0, 1 2. The area of the triangle formed by the tangent

More information

MATHEMATICS. SECTION A (80 Marks) Find the number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together.

MATHEMATICS. SECTION A (80 Marks) Find the number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together. MATHEMATICS (Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) ---------------------------------------------------------------------------------------------------------------------

More information

Mathematics Extension 1 Time allowed: 2 hours (plus 5 minutes reading time)

Mathematics Extension 1 Time allowed: 2 hours (plus 5 minutes reading time) Name: Teacher: Class: FORT STREET HIGH SCHOOL 014 HIGHER SCHOOL CERTIFICATE COURSE ASSESSMENT TASK 3: TRIAL HSC Mathematics Etension 1 Time allowed: hours (plus 5 minutes reading time) Syllabus Assessment

More information

MATHEMATICS EXTENSION 2

MATHEMATICS EXTENSION 2 Sydney Grammar School Mathematics Department Trial Eaminations 008 FORM VI MATHEMATICS EXTENSION Eamination date Tuesday 5th August 008 Time allowed hours (plus 5 minutes reading time) Instructions All

More information

SYLLABUS FOR ENTRANCE EXAMINATION NANYANG TECHNOLOGICAL UNIVERSITY FOR INTERNATIONAL STUDENTS A-LEVEL MATHEMATICS

SYLLABUS FOR ENTRANCE EXAMINATION NANYANG TECHNOLOGICAL UNIVERSITY FOR INTERNATIONAL STUDENTS A-LEVEL MATHEMATICS SYLLABUS FOR ENTRANCE EXAMINATION NANYANG TECHNOLOGICAL UNIVERSITY FOR INTERNATIONAL STUDENTS A-LEVEL MATHEMATICS STRUCTURE OF EXAMINATION PAPER. There will be one -hour paper consisting of 4 questions..

More information

(c) n (d) n 2. (a) (b) (c) (d) (a) Null set (b) {P} (c) {P, Q, R} (d) {Q, R} (a) 2k (b) 7 (c) 2 (d) K (a) 1 (b) 3 (c) 3xyz (d) 27xyz

(c) n (d) n 2. (a) (b) (c) (d) (a) Null set (b) {P} (c) {P, Q, R} (d) {Q, R} (a) 2k (b) 7 (c) 2 (d) K (a) 1 (b) 3 (c) 3xyz (d) 27xyz 318 NDA Mathematics Practice Set 1. (1001)2 (101)2 (110)2 (100)2 2. z 1/z 2z z/2 3. The multiplication of the number (10101)2 by (1101)2 yields which one of the following? (100011001)2 (100010001)2 (110010011)2

More information

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time) HIGHER SCHOOL CERTIFICATE EXAMINATION 998 MATHEMATICS / UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of equal value.

More information

KEAM (ENGINEERING) ANSWER KEY 2017

KEAM (ENGINEERING) ANSWER KEY 2017 MTHMTICS KM KY 07 PG: KM (NGINRING) KY 07 PPR II MTHMTICS QUSTIONS & S. p q r p q r + is equal to () q p () q + p (C) q () p () 0 5 0. Let = 0 5 5 () 0 and () 0 = 0. If + 5 C = 0, then C is 0 5 5 5 5 0

More information

Centres at Pallavaram Opp. St. therasa s School Pammal Krishna Nagar Adyar Kasturiba Nagar Chrompet - Opp. MIT Selaiyur Near Camp Road Junction

Centres at Pallavaram Opp. St. therasa s School Pammal Krishna Nagar Adyar Kasturiba Nagar Chrompet - Opp. MIT Selaiyur Near Camp Road Junction Adyar Adambakkam Pallavaram Pammal Chromepet Now also at SELAIYUR Day - wise Portions Day 1 : Day 2 : Day 3 : Matrices and Determinants, Complex Numbers and Vector Algebra Analytical Geometry, Discrete

More information

ANSWER KEY 1. [A] 2. [C] 3. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A] 10. [A] 11. [D] 12. [A] 13. [D] 14. [C] 15. [B] 16. [C] 17. [D] 18.

ANSWER KEY 1. [A] 2. [C] 3. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A] 10. [A] 11. [D] 12. [A] 13. [D] 14. [C] 15. [B] 16. [C] 17. [D] 18. ANSWER KEY. [A]. [C]. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A]. [A]. [D]. [A]. [D] 4. [C] 5. [B] 6. [C] 7. [D] 8. [B] 9. [C]. [C]. [D]. [A]. [B] 4. [D] 5. [A] 6. [D] 7. [B] 8. [D] 9. [D]. [B]. [A].

More information

Transweb Educational Services Pvt. Ltd Tel:

Transweb Educational Services Pvt. Ltd     Tel: . An aeroplane flying at a constant speed, parallel to the horizontal ground, km above it, is observed at an elevation of 6º from a point on the ground. If, after five seconds, its elevation from the same

More information

MODEL PAPER - I MATHEMATICS. Time allowed : 3 hours Maximum marks : 100

MODEL PAPER - I MATHEMATICS. Time allowed : 3 hours Maximum marks : 100 MODEL PAPER - I MATHEMATICS Time allowed : 3 hours Maimum marks : General Instructions. All questions are compulsy.. The question paper consists of 9 questions divided into three sections A, B and C. Section

More information

TARGET QUARTERLY MATHS MATERIAL

TARGET QUARTERLY MATHS MATERIAL Adyar Adambakkam Pallavaram Pammal Chromepet Now also at SELAIYUR TARGET QUARTERLY MATHS MATERIAL Achievement through HARDWORK Improvement through INNOVATION Target Centum Practising Package +2 GENERAL

More information

C.B.S.E Class XII Delhi & Outside Delhi Sets

C.B.S.E Class XII Delhi & Outside Delhi Sets SOLVED PAPER With CBSE Marking Scheme C.B.S.E. 8 Class XII Delhi & Outside Delhi Sets Mathematics Time : Hours Ma. Marks : General Instructions : (i) All questions are compulsory. (ii) The question paper

More information

Mathematics. Knox Grammar School 2012 Year 11 Yearly Examination. Student Number. Teacher s Name. General Instructions.

Mathematics. Knox Grammar School 2012 Year 11 Yearly Examination. Student Number. Teacher s Name. General Instructions. Teacher s Name Student Number Kno Grammar School 0 Year Yearly Eamination Mathematics General Instructions Reading Time 5 minutes Working Time 3 hours Write using black or blue pen Board approved calculators

More information

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2 CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5

More information

MATHEMATICS. Time allowed : 3 hours Maximum Marks : 100

MATHEMATICS. Time allowed : 3 hours Maximum Marks : 100 MATHEMATICS Time allowed : hours Maimum Marks : General Instructions:. All questions are compulsory.. The question paper consists of 9 questions divided into three sections, A, B and C. Section A comprises

More information

130 Important Questions for XI

130 Important Questions for XI 130 Important Questions for XI E T V A 1 130 Important Questions for XI PREFACE Have you ever seen a plane taking off from a runway and going up and up, and crossing the clouds but just think again that

More information

Mathematics Grade: XI

Mathematics Grade: XI Mathematics Grade: XI Full Marks: 100 Teaching hours: 150 I. Introduction: This course deals with the fundamentals of advanced mathematical concepts. It also tries to consolidate the concepts and skills

More information

Mathematics. Single Correct Questions

Mathematics. Single Correct Questions Mathematics Single Correct Questions +4 1.00 1. If and then 2. The number of solutions of, in the interval is : 3. If then equals : 4. A plane bisects the line segment joining the points and at right angles.

More information

4) If ax 2 + bx + c = 0 has equal roots, then c is equal. b) b 2. a) b 2

4) If ax 2 + bx + c = 0 has equal roots, then c is equal. b) b 2. a) b 2 Karapettai Nadar Boys Hr. Sec. School One Word Test No 1 Standard X Time: 20 Minutes Marks: (15 1 = 15) Answer all the 15 questions. Choose the orrect answer from the given four alternatives and write

More information

Important Instructions to the Examiners:

Important Instructions to the Examiners: (ISO/IEC - 7 - Certified) Winter Eamination Subject & Code: Applied Maths (7) Model Answer Page No: /6 Important Instructions to the Eaminers: ) The answers should be eamined by key words and not as word-to-word

More information

FILL THE ANSWER HERE

FILL THE ANSWER HERE HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP. If A, B & C are matrices of order such that A =, B = 9, C =, then (AC) is equal to - (A) 8 6. The length of the sub-tangent to the curve y = (A) 8 0 0 8 ( ) 5 5

More information

INDIAN SCHOO MUSCAT QUESTION BANK DEPARTMENT OF MATHEMATICS SENIOR SECTION. Relations and Functions

INDIAN SCHOO MUSCAT QUESTION BANK DEPARTMENT OF MATHEMATICS SENIOR SECTION. Relations and Functions INDIAN SCHOO MUSCAT QUESTION BANK 07-8 DEPARTMENT OF MATHEMATICS SENIOR SECTION Relations and Functions mark (For conceptual practice) Which of the following graphs of relations defines a transitive relation

More information

are in c) A B (D) 2 = {4,5,6} by = {(4,4), (5,5), (6,6)} is (C) (B) 0 < (C) 0 = 8, = 5 = 8, = 8 (B) (D) (C) 2 +

are in c) A B (D) 2 = {4,5,6} by = {(4,4), (5,5), (6,6)} is (C) (B) 0 < (C) 0 = 8, = 5 = 8, = 8 (B) (D) (C) 2 + 1. If are in GP then AP GP are in HP 2. The sum to infinity of the series 1 3. The set B-A a subset of a) A c) A B b) B d)null set 4. The converse of the statement if 3 3 6 then I am the president of USA

More information

I K J are two points on the graph given by y = 2 sin x + cos 2x. Prove that there exists

I K J are two points on the graph given by y = 2 sin x + cos 2x. Prove that there exists LEVEL I. A circular metal plate epands under heating so that its radius increase by %. Find the approimate increase in the area of the plate, if the radius of the plate before heating is 0cm.. The length

More information

MockTime.com. (b) (c) (d)

MockTime.com. (b) (c) (d) 373 NDA Mathematics Practice Set 1. If A, B and C are any three arbitrary events then which one of the following expressions shows that both A and B occur but not C? 2. Which one of the following is an

More information

CBSE 2018 ANNUAL EXAMINATION DELHI

CBSE 2018 ANNUAL EXAMINATION DELHI CBSE 08 ANNUAL EXAMINATION DELHI (Series SGN Code No 65/ : Delhi Region) Ma Marks : 00 Time Allowed : Hours SECTION A Q0 Find the value of tan cot ( ) Sol 5 5 tan cot ( ) tan tan cot cot 6 6 6 0 a Q0 If

More information

1 is equal to. 1 (B) a. (C) a (B) (D) 4. (C) P lies inside both C & E (D) P lies inside C but outside E. (B) 1 (D) 1

1 is equal to. 1 (B) a. (C) a (B) (D) 4. (C) P lies inside both C & E (D) P lies inside C but outside E. (B) 1 (D) 1 Single Correct Q. Two mutuall perpendicular tangents of the parabola = a meet the ais in P and P. If S is the focus of the parabola then l a (SP ) is equal to (SP ) l (B) a (C) a Q. ABCD and EFGC are squares

More information

Question Bank (I scheme )

Question Bank (I scheme ) Question Bank (I scheme ) Name of subject: Applied Mathematics Subject code: 22206/22224/22210/22201 Course : CH/CM/CE/EJ/IF/EE/ME Semester: II UNIT-3 (CO3) Unit Test : II (APPLICATION OF INTEGRATION)

More information

PRACTICE PAPER 6 SOLUTIONS

PRACTICE PAPER 6 SOLUTIONS PRACTICE PAPER 6 SOLUTIONS SECTION A I.. Find the value of k if the points (, ) and (k, 3) are conjugate points with respect to the circle + y 5 + 8y + 6. Sol. Equation of the circle is + y 5 + 8y + 6

More information

MODEL TEST PAPER I. Time : 3 hours Maximum Marks : 100

MODEL TEST PAPER I. Time : 3 hours Maximum Marks : 100 MODEL TEST PAPER I Time : 3 hours Maimum Marks : 00 General Instructions : (i) (ii) (iii) (iv) (v) All questions are compulsory. Q. to Q. 0 of Section A are of mark each. Q. to Q. of Section B are of 4

More information

STRATHFIELD GIRLS HIGH SCHOOL TRIAL HIGHER SCHOOL CERTIFICATE MATHEMATICS. Time allowed Three hours (Plus 5 minutes reading time)

STRATHFIELD GIRLS HIGH SCHOOL TRIAL HIGHER SCHOOL CERTIFICATE MATHEMATICS. Time allowed Three hours (Plus 5 minutes reading time) STRATHFIELD GIRLS HIGH SCHOOL TRIAL HIGHER SCHOOL CERTIFICATE 00 MATHEMATICS Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of

More information

12 STD BUSINESS MATHEMATICS

12 STD BUSINESS MATHEMATICS STD BUSINESS MATHEMATICS 6 MARK FAQ S: CHAPTER :. APPLICATION OF MATRICES AND DETERMINANTS. Given, A verify that A AdjA (J 7; O 7 ; O ). Find the inverse of, b a A and verify that I AA. (J 6). Verify A

More information

CDS-I 2019 Elementary Mathematics (Set-C)

CDS-I 2019 Elementary Mathematics (Set-C) 1 CDS-I 019 Elementary Mathematics (Set-C) Direction: Consider the following for the next three (03) items : A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the

More information

JEE-ADVANCED MATHEMATICS. Paper-1. SECTION 1: (One or More Options Correct Type)

JEE-ADVANCED MATHEMATICS. Paper-1. SECTION 1: (One or More Options Correct Type) JEE-ADVANCED MATHEMATICS Paper- SECTION : (One or More Options Correct Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR

More information

1. SETS AND FUNCTIONS

1. SETS AND FUNCTIONS . SETS AND FUNCTIONS. For two sets A and B, A, B A if and only if B A A B A! B A + B z. If A B, then A + B is B A\ B A B\ A. For any two sets Pand Q, P + Q is " x : x! P or x! Q, " x : x! P and x b Q,

More information

SECTION A Time allowed: 20 minutes Marks: 20

SECTION A Time allowed: 20 minutes Marks: 20 Mathcity.org Merging man and maths Federal Board HSSC-II Eamination Mathematics Model Question Paper Roll No: Answer Sheet No: FBISE WE WORK FOR EXCELLENCE Signature of Candidate: Signature of Invigilator:

More information

QUESTION BANK ON STRAIGHT LINE AND CIRCLE

QUESTION BANK ON STRAIGHT LINE AND CIRCLE QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,

More information

GAT-UGTP-2018 Page 1 of 5

GAT-UGTP-2018 Page 1 of 5 SECTION A: MATHEMATICS UNIT 1 SETS, RELATIONS AND FUNCTIONS: Sets and their representation, Union, Intersection and compliment of sets, and their algebraic properties, power set, Relation, Types of relation,

More information

abc Mathematics Further Pure General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES

abc Mathematics Further Pure General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES abc General Certificate of Education Mathematics Further Pure SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER

More information

Mathematics Guide Page 9

Mathematics Guide Page 9 Mathematics 568-536 Guide Page 9 Part C Questions 15 to 5 4 marks each No marks are to be given if work is not shown. Eamples of correct solutions are given. However, other acceptable solutions are possible.

More information

DIRECTORATE OF EDUCATION GOVT. OF NCT OF DELHI

DIRECTORATE OF EDUCATION GOVT. OF NCT OF DELHI 456789045678904567890456789045678904567890456789045678904567890456789045678904567890 456789045678904567890456789045678904567890456789045678904567890456789045678904567890 QUESTION BANK 456789045678904567890456789045678904567890456789045678904567890456789045678904567890

More information

STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING TNCF DRAFT SYLLABUS.

STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING TNCF DRAFT SYLLABUS. STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING TNCF 2017 - DRAFT SYLLABUS Subject :Mathematics Class : XI TOPIC CONTENT Unit 1 : Real Numbers - Revision : Rational, Irrational Numbers, Basic Algebra

More information

Class XI Subject - Mathematics

Class XI Subject - Mathematics Class XI Subject - Mathematics Max Time: 3 hrs. Max Marks: 100 General Instructions: i. All questions are compulsory. ii. The question paper consists of 29 questions divided in three sections A, B and

More information

SET-I SECTION A SECTION B. General Instructions. Time : 3 hours Max. Marks : 100

SET-I SECTION A SECTION B. General Instructions. Time : 3 hours Max. Marks : 100 General Instructions. All questions are compulsor.. This question paper contains 9 questions.. Questions - in Section A are ver short answer tpe questions carring mark each.. Questions 5- in Section B

More information

TMTA Calculus and Advanced Topics Test 2010

TMTA Calculus and Advanced Topics Test 2010 . Evaluate lim Does not eist - - 0 TMTA Calculus and Advanced Topics Test 00. Find the period of A 6D B B y Acos 4B 6D, where A 0, B 0, D 0. Solve the given equation for : ln = ln 4 4 ln { } {-} {0} {}

More information

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time) N E W S O U T H W A L E S HIGHER SCHOOL CERTIFICATE EXAMINATION 996 MATHEMATICS /3 UNIT (COMMON) Time allowed Three hours (Plus minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL

More information

MockTime.com. (b) 9/2 (c) 18 (d) 27

MockTime.com. (b) 9/2 (c) 18 (d) 27 212 NDA Mathematics Practice Set 1. Let X be any non-empty set containing n elements. Then what is the number of relations on X? 2 n 2 2n 2 2n n 2 2. Only 1 2 and 3 1 and 2 1 and 3 3. Consider the following

More information

Mathematics. Guess Paper: 2014 Class: XII. Time Allowed: 3Hours Maximum Marks: 70. Section A

Mathematics. Guess Paper: 2014 Class: XII. Time Allowed: 3Hours Maximum Marks: 70. Section A Mathematics Guess Paper: 04 Class: XII Time llowed: Hours Maimum Marks: 70 General Instructions:. The question paper consists of 9 questions divided into three sections, B and C.. Section comprises of

More information

All Rights Reserved Wiley India Pvt. Ltd. 1

All Rights Reserved Wiley India Pvt. Ltd. 1 Question numbers to carry mark each. CBSE MATHEMATICS SECTION A. If R = {(, y) : + y = 8} is a relation of N, write the range of R. R = {(, y)! + y = 8} a relation of N. y = 8 y must be Integer So Can

More information

3. Total number of functions from the set A to set B is n. 4. Total number of one-one functions from the set A to set B is n Pm

3. Total number of functions from the set A to set B is n. 4. Total number of one-one functions from the set A to set B is n Pm ASSIGNMENT CLASS XII RELATIONS AND FUNCTIONS Important Formulas If A and B are finite sets containing m and n elements, then Total number of relations from the set A to set B is mn Total number of relations

More information

FIITJEE SOLUTION TO AIEEE-2005 MATHEMATICS

FIITJEE SOLUTION TO AIEEE-2005 MATHEMATICS FIITJEE SOLUTION TO AIEEE-5 MATHEMATICS. If A A + I =, then the inverse of A is () A + I () A () A I () I A. () Given A A + I = A A A A + A I = A (Multiplying A on both sides) A - I + A - = or A = I A..

More information

Secondary School Mathematics & Science Competition. Mathematics. Date: 1 st May, 2013

Secondary School Mathematics & Science Competition. Mathematics. Date: 1 st May, 2013 Secondary School Mathematics & Science Competition Mathematics Date: 1 st May, 01 Time allowed: 1 hour 15 minutes 1. Write your Name (both in English and Chinese), Name of School, Form, Date, Se, Language,

More information

INDIRA GANDHI INSTITUTE OF DEVELOPMENT RESEARCH. M.Phil-Ph.D ENTRANCE EXAM SAMPLE QUESTIONS BASIC MATHEMATICS

INDIRA GANDHI INSTITUTE OF DEVELOPMENT RESEARCH. M.Phil-Ph.D ENTRANCE EXAM SAMPLE QUESTIONS BASIC MATHEMATICS INDIRA GANDHI INSTITUTE OF DEVELOPMENT RESEARCH General A.K. Vaidya Marg, Santosh Nagar, Goregaon (East), Mumbai - 400 065 M.Phil-Ph.D ENTRANCE EXAM SAMPLE QUESTIONS BASIC MATHEMATICS This document consists

More information

CHAPTER 10 VECTORS POINTS TO REMEMBER

CHAPTER 10 VECTORS POINTS TO REMEMBER For more important questions visit : www4onocom CHAPTER 10 VECTORS POINTS TO REMEMBER A quantity that has magnitude as well as direction is called a vector It is denoted by a directed line segment Two

More information

PURE MATHEMATICS AM 27

PURE MATHEMATICS AM 27 AM SYLLABUS (2020) PURE MATHEMATICS AM 27 SYLLABUS 1 Pure Mathematics AM 27 (Available in September ) Syllabus Paper I(3hrs)+Paper II(3hrs) 1. AIMS To prepare students for further studies in Mathematics

More information

2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2

2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2 29 April PreCalculus Final Review 1. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line: y = 3x + 13 2. Determine the domain of the function. Verify your result with

More information

Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS

Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS (i) Sets and their Representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Power set; Universal set; Venn Diagrams;

More information

MATHEMATICS. r Statement I Statement II p q ~p ~q ~p q q p ~(p ~q) F F T T F F T F T T F T T F T F F T T T F T T F F F T T

MATHEMATICS. r Statement I Statement II p q ~p ~q ~p q q p ~(p ~q) F F T T F F T F T T F T T F T F F T T T F T T F F F T T MATHEMATICS Directions : Questions number to 5 are Assertion-Reason type questions. Each of these questions contains two statements : Statement- (Assertion) and Statement- (Reason). Each of these questions

More information

CALCULUS BASIC SUMMER REVIEW

CALCULUS BASIC SUMMER REVIEW NAME CALCULUS BASIC SUMMER REVIEW Slope of a non vertical line: rise y y y m run Point Slope Equation: y y m( ) The slope is m and a point on your line is, ). ( y Slope-Intercept Equation: y m b slope=

More information

VECTOR NAME OF THE CHAPTER. By, Srinivasamurthy s.v. Lecturer in mathematics. K.P.C.L.P.U.College. jogfalls PART-B TWO MARKS QUESTIONS

VECTOR NAME OF THE CHAPTER. By, Srinivasamurthy s.v. Lecturer in mathematics. K.P.C.L.P.U.College. jogfalls PART-B TWO MARKS QUESTIONS NAME OF THE CHAPTER VECTOR PART-A ONE MARKS PART-B TWO MARKS PART-C FIVE MARKS PART-D SIX OR FOUR MARKS PART-E TWO OR FOUR 1 1 1 1 1 16 TOTAL MARKS ALLOTED APPROXIMATELY By, Srinivasamurthy s.v Lecturer

More information

Numerical Analysis & Computer Programming

Numerical Analysis & Computer Programming ++++++++++ Numerical Analysis & Computer Programming Previous year Questions from 07 to 99 Ramanasri Institute W E B S I T E : M A T H E M A T I C S O P T I O N A L. C O M C O N T A C T : 8 7 5 0 7 0 6

More information

CLASS XII MATHEMATICS. Weightage (Marks) (i) Relations and Functions 10. Type of Questions Weightage of Number of Total Marks each question questions

CLASS XII MATHEMATICS. Weightage (Marks) (i) Relations and Functions 10. Type of Questions Weightage of Number of Total Marks each question questions CLASS XII MATHEMATICS Units Weightage (Marks) (i) Relations and Functions 0 (ii) Algebra (Matrices and Determinants) (iii) Calculus 44 (iv) Vector and Three dimensional Geometry 7 (v) Linear Programming

More information

APPLICATIONS OF DERIVATIVES OBJECTIVES. The approimate increase in the area of a square plane when each side epands from c m to.0 cm is () 0.00 sq. cm () 0.006 sq. cm () 0.06 sq. cm () None. If y log then

More information

CLASS XII MATHEMATICS. Weightage (Marks) (i) Relations and Functions 10. (ii) Algebra 13. (iii) Calculus 44

CLASS XII MATHEMATICS. Weightage (Marks) (i) Relations and Functions 10. (ii) Algebra 13. (iii) Calculus 44 CLASS XII MATHEMATICS Units Weightage (Marks) (i) Relations and Functions 0 (ii) Algebra (iii) Calculus 44 (iv) Vector and Three Dimensional Geometry 7 (v) Linear Programming 06 (vi) Probability 0 Total

More information

Math Bank - 6. What is the area of the triangle on the Argand diagram formed by the complex number z, -iz, z iz? (a) z 2 (b) 2 z 2

Math Bank - 6. What is the area of the triangle on the Argand diagram formed by the complex number z, -iz, z iz? (a) z 2 (b) 2 z 2 Math Bank - 6 Q.) Suppose A represents the symbol, B represents the symbol 0, C represents the symbol, D represents the symbol 0 and so on. If we divide INDIA by AGRA, then which one of the following is

More information

HEAT-3 APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA MAX-MARKS-(112(3)+20(5)=436)

HEAT-3 APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA MAX-MARKS-(112(3)+20(5)=436) HEAT- APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA TIME-(HRS) Select the correct alternative : (Only one is correct) MAX-MARKS-(()+0(5)=6) Q. Suppose & are the point of maimum and the point of minimum

More information

12 STD BUSINESS MATHEMATICS

12 STD BUSINESS MATHEMATICS STD BUSINESS MATHEMATICS www.kalvisolai.com 0 MARK FAQ S: CHAPTER :. APPLICATION OF MATRICES AND DETERMINANTS. If A verify that AAdjA AdjA A AI. (M 0). Show that the equations y + z = 7, + y 5z =, + y

More information

Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics

Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics Pearson Edecel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics Mathematical formulae and statistical tables First certification from 08 Advanced Subsidiary GCE in Mathematics

More information

1. The unit vector perpendicular to both the lines. Ans:, (2)

1. The unit vector perpendicular to both the lines. Ans:, (2) 1. The unit vector perpendicular to both the lines x 1 y 2 z 1 x 2 y 2 z 3 and 3 1 2 1 2 3 i 7j 7k i 7j 5k 99 5 3 1) 2) i 7j 5k 7i 7j k 3) 4) 5 3 99 i 7j 5k Ans:, (2) 5 3 is Solution: Consider i j k a

More information

POINT. Preface. The concept of Point is very important for the study of coordinate

POINT. Preface. The concept of Point is very important for the study of coordinate POINT Preface The concept of Point is ver important for the stud of coordinate geometr. This chapter deals with various forms of representing a Point and several associated properties. The concept of coordinates

More information