All Rights Reserved Wiley India Pvt. Ltd. 1
|
|
- Lucas Merritt
- 5 years ago
- Views:
Transcription
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 be,,, 6 y y 6 6y y Range is {,,}. If tan tan, y y <, then write the value of + y + y. tan tan y y y y y y y tan, y y y. If A is a square matri such that A = A, then write the value of 7A (I + A), where I is an identity matri. A is a square matri A = A 7A (I + A) = 7A (I + A)(I + A)(I + A) = 7A (II + IA + AI + A )(I + A) = 7A (I + A + A + A)(I + A) All Rights Reserved 8. Wiley India Pvt. Ltd.
2 = 7A (I + A)(I + A) = 7A (II + IA + AI + AA) = 7A (I + A + A) = 7A (I + 7A) = I. If y z, y w 5 find the value of + y. y z y 5 y & z y & 5 y y + y = 5. If 7 8 7, 6 find the value of If f ( ) t sin t dt, then write the value of f ( ). f t sin t dt cos cos d By Parts f t t t t cos sin t f cos sin differentiate w.r.t f () = ( sin) cos + cos = sin All Rights Reserved 8. Wiley India Pvt. Ltd.
3 f () = sin 7. Evaluate: d I d d 7 I ln ln7 ln 5 ln 5 8. Find the value of p for which the vectors iˆ ˆj 9k ˆ and iˆ pj ˆ k ˆ are parallel. let a iˆ ˆj 9kˆ b iˆ pj ˆ kˆ a & b are two parallel vector then a b (i + j + 9k) = λ(i pj + k) equate Coefficient, P, 9 P P P 9. Find a.( b c ), if a iˆ ˆj k ˆ, b iˆ ˆj k ˆ and c iˆ ˆj k ˆ. a iˆ ˆj kˆ, b iˆ ˆj kˆ, c iˆ ˆj kˆ 6 a b c 6 5. If the cartesian equations of a line are y z 6, 5 7 write the vector equation for the line. All Rights Reserved 8. Wiley India Pvt. Ltd.
4 y z 5 7 y z 5 7 Constant Any point on this line is 5, 7, vector equation of line is ˆ ˆ ˆ 5ˆ 7 ˆ ˆ r i j k i j k SECTION B Question numbers to carry marks each.. If the function f : R R be given by f() = + and g : R R be given by g ( ), find fog and gof and hence find fog () and gof ( )., f R R f! g! R R g fog f g g f gof g f f fog 6 gof. Prove that tan cos, All Rights Reserved 8. Wiley India Pvt. Ltd.
5 let y tan let cos,, y tan tan cos cos cos cos use cos sin cos sin cos sin cos, tan tan y y cos OR If tan tan, find the value of. tan tan tan tan Using properties of determinants, prove that y 5 y 8y 8 All Rights Reserved 8. Wiley India Pvt. Ltd. 5
6 y y 5 y 5 y 8y 8 8 8y 8 5 C C C 5 y C C C. Find the value of d at, if = aeθ (sin θ cos θ) and y = ae θ (sin θ + cos θ). sin cos, sin cos ae y ae d ae sin cos ae cos sin ae sin d ae sin cos ae cos sin ae sin d d ae cos cot d d d ae sin d 5. If y = Pe a + Qe b, show that d y a b y Pe Qe ( a b) aby d d a b ape bqe d differentiate w.r.t to d y a b a Pe b Qe d d y d d a b a b a b a b aby a Pe b Qe a bape bqe abpe Qe a b a b a b a b a Pe b Qe a Pe abqe bape b Qe abpe Qabe 6. Find the value(s) of for which y = [( )] is an increasing function. All Rights Reserved 8. Wiley India Pvt. Ltd. 6
7 y = ( ) differentiate w.r.t d Sign schemes of d y d f y is increasing,, OR Find the equations of the tangent and normal to the curve Equation of Hyperbola is a y b Equation of tangent to Hyperbola at point P a, b a y b at the point ( ab, ). a y b y a b a b b Slope of tangent a a Slope of normal b Equation of normal at point P a, b a y b a b b y b a a a by a b 7. Evaluate: Let sin d cos All Rights Reserved 8. Wiley India Pvt. Ltd. 7
8 I sin d cos cos sin I d u sing porperty sin I d cos sin sin I d d cos cos OR tan cos tan cos tan cos Evaluate: d 5 6 I d 56 5 d d d d ln C ln 5 6 C 8. Find the particular solution of the differential equation d y y, =. given that y = when All Rights Reserved 8. Wiley India Pvt. Ltd. 8
9 y y d ( ) y( ) d ( )( y) d ( )d c (Variable Separable method) y ln( y ) c at, y ln c c / ln( y ) ln( y ) Solution is y e 9. Solve the differential equation tan ( ) y e. d y e d tan tan tan tan e y d linear differential equation. Integrating factor = e d d tan tan tan tan e e ye d C tan tan tan e e ye d C e e t tan tan tan tan d dt tan tan e e e t d t dt C ye e y e C e C All Rights Reserved 8. Wiley India Pvt. Ltd. 9
10 . Show that the four points A, B, C and D with position vectors iˆ 5 ˆj k ˆ, ˆ j k ˆ, iˆ 9 ˆj k ˆ and ( iˆ ˆj k ˆ) respectively are coplanar. Position vector of Points are OA i 5 j k, OB j k, OC i 9 j k, OD i j k AB OB OA j k i 5 j k i 6 j k AC OC OA i 9 j k i 5 j k i j k AD OD OA i j k i 5 j k 8i j k AD, AC & AD vector are coplanar than scalar triple product these vector is. AB AC AD AB AC AD OR The scalar product of the vector a iˆ ˆj k ˆ with a unit vector along the sum of vectors b iˆ ˆj 5k ˆ and c iˆ ˆj k ˆ is equal to one. Find the value of λ and hence find the unit vector along b c. a i j k u d b c i j 5k i j k i 6 j k Unit vector dˆ iˆ 6ˆj kˆ 6 i j k i 6j k a dˆ ˆ i 6 j k i 6 j k d 9 7 All Rights Reserved 8. Wiley India Pvt. Ltd.
11 . A line passes through (,, ) and is perpendicular to the lines r ( iˆ ˆj kˆ) (iˆ ˆj k ˆ) and r (iˆ ˆj kˆ) ( iˆ ˆj k ˆ). Obtain its equation in vector and cartesian form. Line passing through (,,) is ˆ ˆ r i j k li mj nk l, m, n are direction of line which is perpendicular to given lines & r i j k i j k r i j k i j k Dot product of direction is zero. l m n l m n l n l n l m l l m Direction ratio of required line is l, l, l,,,, vector equation of line is r i j k i j k Cartesian equation of line is y z. An eperiment succeeds thrice as often as it fails. Find the probability that in the net five trials, there will be at least successes. Let the chances of success of an eperiment is = p & the chances of an eperiment is = q p + q = p = q q q p All Rights Reserved 8. Wiley India Pvt. Ltd.
12 Probability of at least success out of 5 trial is C p q C p q C p C C C Question numbers to 9 carry 6 marks each. SECTION C. Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award ` each, ` y each and ` z each for the three respective values to, and students respectively with a total award money of `,6. School B wants to spend `, to award its, and students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is < 9, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award. Name of schoolof their no of Student Award for Sincenty( ) Award for Truthful ness( y) Award for Helpless( z) A B Student for each value School A award the money + y + z = 6 () School B award the money + y + z = () Total amount of award for one Prize +y + z = 9 () On each value is let P, X y z 6 Q 9 PX Q Det ( P) ( ) ( ) ( ) 6 5 Matri P is non Singular matri All Rights Reserved 8. Wiley India Pvt. Ltd.
13 X = P t Q Cofactor is of P is C, C, C 5 C ( ), C, C 5 C, C, C 5 5 adjp t (adjp) P 5 (Det P) 5 5 / 5 / 5 t P / 5 / 5 / 5 / 5 / 5 / 5 6 y / 5 / 5 z / 5 / 5 9, y, z. Show that the altitude of the right circular cone of maimum volume that can be inscribed in a sphere of radius r is r. Also show that the maimum volume of the cone is 8 of the volume of the 7 sphere. OBD OD OD BD cos =, sin OB r OB OD rcos BD rsin Volume of right Circular Cone is All Rights Reserved 8. Wiley India Pvt. Ltd.
14 V R h R Radiusof Cone h height of Cone h r r cos R rsin V r sin ( r r cos ) V r (sin sin cos ) dv d dv d dv cos cos cos d cos cos r (sin cos sin cos sin ) (differentiatic w.r.t ) r sin ( cos cos sin ) (cos )(cos ) cos 7 cos / / sin r r hieght = r Volumeof Cone r ( r sin ) r sin 9 8 r 9 9 r 8 8 r 7 8 volumeof sphase 7 5. Evaluate: Rh d cos sin All Rights Reserved 8. Wiley India Pvt. Ltd.
15 Let I d cos sin sec I d tan Put tan t sec d dt sec t I dt dt t t ( / t ) I dt t t I ( / t ) ( t / t) ( ) t z dt dz t t I dz z tan ( ) I z t / t tan C tan cot tan C C 6. Using integration, find the area of the region bounded by the triangle whose vertices are (, ), (, 5) and (, ). Coordinate of Vertices of ΔABC is A(, ) B(,5) & C(, ) Equation of line AB is 5 y z ( ) y y 7 7 y Equation of line AC is All Rights Reserved 8. Wiley India Pvt. Ltd. 5
16 y z ( ) y 8 y 5 y Equation of line BC is 5 y ( ) y 8 y 7 5 Area of ABCis = d d d 6 sq. unit t t Area of ABC ( 7)d ( )d ( 5)d 7 ) sq.unit. 7. Find the equation of the plane through the line of intersection of the planes + y + z = and + y + z = 5 which is perpendicular to the plane y + z =. Also find the distance of the plane obtained above, from the origin. Equation of plane passing through the line of Intersection of two given plane is given by ( y z) ( y z 5) ( ) y( ) z( ) ( 5 ) This plane is perpendicular to y + z = ( ) Hence plane is y z z y z 5 z All Rights Reserved 8. Wiley India Pvt. Ltd. 6
17 Distance of Plane from origin OR Find the distance of the point (,, 5) from the point of intersection of the line r iˆ ˆj kˆ (iˆ ˆj k ˆ) and the plane r.( iˆ ˆj k ˆ). n Eq of plane is r ( i j k) ( i yj zk) ( i j k) y z & Eq n of line is r i j k ( si j k) r i( ) j( ) k( ) any point on this line is ( ) lies in the Plane 8 8 Point of Intersection of plane & line is (,, ) (,,5) Distance b/w given point & this point is ( ) ( ) ( 5) A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and labour hour for finishing. Each type of B requires labour hours for fabricating and labour hours for finishing. For fabricating and finishing, the maimum labour hours available per week are 8 and respectively. The company makes a profit of ` 8 on each piece of type A and ` on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maimum profit? Make it as an LPP and solve graphically. What is the maimum profit per week? Let no. of pieces of type A manufactured per week = Let no. of pieces of type B manufactured per week =y Type of pieces hour for fabrication hour for finishing A B 9 All Rights Reserved 8. Wiley India Pvt. Ltd. 7
18 for A Maimum no. of fabrication 9 hours is 8. 9 y 8 y 6 Ma m no. of finishing hour for B is. y Profit 8 y P Where y y y 6 5 y y Graphically Plotting of this y gy 9 y6 5y y 6 8 P 8 y Q(, b) Pr ofit P S(,) P 8 R(,) P 8 6 T(,5) P Maimum Profit occur at T(, 5) Where Teaching aid from A= All Rights Reserved 8. Wiley India Pvt. Ltd. 8
19 Teaching aid from B=5 9. There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails % of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin? Number of Coin= For coin P Probability of P Heads is P(H/P) = For coin Q Probability of P Heads is P(H/Q) = 75 / For coin R Probability of P Heads is in 6 P(H R) 5 Prob of choosing one Coin out of coins is =/ P P P Q P R P(P/H) Prob. Of Head from coin P, same other Prob of Head P(H)=P(P) P(H/P)+P(Q)P(H/Q)+P(R) P(H/R) P(P) P(H/P) P(P/H)= P(H) 7 7 OR Two numbers are selected at random (without replacement) from the first si positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X, and hence find the mean of the distribution. First si positive Integer is {,,,,5,6} X is greatest no out of chosen of no. X = 5 6 If = favourable Case is (,) P ( ) 6 C 5 If = favourable Case is All Rights Reserved 8. Wiley India Pvt. Ltd. 9
20 (,) & (,) P ( ) 6 C 5 If = favourable case is (,), (,), (,) P ( ) 6 C 5 If = s fav. Case is (,5), (,5), (,5), (,5) P ( 5) 6 C 5 If = 6 fav Case is (,6),(,6,),(,6),(,6),(5,6) 5 5 P ( 6) 6 C 5 Variable X 5 6 Corresponding 5 Probability Mean of distribution ( 6 ) All Rights Reserved 8. Wiley India Pvt. Ltd.
Rao IIT Academy/ ISC - Board 2018_Std XII_Mathematics_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS. XII - ISC Board
Rao IIT Academy/ ISC - Board 8_Std XII_Mathematics_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS XII - ISC Board MATHEMATICS - QP + SOLUTIONS Date: 6..8 Ma. Marks : Question SECTION - A (8 Marks)
More informationCBSE Examination Papers
CBSE Eamination Papers (Foreign 0) Time allowed: hours Maimum marks: 00 General Instructions: As given in CBSE Sample Question Paper. Set I SECTION A Question numbers to 0 carry mark each.. Write the principal
More informationMATHEMATICS. 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 informationCBSE 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 informationANNUAL EXAMINATION - ANSWER KEY II PUC - MATHEMATICS PART - A
. LCM of and 6 8. -cosec ( ) -. π a a A a a. A A A A 8 8 6 5. 6. sin d ANNUAL EXAMINATION - ANSWER KEY -7 + d + + C II PUC - MATHEMATICS PART - A 7. or more vectors are said to be collinear vectors if
More informationOperating C 1 C 1 C 2 and C 2 C 2 C 3, we get = 0, as R 1 and R 3 are identical. Ans: 0
Q. Write the value of MATHEMATICS y y z z z y y y z z z y Operating R R + R, we get y z y z z y z y ( y z) z y Operating C C C and C C C, we get 0 0 0 0 ( y z) z y y ( y z)( ) z y y 0 0 0 0 = 0, as R and
More informationC.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 information12 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 informationCLASS XII-COMMON PRE-BOARD EXAMINATION
CLASS XII-COMMON PRE-BOARD EXAMINATION Subject: Mathematics General Instructions: Time Allotted: 3 Hours. Max.Marks:100 a. All the questions are compulsory b. The question paper consists of 29 questions
More informationCBSE Board Paper Class-XII. Time allowed : 3 hours Maximum Marks : 100
L.K.Gupta (Mathematic Classes) www.poineermathematics.com. MOBILE: 98155771, 461771 CBSE Board Paper -011 Class-XII (SET-1) Time allowed : hours Maimum Marks : 100 General Instructions: (i) All questions
More informationSAMPLE QUESTION PAPER MATHEMATICS CLASS XII:
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII: 05-6 Question numbers to 6 carry mark each. SAMPLE PAPER II Section A Q. Evaluate: - 3 sin(cos (- )). 5 Q. State the reason for the following Binary Operation
More informationMINIMUM 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 informationMarking Scheme. Section A 3. 2 [1] l m n 1 n 1 cos [1] Direction ratios of the given line are 2, 1, 2.
Marking Scheme Section A. B. AB 6 A B 6. sin( ) cos( ) or sin( ). 4. l m n n cos 45 or 6 4 OR Direction ratios of the given line are,,. [/] Hence, direction cosines of the line are:,, or,, [/] Section
More information02. 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 informationCBSE Mathematics 2016 Solved paper for Class XII(10+2) Section - A. Q. 1 For what value of k, the system of linear equations.
A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH CBSE Mathematics 06 Solved paper for Class XII(0+) Section - A Q. For what value of k, the system of linear equations. y z y z
More informationMATHEMATICS. Time allowed : 3 hours Maximum Marks: 100
MATHEMATICS Time allowed : 3 hours Maimum Marks: 00 General Instructions:. All questions are compulsory.. This question paper contains 9 questions. 3. Questions 4 in Section A are very short-answer type
More informationSeries SC/SP Code No. SP-16. Mathematics. Time Allowed: 3 hours Maximum : 100
Sample Paper (CBSE) Series SC/SP Code No. SP-16 Mathematics Time Allowed: 3 hours Maximum : 100 General Instructions: (i) (ii) (iii) (iv) (v) (vi) There are 26 questions in all. All questions are compulsory.
More informationMATHEMATICS (SET -3) Labour cost Z 300x 400y (to be minimized) The constraints are: SECTION - A 1. f (x) is continuous at x 3 f (3) lim f (x)
8 Class th (SET -) BD PPER -7 M T H E M T I C S () SECTION -. f () is continuous at f () lim f () ( ) 6 k lim ( )( 6) k lim ( ) k. adj I 8 I 8 I 8I 8. P : z 5 5 P : 5 5z z 8 Distance between P & P sin
More informationSOLUTION CLASS-XII / (CBSE)
CBSE XII EXAMINATION-6 SOLUTION--6 CBSE th Board MATHEMATICS SET- CLASS-XII / CBSE Corporate Office : CG Tower, A-6 &, IPIA, Near Cit Mall, Jhalawar Road, Kota Raj.- PCCP Head Office: J-, Jawahar Nagar,
More informationSAMPLE QUESTION PAPER MATHEMATICS CLASS XII :
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII : 05-6 TYPOLOGY VSA ( M) L A I (4M) L A II (6M) MARKS %WEIGHTAGE Remembering 3, 6, 8, 9, 5 0 0% Understanding, 9, 0 4, 6 % Applications 4 3, 5, 6, 7, 0 9 9%
More informationRao IIT Academy/ 2015/ XII - CBSE - Board Mathematics Code(65 /2 /MT) Set-2 / Solutions XII - CBSE BOARD CODE (65/2/MT) SET - 2
Rao IIT Academ/ 5/ XII - CBSE - Board Mathematics Code(65 / /MT) Set- / Solutions XII - CBSE BOARD CODE (65//MT) SET - Date: 8.3.5 MATHEMATICS - SOLUTIONS. Let a iˆ 3iˆ kˆ b iˆ ˆj and a b 3 5, b a b Projection
More information1 are perpendicular to each other then, find. Q06. If the lines x 1 z 3 and x 2 y 5 z
Useful for CBSE Board Examination of Math (XII) for 6 For more stuffs on Maths, please visit : www.theopgupta.com Time Allowed : 8 Minutes Max. Marks : SECTION A 3 Q. Evaluate : sin cos 5. Q. State the
More informationMATHEMATICS Paper & Solutions
CBSE-XII-8 EXAMINATION Series SGN MATHEMATICS Paper & Solutions SET- Code : 6/ Time : Hrs. Ma. Marks : General Instruction : (i) All questions are compulsor. (ii) The question paper consists of 9 questions
More informationMATHEMATICS (SET -1)
8 Class th (SET ) BD PPER -7 M T H E M T I C S (). adj 8 I 8 I 8I 8 SECTION - I. f () is continuous at f () lim f () ( ) 6 k lim ( )( 6) k lim ( ) k sin cos d tan cot d sin cos ln sec ln sin C.. P : z
More informationMATHEMATICS. 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 informationBoard Answer Paper: MARCH 2014
Board Answer Paper: MARCH 04 and Statistics SECTION I Q.. (A) Select and write the correct answer from the given alternatives in each of the following: i. (C) Let l 0, m 3, n be the direction cosines of
More informationCBSE Examination Paper, Foreign-2014
CBSE Eamination Paper, Foreign-4 Time allowed: hours Maimum marks: General Instructions: As per given in CBSE Eamination Paper Delhi-4. SET I SECTION A Question numbers to carr mark each.. Let R = {(a,
More informationHSC - BOARD MATHEMATICS (40) - SOLUTIONS
Date: 8..5 Q. (A) SECTION - I (i) (d) A () (ii) (c) A A I 6 6 6 A I 64 I I A A 6 (iii) (a) fg cos A cos HSC - BOARD - 5 MATHEMATICS (4) - SOLUTIONS cos cos ch () hy g fy c...(i) Comparing with A Hy By
More informationJEE MAIN 2013 Mathematics
JEE MAIN 01 Mathematics 1. The circle passing through (1, ) and touching the axis of x at (, 0) also passes through the point (1) (, 5) () (5, ) () (, 5) (4) ( 5, ) The equation of the circle due to point
More informationTransweb 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 informationANSWER 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 informationWBJEEM 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 informationTime allowed : 3 hours Maximum Marks : 100
CBSE XII EXAMINATION-8 Series SGN SET- Roll No. Candiates must write code on the title page of the answer book Please check that this question paper contains printed pages. Code number given on the right
More informationMarking Scheme (Mathematics XII )
Sr. No. Marking Scheme (Mathematics XII 07-8) Answer Section A., (, ) A A: (, ) A A: (,),(,) Mark(s). -5. a iˆ, b ˆj. (or an other correct answer). 6 6 ( ), () ( ) ( ). Hence, is not associative. Section
More informationCBSE MATHS 2010 YEAR PAPER
CBSE MATHS YEAR PAPER Important Instructions: (i) The question papers consists of three sections A B and C. (ii) All questions are compulsory. (iii) Internal choices have been provided in some questions.
More informationXII HSC - BOARD
Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS Date: 0.0.08 XII HSC - BOARD - 08 MATHEMATICS (40) - SOLUTIONS Q. (A) SECTION - I (i) If
More informationEINSTEIN 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 informationCBSE Board Paper Foreign 2013
CBSE Board Paper Foreign 03 Set - I Time: 3 Hours Max Marks: 00 General Instructions (i) All questions are compulsory (ii) The question paper consists of 9 questions divided into three sections A, B and
More informationSAMPLE QUESTION PAPER MATHEMATICS CLASS XII ( ) BLUE PRINT. Unit VSA (1) SA (4) LA (6) Total. I. Relations and Functions 1 (1) 4 (1) 5 (2)
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII (2013-14) BLUE PRINT Unit VSA (1) SA (4) LA (6) Total I. Relations and Functions 1 (1) 4 (1) 5 (2) Inverse Trigonometric Functions 1 (1) *4 (1) 5 (2) II. Matrices
More informationSaturday, March 27, :59 PM Annexure 'F' Unfiled Notes Page 1
Annexure 'F' CLASS-XII SAMPLE QUESTION PAPER MATHEMATICS CLASS XII (2013-14) BLUE PRINT Unit VSA (1) SA (4) LA (6) Total I. Relations and Functions 1 (1) 4 (1) 5 (2) Inverse Trigonometric Functions
More informationy mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent
Mathematics. The sides AB, BC and CA of ABC have, 4 and 5 interior points respectively on them as shown in the figure. The number of triangles that can be formed using these interior points is () 80 ()
More informationMODEL 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 informationCLASS 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 informationSample Paper-05 Mathematics Class XII. Time allowed: 3 hours Answers Maximum Marks: 100. Section A. Section B
Sample Paper-05 Mathematics Class XII Time allowed: hours Answers Maimum Marks: 00. No. (, ) R but (, ) R r. a () + ( ) + ( 5) 8 5 l, m, n 8 8 8. [0, ]. A A ( 8) 8 ( 6) A 8 Hence Prove tan cos sin sin
More informationMATHEMATICS SOLUTION
MATHEMATICS SOLUTION MHT-CET 6 (MATHEMATICS). (A) 5 0 55 5 9 6 5 9. (A) If the school bus does not come) (I will not go to school) ( I shall meet my friend) (I shall go out for a movie) ~ p ~ q r s ~ p
More informationMockTime.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 informationIIT-JEE (2012) (Vector+3D+Probability) Solutions
L.K. Gupta (Mathematic Classes) www.pioneermathematics.com MOBILE: 985577, 4677 PAPER -A IIT-JEE (0) (Vector+D+Probability) Solutions TOWARDS IIT- JEE IS NOT A JOURNEY, IT S A BATTLE, ONLY THE TOUGHEST
More informationCLASS 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 informationSECTION A 1. Find the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is 2iˆ
Session: 01-17 Subject: Mathematics Class XII Duration: 3 hr. M.M: 100 General Instructions: (i) All questions are compulsor. (ii) This question paper contains 9 questions. (iii) Question 1 in Section
More informationVectors. Teaching Learning Point. Ç, where OP. l m n
Vectors 9 Teaching Learning Point l A quantity that has magnitude as well as direction is called is called a vector. l A directed line segment represents a vector and is denoted y AB Å or a Æ. l Position
More informationSUBJECT : PAPER I MATHEMATICS
Question Booklet Version SUBJECT : PAPER I MATHEMATICS Instruction to Candidates. This question booklet contains 50 Objective Type Questions (Single Best Response Type) in the subject of Mathematics..
More information(iii) For each question in Section III, you will be awarded 4 Marks if you darken only the bubble corresponding to the
FIITJEE Solutions to IIT - JEE 8 (Paper, Code 4) Time: hours M. Marks: 4 Note: (i) The question paper consists of parts (Part I : Mathematics, Part II : Physics, Part III : Chemistry). Each part has 4
More informationMathematics. 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 informationQUESTION PAPER CODE 65/2/2/F EXPECTED ANSWER/VALUE POINTS
QUESTION PAPER CODE EXPECTED ANSWER/VALUE POINTS SECTION A. P 6 (A A ) P 6 9. (a b c) (a b c) 0 a b c (a b b c c a) 0 a b b c c a. a b sin θ a b cos θ 400 b 4 4. x z 5 or x z 5 mark for dc's of normal
More informationKENDRIYA VIDYALAYA SANGATHAN, CHENNAI REGION CLASS XII-COMMON PRE-BOARD EXAMINATION. Answer key (Mathematics) Section A
KENDRIYA VIDYALAYA SANGATHAN, CHENNAI REGION CLASS XII-COMMON PRE-BOARD EXAMINATION Answer key (Mathematics) Section A. x =. x + y = 6. degree =. π 5. 6. 7. 5 8. x + y + z = 9.. 66 Section B. Proving Reflexive
More information22 (Write this number on your Answer Sheet)
Question Booklet Version (Write this number on your Answer Sheet) Day and Date : Thursday, 0th May, 08 QUESTION BOOKLET (MHT-CET - 08) Subjects : Paper I : Mathematics MH-CET 08 Roll No. Question Booklet
More informationSET-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 informationSAMPLE QUESTION PAPER MATHEMATICS (041) CLASS XII
SAMPLE QUESTION PAPER MATHEMATICS (01) CLASS XII 017-18 Time allowed: hours Maimum Marks: 100 General Instructions: (i) All questions are compulsory. (ii) This question paper contains 9 questions. (iii)
More informationPES 1110 Fall 2013, Spendier Lecture 5/Page 1
PES 1110 Fall 2013, Spendier Lecture 5/Page 1 Toda: - Announcements: Quiz moved to net Monda, Sept 9th due to website glitch! - Finish chapter 3: Vectors - Chapter 4: Motion in 2D and 3D (sections 4.1-4.4)
More informationCHAPTER 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 informationSOLUTIONS TO CONCEPTS CHAPTER 2
SOLUTIONS TO CONCPTS CHAPTR 1. As shown in the figure, The angle between A and B = 11 = 9 A = and B = 4m Resultant R = A B ABcos = 5 m Let be the angle between R and A 4 sin9 = tan 1 = tan 1 (4/) = 5 4cos9
More informationGOVERNMENT 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 informationFIITJEE 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 informationKEAM (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 informationSAMPLE QUESTION PAPER
SAMPLE QUESTION PAPER CLASS-XII (201-17) MATHEMATICS (01) Time allowed: 3 hours Maximum Marks: 100 General Instructions: (i) All questions are compulsory. (ii) This question paper contains 29 questions.
More informationDIRECTORATE OF EDUCATION GOVT. OF NCT OF DELHI
456789045678904567890456789045678904567890456789045678904567890456789045678904567890 456789045678904567890456789045678904567890456789045678904567890456789045678904567890 QUESTION BANK 456789045678904567890456789045678904567890456789045678904567890456789045678904567890
More information10 th MATHS SPECIAL TEST I. Geometry, Graph and One Mark (Unit: 2,3,5,6,7) , then the 13th term of the A.P is A) = 3 2 C) 0 D) 1
Time: Hour ] 0 th MATHS SPECIAL TEST I Geometry, Graph and One Mark (Unit:,3,5,6,7) [ Marks: 50 I. Answer all the questions: ( 30 x = 30). If a, b, c, l, m are in A.P. then the value of a b + 6c l + m
More informationMathematics. Section B. CBSE XII Mathematics 2012 Solution (SET 2) General Instructions:
CBSE XII Mathematics 0 Solution (SET ) General Instructions: Mathematics (i) (ii) (iii) (iv) (v) All questions are compulsor. The question paper consists of 9 questions divided into three Sections A, B
More informationObjective Mathematics
Chapter No - ( Area Bounded by Curves ). Normal at (, ) is given by : y y. f ( ) or f ( ). Area d ()() 7 Square units. Area (8)() 6 dy. ( ) d y c or f ( ) c f () c f ( ) As shown in figure, point P is
More informationCLASS 12 SUBJECT : MATHEMATICS
CLASS 2 SUBJECT : MATHEMATICS CBSE QUESTION PAPER 27(FOREIGN) General Instructions: (i) All questions are compulsory. (ii) Questions 4 in Section A carrying mark each (iii) Questions 5 2 in Section B carrying
More informationMATHEMATICS QUESTION PAPER CODE 65/1/1 SECTION A
MATHEMATICS Time allowed : hours Maimum Marks : General Instructions : (i) (ii) The question paper consists of three sections A, B and C. Section A is compulsory for all students. In addition to Section
More informationMATHEMATICS PAPER IB COORDINATE GEOMETRY(2D &3D) AND CALCULUS. Note: This question paper consists of three sections A,B and C.
MATHEMATICS PAPER IB COORDINATE GEOMETRY(D &3D) AND CALCULUS. TIME : 3hrs Ma. Marks.75 Note: This question paper consists of three sections A,B and C. SECTION A VERY SHORT ANSWER TYPE QUESTIONS. 0X =0.
More informationBASIC MATHEMATICS - XII SET - I
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
More information2 nd ORDER O.D.E.s SUBSTITUTIONS
nd ORDER O.D.E.s SUBSTITUTIONS Question 1 (***+) d y y 8y + 16y = d d d, y 0, Find the general solution of the above differential equation by using the transformation equation t = y. Give the answer in
More informationCLASS 12 SUBJECT: MATHEMATICS CBSE QUESTION PAPER : 2016 (DELHI PAPER)
CLASS 12 SUBJECT: MATHEMATICS CBSE QUESTION PAPER : 2016 (DELHI PAPER) General Instructions: (i) All questions are compulsory. (ii) Questions 1 6 in Section A carrying 1 mark each (iii) Questions 7 19
More information2013 Bored of Studies Trial Examinations. Mathematics SOLUTIONS
03 Bored of Studies Trial Examinations Mathematics SOLUTIONS Section I. B 3. B 5. A 7. B 9. C. D 4. B 6. A 8. D 0. C Working/Justification Question We can eliminate (A) and (C), since they are not to 4
More informationSECTION A(1) k k 1= = or (rejected) k 1. Suggested Solutions Marks Remarks. 1. x + 1 is the longest side of the triangle. 1M + 1A
SECTION A(). x + is the longest side of the triangle. ( x + ) = x + ( x 7) (Pyth. theroem) x x + x + = x 6x + 8 ( x )( x ) + x x + 9 x = (rejected) or x = +. AP and PB are in the golden ratio and AP >
More informationDesign of Question Paper Mathematics - Class XII
Design of Question Paper Mathematics - Class XII Time : 3 hours Max. Marks : 100 Weightage of marks over different dimensions of the question paper shall be as follows : A. Weightage to different topics/content
More informationFILL 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 informationLIST OF MEMBERS WHO PREPARED QUESTION BANK FOR MATHEMATICS FOR CLASS XII TEAM MEMBERS. Sl. No. Name Designation
LIST OF MEMBERS WHO PREPARED QUESTION BANK FOR MATHEMATICS FOR CLASS XII TEAM MEMBERS Sl. No. Name Designation. Sh. S.B. Tripathi R.S.B.V., Jheel Khuranja (Group Leader) Delhi. (M. 98086). Sh. Sanjeev
More informationBLUE PRINT: CLASS XII MATHS
BLUE PRINT: CLASS XII MATHS CHAPTER S NAME MARK 4 MARKS 6 MARKS TOTAL. RELATIONS AND FUNCTIONS 5. INVERSE TRIGONOMETRIC 5 FUNCTIONS 3. MATRICES 7 4. DETERMINANTS 6 5. 8 DIFFERENTIATION 6 APPLICATION OF
More informationRegn. No. North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-09, Ph: ,
1. Section-A contains 0 Multiple Choice Questions (MCQ). Each question has 4 choices (a), (b), (c) and (d), for its answer, out of which ONLY ONE is correct. From Q.1 to Q.10 carries 1 Marks and Q.11 to
More informationSTRAIGHT LINES EXERCISE - 3
STRAIGHT LINES EXERCISE - 3 Q. D C (3,4) E A(, ) Mid point of A, C is B 3 E, Point D rotation of point C(3, 4) by angle 90 o about E. 3 o 3 3 i4 cis90 i 5i 3 i i 5 i 5 D, point E mid point of B & D. So
More informationAnswers for NSSH exam paper 2 type of questions, based on the syllabus part 2 (includes 16)
Answers for NSSH eam paper type of questions, based on the syllabus part (includes 6) Section Integration dy 6 6. (a) Integrate with respect to : d y c ( )d or d The curve passes through P(,) so = 6/ +
More informationSURA's Guides for 3rd to 12th Std for all Subjects in TM & EM Available. MARCH Public Exam Question Paper with Answers MATHEMATICS
SURA's Guides for rd to 1th Std for all Subjects in TM & EM Available 10 th STD. MARCH - 017 Public Exam Question Paper with Answers MATHEMATICS [Time Allowed : ½ Hrs.] [Maximum Marks : 100] SECTION -
More informationKEAM (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 informationQUESTION 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 informationTime : 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 information3. 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 information38. The total number of carboxylic acid groups in the product P is 38. [2] O C HO 3 O C C O C O C O. Total no. of carboxylic group = 2
(6) Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution 8. The total number of carboxylic acid groups in the product P is 8. [] C.... + H Heat C Total no. of carboxylic group = C C H 9. A tetrapeptide
More informationTABLE OF CONTENTS 2 CHAPTER 1
TABLE OF CONTENTS CHAPTER 1 Quadratics CHAPTER Functions 3 CHAPTER 3 Coordinate Geometry 3 CHAPTER 4 Circular Measure 4 CHAPTER 5 Trigonometry 4 CHAPTER 6 Vectors 5 CHAPTER 7 Series 6 CHAPTER 8 Differentiation
More informationMARKSCHEME SPECIMEN MATHEMATICS
SPEC/5/MATHL/HP/ENG/TZ/XX/M MARKSCHEME SPECIMEN MATHEMATICS Higher Level Paper pages 5 SPEC/5/MATHL/HP/ENG/TZ/XX/M SECTION A. (a) 8 sin [ mark] 8 8 tan 8 7 4 7 [ marks] (c) cos 6 cos [ marks] Total [6
More informationINDIAN 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 informationPage 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 informationPART B MATHEMATICS (2) (4) = +
JEE (MAIN)--CMP - PAR B MAHEMAICS. he circle passing through (, ) and touching the axis of x at (, ) also passes through the point () (, ) () (, ) () (, ) (4) (, ) Sol. () (x ) + y + λy = he circle passes
More information1 / 23
CBSE-XII-07 EXAMINATION CBSE-X-009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper
More informationMATHEMATICS Class: XII Mock Paper 1 Solutions
MATHEMATICS Class: XII Mock Paper Solutions Section A. If A { a, b, c } and B {,, } and a function f : A B is given by f { (a, ), ( b, ), ( c, ) } Every element of set A is mapped to the unique element
More information1. 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 informationPossible C4 questions from past papers P1 P3
Possible C4 questions from past papers P1 P3 Source of the original question is given in brackets, e.g. [P January 001 Question 1]; a question which has been edited is indicated with an asterisk, e.g.
More informationCHAPTER TWO. 2.1 Vectors as ordered pairs and triples. The most common set of basic vectors in 3-space is i,j,k. where
40 CHAPTER TWO.1 Vectors as ordered pairs and triples. The most common set of basic vectors in 3-space is i,j,k where i represents a vector of magnitude 1 in the x direction j represents a vector of magnitude
More information