(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
|
|
- Caroline Chambers
- 5 years ago
- Views:
Transcription
1 318 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? ( )2 ( )2 ( )2 ( )2 4. R is reflexive only R is symmetric only R is transitive only R is reflexive and transitive n n 2 8. If A and B are two disjoint sets, then which one of the following is correct? 9. Null set {P} {P, Q, R} {Q, R} 10. Complement of A Complement of B B A {(2, 4), (3, 5), (1, 5)} {(1, 4), (2, 4), (3, 4)} {(1, 4), (2, 5), (3, 4)} {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)} Sets A and B have n elements in common. How many elements will (A B) and (B A) have in common? 0 1 2k 7 2 K xyz 27xyz 13. Signs of a and c should be like Signs of b and c should be like Signs of a and b should be like None of the ablve 14.
2 319 A quadratic polynomial with two distinct roots has one real root. Then, the other root is Not necessarily real, if the coefficients are real Always imaginary Always real Real, if the coefficients are real If, for positive real numbers x, y, z, the numbers x + y, 2y and y + z are in harmonic progression, then which one of the following is correct? x, y, z are in geometric progression x, y, z are in arithmetic progression x, y, z are in harmonic progression None of the above 21. always complex always real always purely imaginary None of these If the roots of a quadratic equation are m + n and m n, then the quadratic equation will : 19. What is the product of first 2n + 1 terms of a geometric progression? The (n + 1)th power of the nth term of the GP The (2n + 1)th power of the nth term of the GP The (2n + 1)th power of the (n + 1)th term of the GP The nth power of the (n + 1)th terms of the GP 22. The 59th term of an AP is 449 and the 449th term is 59. Which term is equal to 0 (zero)? 501 st term 502 nd term 508 th term 509 th term 23. Which one of the following options is correct? sin 2 30, sin 2 45, sin 2 60 are in GP cos 2 30, cos 2 45, cos 2 60 are in GP cot 2 30, cot 2 45, cot 2 60 are in GP tan 2 30, tan 2 45, tan 2 60 are in GP 24. Consider the following statements: 1. The sum of cubes of first 20 natural numbers is The sum of squares of first 20 natural numbers is Which of the above statements is/are correct? 1 only 2 only Both 1 and 2 Neither 1 nor 2 25.
3 ω ω What is the number of words that can be formed from the letters of the word UNIVERSAL, the vowels remaining always together? The lines (p + 2q) x + (p 3q) y = p q for different values of p and q pass through the fixed point given by which one of the following? What is the approximate value of (1.02) 8? In the expansion of [1 + x] n, what is the sum of even binomial coefficients? 2 n 2 n 1 2 n + 1 None of the above 31. A group consists of 5 men and 5 women. If the number of different five-person committees containing k men and (5 k) women is 100, what is the value of k? 2 only 3 only 2 or If O be the origin and A (x1, y1), B (x2, y2) are two points, then what is (OA) (OB) cos AOB? 35. What is the equation to the straight line joining the origin to the point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1? x + y = 0 x + y +1 = 0 x y = 0 x + y + 2 = How many diagonal will be there in an n-sided regular polygon?
4 What is the perpendicular distance between the parallel lines 3x + 4y = 9 and 9x + 12y + 28 = 0? 7/3 units 8/3 units 10/3 units 11/3 units 38. What is the locus of the point of intersection of the straight lines (x/a) + (y/b) = m and (x/a) (y/b) = 1/m? Circle Parabola Ellipse Hyperbola 39. The equation of the circle which touches the axes at a distance 5 from the origin is y 2 + x 2 2ax 2ay + a 2 =0. What is the value of a? What is the equation of the parabola, whose vertex and focus are on the x-axis at distance a and b from the origin respectively? (b > a > 0) y 2 = 8 (b a) (x a) y 2 = 4(b + a)( x a) y 2 = 4(b a)( x +a) y 2 = 4(b a)(x a) 41. A circle is drawn with the two foci of an ellipse x 2 /a 2 + y 2 /b 2 = 1 at the end of the diameter. What is the equation of the circle? x 2 + y 2 = a 2 + b 2 x 2 + y 2 = a 2 b 2 x 2 + y 2 = 2(a 2 + b 2 ) x 2 + y 2 = 2(a 2 b 2 ) 42. The difference of two angles is 1 ; the circular measure of their sum is 1. What is the smaller angle in circular measure? 43. If sin 3 θ + cos 3 θ = 0, then what is the value of θ? -π/4 0 π/4 π/3 44. Let 0 < θ < 45. Which one of the following is correct? sin 2 θ + cos 6 θ = sin 6 θ cos 2 θ cosec 2 θ + cot 6 θ = cosec 6 θ cot 2 θ sin 2 θ cos 4 θ = sin 4 θ cos 2 θ cosec 2 θ cot 4 θ = cosec 4 θ cot 2 θ 45. How many values of θ between 0 and 360 satisfy tan θ = k 0, where k is a given number? Many 46. If cos θ < sin θ and θ lies in the first quadrant, then which one of the following is correct? 0 < θ < π/4 π/4 < θ < π/2 0 < θ < π/3 π/3 < θ < π/2 47. What is the value of 3 cosec 20 sec 20? If tan A = 3/4 and tan B = 12/5, then how many values can cot (A B) have depending on the actual values of A and B? If sinθ = cos 2 θ, then what is cos 2 θ (1 + cos 2 θ) equal to? 1 0 cos 2 θ 2 sin θ 50.
5 322 π/6 π/3 π/4 π/8 51. If cosecθ + cotθ = c, then what is cosθ equal to? 52. If the perimeter of a triangle ABC is 30 cm, then what is the value of a cos 2 (C/2) + c cos 2 (A/2)? 15 cm 10 cm 15/2 cm 13 cm 53. Let 1 x 1. If cos (sin 1 x) = 1/2, then how many value does tan (cos 1 x) assume? One Two Four Infinite 54. If angles A, B and C are in AP, then what is sin A + 2 sin B + sin C equal to? elevation of the top of the flag at the foot of the ladder is 60 )? 20 feet 30 feet 40 feet 20 2 feet 57. Two poles are 10 m and 20 m high. The line joining their tips makes an angle of 15 with the horizontal. What is the distance between the poles? 10( 3 1) m 5( ) m 20( 3 + 1) m 10 ( 3 + 1) m /4 5/16 25/ Both 0 and 1 None of these If the sides of a triangle are in the ratio 2: 6 : 1 + 3, then what is the smallest angle of the triangle? What should be the height of a flag where a 20 feet long ladder reaches 20 feet below the flag (The angle of e e 2 e 4 e At how many points is the function f(x) = [x] discontinuous? 1 2 3
6 323 Infinite 63. Let f: R R be a function whose inverse is x + 5/3. What is f (x) equal to? f (x) = 3x + 5 f (x) = 3x 5 f (x) = 5x 3 f (x) does not exist 64. The probability that a student passes in mathematics is 4/9 and that he passes in physics is 2/5. Assuming that passing in mathematics and physics are independent of each other, what is the probability that he passes in mathematics but fails in physics? 4/15 8/45 26/45 19/ What is the probability that in a family of 4 children there will be at least one boy? 15/16 3/8 1/16 7/8 66. Given that P(A) = 1/3, P(B) = 1/4, P(A/B) = 1/6, then what is P(B/ A) equal to? 1/4 1/8 3/4 1/2 67. Consider the following statements: 1. The probability that there are 53 Sundays in a leap year is twice the probability that there are 53 Sundays in a non-leap year. 2. The probability that there are 5 Mondays in the month of March is thrice the probability that there are 5 Mondays in the month of April. Which of the statements given above is/are correct? 1 only 2 only Both 1 and 2 Neither 1 nor Two letters are drawn at random from the word HOME. What is the probability that both the letters are vowels? 1/6 5/6 1/ 2 1/3 69. An urn contains one black ball and one green ball. A second urn contains one white and one green ball. One ball is drawn at random from each urn. Q. What is the probability of getting at least one green ball? 1/2 1/3 2/3 ¾ 70. A line makes 45 with positive x-axis and makes equal angles with positive y, z axes, respectively. What is the sum of the three angles which the line makes with positive x, y and z axes? The line passing through (1, 2, 3) and having direction ratios given by < 1, 2, 3 > cuts the x-axis at a distance k from origin. What is the value of k? What is the equation of the sphere which has its centre at (6, 1, 2) and touches the plane 2x y + 2z 2 = 0? x 2 + y 2 + z x 2y + 4z + 16 = 0 x 2 + y 2 + z x 2y + 4z 16 = 0 x 2 + y 2 + z 2 12x + 2y 4z + 16 = 0 x 2 + y 2 + z 2 12x + 2y 4z + 25 = What is the angle between the lines whose direction cosines are proportional to (2, 3, 4) and (1, 2, 1) respectively?
7 What is the equation to the plane through (1, 2, 3) parallel to 3x + 4y 5z = 0? 3x + 4y + 5z + 4 = 0 3x + 4y 5z + 14 = 0 3x + 4y 5z + 4 = 0 3x + 4y 5z 4 = (28, 13) (23, 18) (31, 10) (25, 16) 77. If AM of numbers x1, x2... xn is μ, then what is the AM of the numbers which are increased by 1, 2, 3,...n respectively? For a set of discrete numbers, three measures of central tendency are given below 1. Arithmetic mean 2. Median 3. Geometric mean Which of the above measures may not have a meaningful definition? 1 only 2 only 3 only All of them are meaningfully defined What is the mean of first n odd natural numbers?
8 Variance is always independent of the change of origin but not scale scale only both origin and scale None of the above The motion of a particle is described as s = 2 3t + 4t 3. What is the acceleration of the particle at the point where its velocity is zero? 0 4 unit 8 unit 12 unit 89. A stone thrown vertically upward satisfies the equation s = 64t 16t 2, where s is in meter and t is in second. What is the time required to reach the maximum height? 1s 2s 3s 4s Which one of the following statement is correct? e x is an increasing function e x is a decreasing function e x is neither increasing nor decreasing function e x is a constant function 92. cosx log tanx + log tan (x/2) + c cosx log tanx + log tan (x/2) + c cosx log tanx + log cot (x/2) + c cosx log tanx + log cot (x/2) + c 93.
9 What is the solution of the differential equation xdy y dx = xy 2 dx? y + x 2 = c y 2 + 2x 1 = c y + x 1 = c x 2 + 2xy 1 = c Both A and R are individually true and R is the correct explanation of A Both A and R are individually true but R is not the correct explanation A A is true but R is false A is false but R is true 95. What is the area bounded by the curve y = 4x x 2 3 and the x-axis? 2/3 sq unit 4/3 sq unit 5/3 sq unit 4/5 sq unit 96. What is the area enclosed by the equation x 2 + y 2 = 2? 4π square units 2π square units 4π 2 square units 4 square units 97. What is the area of the region enclosed by y = 2 x and y = 4? 2 square unit 4 square unit 8 square unit 16 square unit 98. What is the solution of the differential equation (x + y) (dx dy) = dx + dy? Let A and B be two matrices such that AB is defined. If AB = 0, then which one of the following can be definitely concluded? A = 0 or B = 0 A = 0 and B = 0 A and B are non-zero square matrices A and B cannot both be non-singular 103. Let A be an m n matrix.under which one of the following conditions does A 1 exist? m = n only m = n and det A 0 m = n and det A= 0 m n 104. If the matrix B is the adjoint of the square matrix A and a is the value of the determinant of A, then what is AB equal to?
10 A matrix X has (a + b) rows and (a + 2) columns; and a matrix Y has (b + 1) rows and (a + 3) columns. If both XY and YX exist, then what are the values of a, b respectively? 3, 2 2, 3 2, 4 4, If A is a square matrix, then what is adj A T (adj A) T equal to? 2 A 2 A I Null Matrix Unit Matrix 111. m takes 1 value, n takes 1 value m takes 1 value, n takes 2 values m takes 2 value, n takes 1 value m takes 2 value, n takes 2 values /8 9/
11 What is the area of the triangle with vertices (0, 2, 2), (2, 0, 1) and (3, 4, 0)? 15/2 sq unit 15 sq unit 7/2 sq unit 7 sq unit 115. r > s > q > p s > r > p > q r > s > p > q s > r > q > p an integer a rational number but not an integer an irrational number none of the above d 2. b 3. b 4. d 5. d 6. d 7. d 8. a 9. b 10. d 11. b 12. d 13. a 14. c 15. b 16. d 17. b 18. c 19. c 20. a 21. b 22. c 23. d 24. b 25. a 26. b 27. c 28. b 29. a 30. b 31. c 32. c 33. d 34. c 35. c 36. b 37. d 38. d 39. b 40. d 41. b 42. c 43. a 44. d 45. b 46. b 47. a 48. d 49. a 50. b 51. c 52. a 53. b 54. b 55. c 56. b 57. b 58. c 59. b 60. c 61. d 62. d 63. b 64. a 65. a 66. b 67. a 68. c 69. d 70. b 71. c 72. a 73. c 74. a 75. c 76. c 77. a 78. d 79. a 80. b 81. a 82. a 83. a 84. b 85. b 86. a 87. a 88. c 89. b 90. d 91. a 92. b 93. a 94. b 95. b 96. b 97. c 98. b 99. d 100. c 101. c 102. c 103. b 104. d 105. d 106. b 107. c 108. d 109. b 110. d 111. d 112. c 113. c 114. a 115. c 116. c 117. b 118. b 119. b 120. b
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
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 informationMockTime.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 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 informationMockTime.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 informationDO 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 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 informationare 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 informationMathematics. 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 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 informationQUESTION 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(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 informationTest Codes : MIA (Objective Type) and MIB (Short Answer Type) 2007
Test Codes : MIA (Objective Type) and MIB (Short Answer Type) 007 Questions will be set on the following and related topics. Algebra: Sets, operations on sets. Prime numbers, factorisation of integers
More informationTARGET 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 information4.Let A be a matrix such that A. is a scalar matrix and Then equals :
1.Consider the following two binary relations on the set A={a, b, c} : R1={(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and R2={(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}. Then : both R1
More informationCHAPTER-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 informationComplete 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 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 informationSince x + we get x² + 2x = 4, or simplifying it, x² = 4. Therefore, x² + = 4 2 = 2. Ans. (C)
SAT II - Math Level 2 Test #01 Solution 1. x + = 2, then x² + = Since x + = 2, by squaring both side of the equation, (A) - (B) 0 (C) 2 (D) 4 (E) -2 we get x² + 2x 1 + 1 = 4, or simplifying it, x² + 2
More informationMath 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 informationMath Bank - 9. If cos ecθ= x + then the value of cos ecθ + cot θ is. (a) 2x (b) -2x. = and ( ) sec A + C = 2, then. (b), (c), (d) None of these
Math Bank - 9. If cos ecθ= + then the value of cos ecθ + cot θ - / (d) -/. If sin ( A + B + C) =, tan ( A B) = and ( ) 0 0 0 A= 90,B= 60,C= 0 0 0 0 A = 0,B = 60,C = 0 0 0 0 A= 60,B= 0,C= 0. 9 5 The value
More informationRAJASTHAN 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 informationCOORDINATE GEOMETRY LOCUS EXERCISE 1. The locus of P(x,y) such that its distance from A(0,0) is less than 5 units is x y 5 ) x y 10 x y 5 4) x y 0. The equation of the locus of the point whose distance
More information2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is
. If P(A) = x, P = 2x, P(A B) = 2, P ( A B) = 2 3, then the value of x is (A) 5 8 5 36 6 36 36 2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time
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 information63487 [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 information130 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 informationX- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS. 1. Commutative property i ii. 2. Associative property i ii
X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS 1. Commutative property i ii 2. Associative property i ii 3. Distributive property i ii 4. De Morgan s laws i ii i ii 5. Cardinality of
More informationPrerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , PART III MATHEMATICS
R Prerna Tower, Road No, Contractors Area, Bistupur, Jamshedpur 8300, Tel (0657)89, www.prernaclasses.com Jee Advance 03 Mathematics Paper I PART III MATHEMATICS SECTION : (Only One Option Correct Type)
More informationPractice Set for IIT JEE. Paper I
Objective Questions I [Only one correct option] Practice Set for IIT JEE Paper I Q 1. The number of lines in the xy-plane, Whose distance from (-1, 2) is 2 and from (2, 6) is 3, is a. 2 b. 3 c. 4 d. None
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 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 informationX- MATHS IMPORTANT FORMULAS SELF EVALUVATION
X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS 1. Commutative property i ii 2. Associative property i ii 3. Distributive property i ii 4. De Morgan s laws i ii i ii 5. Cardinality of
More informationMATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT )
Total No. of Printed Pages 6 X/5/M 0 5 MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 80 Pass Marks : 4 ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 00
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 informationMULTIPLE 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 information4) 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 informationCLASS XI Maths : Sample Paper-1
CLASS XI Maths : Sample Paper-1 Allotted Time : 3 Hrs Max. Marks : 100 Instructions 1. This questionnaire consists of 30 questions divided in four sections. Please verify before attempt. 2. Section I consists
More informationJEE-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 informationPreparation Mathematics 10 for
Preparation Mathematics 0 for 208-9 You have four choices for each objective type question as A, B, C and D. The choice which you think is correct; fill that circle in front of that question number. Use
More informationWBJEE Answer Keys by Aakash Institute, Kolkata Centre
WBJEE - 08 Answer Keys by, Kolkata Centre MATHEMATICS Q.No. 0 A B C D 0 C D A B 0 B D A C 04 C B A B 05 C A C C 06 A C D C 07 B A C C 08 B *C,D C A 09 C D D B 0 D A C D B A B C C D A B B A A C 4 C C B
More informationTABLE OF CONTENTS. Our aim is to give people math skillss in a very simple way Raymond J. Page 2 of 29
TABLE OF CONTENTS Topic.Page# 1. Numbers..04 2. Ratio, Profit & Loss 06 3. Angles......06 4. Interest..06 5. Algebra..07 6. Quadratic Equations.08 7. Logarithms...09 8. Series..10 9. Sphere.11 10. Coordinate
More informationS.S.L.C. - MATHS BOOK BACK ONE MARK STUDY MATERIAL
1 S.S.L.C. - MATHS BOOK BACK ONE MARK STUDY MATERIAL DEAR STUDENTS, I have rearranged MATHS-one mark book questions in the order based on value of the answer so that, you can understand easily Totally
More informationPGT Mathematics. 1. The domain of f(x) = is:-
PGT Mathematics 1. The domain of f(x) = is:- a. (-2, + ) b. R-{-1, -2, -3} c. (-3, + )-{-1, -2} d. R-{-1, -2} 2. If f is a function such that f(0) = 2, f(1) = 3 & f(x+2) = 2f(x)-f(x + 1) for every real
More informationCDS-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 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 informationCode : N. Mathematics ( ) ( ) ( ) Q c, a and b are coplanar. x 2 = λ µ... (ii) 1. If (2, 3, 5) is one end of a diameter of the sphere
Mathematics. If (, 3, ) is one end of a diameter of the sphere x + y + z 6x y z + 0 = 0, then the coordinates of the other end of the diameter are () (4, 3, 3) () (4, 9, 3) (3) (4, 3, 3) (4) (4, 3, ) Sol.
More informationDISCUSSION CLASS OF DAX IS ON 22ND MARCH, TIME : 9-12 BRING ALL YOUR DOUBTS [STRAIGHT OBJECTIVE TYPE]
DISCUSSION CLASS OF DAX IS ON ND MARCH, TIME : 9- BRING ALL YOUR DOUBTS [STRAIGHT OBJECTIVE TYPE] Q. Let y = cos x (cos x cos x). Then y is (A) 0 only when x 0 (B) 0 for all real x (C) 0 for all real x
More informationoo 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 informationADDITIONAL MATHEMATICS
005-CE A MATH HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 005 ADDITIONAL MATHEMATICS :00 pm 5:0 pm (½ hours) This paper must be answered in English 1. Answer ALL questions in Section A and any FOUR
More informationPolynomials and Rational Functions. Quadratic Equations and Inequalities. Remainder and Factor Theorems. Rational Root Theorem
Pre-Calculus Pre-AP Scope and Sequence - Year at a Glance Pre-Calculus Pre-AP - First Semester Pre-calculus with Limits; Larson/Hostetler Three Weeks 1 st 3 weeks 2 nd 3 weeks 3 rd 3 weeks 4 th 3 weeks
More informationIIT JEE Maths Paper 2
IIT JEE - 009 Maths Paper A. Question paper format: 1. The question paper consists of 4 sections.. Section I contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for
More informationGrade 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 informationTEST CODE: MMA (Objective type) 2015 SYLLABUS
TEST CODE: MMA (Objective type) 2015 SYLLABUS Analytical Reasoning Algebra Arithmetic, geometric and harmonic progression. Continued fractions. Elementary combinatorics: Permutations and combinations,
More informationDELHI 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 informationPoornima University, For any query, contact us at: , 18
AIEEE//Math S. No Questions Solutions Q. Lets cos (α + β) = and let sin (α + β) = 5, where α, β π, then tan α = 5 (a) 56 (b) 9 (c) 7 (d) 5 6 Sol: (a) cos (α + β) = 5 tan (α + β) = tan α = than (α + β +
More informationMath 370 Semester Review Name
Math 370 Semester Review Name 1) State the following theorems: (a) Remainder Theorem (b) Factor Theorem (c) Rational Root Theorem (d) Fundamental Theorem of Algebra (a) If a polynomial f(x) is divided
More informationINDIRA 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 informationTime: 3 Hrs. M.M. 90
Class: X Subject: Mathematics Topic: SA1 No. of Questions: 34 Time: 3 Hrs. M.M. 90 General Instructions: 1. All questions are compulsory. 2. The questions paper consists of 34 questions divided into four
More informationChapter 2 Differentiation. 2.1 Tangent Lines and Their Slopes. Calculus: A Complete Course, 8e Chapter 2: Differentiation
Chapter 2 Differentiation 2.1 Tangent Lines and Their Slopes 1) Find the slope of the tangent line to the curve y = 4x x 2 at the point (-1, 0). A) -1 2 C) 6 D) 2 1 E) -2 2) Find the equation of the tangent
More informationClass X Mathematics Sample Question Paper Time allowed: 3 Hours Max. Marks: 80. Section-A
Class X Mathematics Sample Question Paper 08-9 Time allowed: Hours Max. Marks: 80 General Instructions:. All the questions are compulsory.. The questions paper consists of 0 questions divided into sections
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 informationDESIGN OF THE QUESTION PAPER Mathematics Class X NCERT. Time : 3 Hours Maximum Marks : 80
DESIGN OF THE QUESTION PAPER Mathematics Class X Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage to Content/ Subject Units : S.No. Content
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 informationFree Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom
Free Response Questions 1969-010 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions
More information4. Factor the expression completely. Begin by factoring out the lowest power of each common factor: 20x 1/2 + 9x 1/2 + x 3/2
M180 Final Exam practice 1.Simplify each expression, and eliminate any negative exponents. st 7 4 1 s t. Simplify the expression. Assume that x, y, and z denote any positive real numbers. 3. Rationalize
More informationTARGET : 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 informationb = 2, c = 3, we get x = 0.3 for the positive root. Ans. (D) x 2-2x - 8 < 0, or (x - 4)(x + 2) < 0, Therefore -2 < x < 4 Ans. (C)
SAT II - Math Level 2 Test #02 Solution 1. The positive zero of y = x 2 + 2x is, to the nearest tenth, equal to (A) 0.8 (B) 0.7 + 1.1i (C) 0.7 (D) 0.3 (E) 2.2 ± Using Quadratic formula, x =, with a = 1,
More informationClass X Mathematics Sample Question Paper Time allowed: 3 Hours Max. Marks: 80. Section-A
Class X Mathematics Sample Question Paper 08-9 Time allowed: Hours Max. Marks: 80 General Instructions:. All the questions are compulsory.. The questions paper consists of 0 questions divided into sections
More informationMATHEMATICS. 61. If letters of the word KUBER are written in all possible orders and arranged as in a dictionary, then rank of the word KUBER will be:
MATHEMATICS 61. If letters of the word KUBER are written in all possible orders and arranged as in a dictionary, then rank of the word KUBER will be: (A) 67 (B) 68 (C) 65 (D) 69 : Alphabetical order of
More informationHow to use this Algebra II - Semester 2 Study Packet
Excellence is not an act, but a habit. Aristotle Dear Algebra II Student, First of all, Congrats! for making it this far in your math career. Passing Algebra II is a huge mile-stone Give yourself a pat
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 informationObjective 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 informationCambridge International Examinations CambridgeOrdinaryLevel
Cambridge International Examinations CambridgeOrdinaryLevel * 2 5 4 0 0 0 9 5 8 5 * ADDITIONAL MATHEMATICS 4037/12 Paper1 May/June 2015 2 hours CandidatesanswerontheQuestionPaper. NoAdditionalMaterialsarerequired.
More informationMATHEMATICS. 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 informationDESIGN OF THE QUESTION PAPER
DESIGN OF THE QUESTION PAPER MATHEMATICS - CLASS XI Time : 3 Hours Max. Marks : 00 The weightage of marks over different dimensions of the question paper shall be as follows:. Weigtage of Type of Questions
More informationConsortium of Medical Engineering and Dental Colleges of Karnataka (COMEDK-2007)
Consortium of Medical Engineering and Dental Colleges of Karnataka (COMEDK-007) MATHEMATICS. Log'f/ is equal to 7 Log 35 5. In the group (G 5 ), where G = {3, 6, 9, }; 5 is multiplication modulo 5, the
More informationby Abhijit Kumar Jha
SET I. If the locus of the point of intersection of perpendicular tangents to the ellipse x a circle with centre at (0, 0), then the radius of the circle would e a + a /a ( a ). There are exactl two points
More information1. The positive zero of y = x 2 + 2x 3/5 is, to the nearest tenth, equal to
SAT II - Math Level Test #0 Solution SAT II - Math Level Test No. 1. The positive zero of y = x + x 3/5 is, to the nearest tenth, equal to (A) 0.8 (B) 0.7 + 1.1i (C) 0.7 (D) 0.3 (E). 3 b b 4ac Using Quadratic
More informationThe Orchid School Weekly Syllabus Overview Std : XI Subject : Math. Expected Learning Objective Activities/ FAs Planned Remark
The Orchid School Weekly Syllabus Overview 2015-2016 Std : XI Subject : Math Month Lesson / Topic Expected Learning Objective Activities/ FAs Planned Remark March APRIL MAY Linear Inequalities (Periods
More informationThings You Should Know Coming Into Calc I
Things You Should Know Coming Into Calc I Algebraic Rules, Properties, Formulas, Ideas and Processes: 1) Rules and Properties of Exponents. Let x and y be positive real numbers, let a and b represent real
More information( ) 2 + ( 2 x ) 12 = 0, and explain why there is only one
IB Math SL Practice Problems - Algebra Alei - Desert Academy 0- SL Practice Problems Algebra Name: Date: Block: Paper No Calculator. Consider the arithmetic sequence, 5, 8,,. (a) Find u0. (b) Find the
More informationReading Mathematical Expressions & Arithmetic Operations Expression Reads Note
Math 001 - Term 171 Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note x A x belongs to A,x is in A Between an element and a set. A B A is a subset of B Between two sets. φ
More informationPADASALAI CENTUM COACHING TEAM 10 TH MATHS FULL PORTION ONE MARKS ONLY
PADASALAI CENTUM COACHING TEAM 10 TH MATHS FULL PORTION ONE MARKS ONLY CHOOSE THE CORRECT ANSWER 100 X 1 = 100 1. If ACB, then A is (a) B (b) A \ B (c) A (d) B \ A 2. If n(a) = 20, n(b) = 30 and n(aub)
More informationNATIONAL BOARD FOR HIGHER MATHEMATICS. M. A. and M.Sc. Scholarship Test. September 24, Time Allowed: 150 Minutes Maximum Marks: 30
NATIONAL BOARD FOR HIGHER MATHEMATICS M. A. and M.Sc. Scholarship Test September 24, 2011 Time Allowed: 150 Minutes Maximum Marks: 30 Please read, carefully, the instructions on the following page 1 INSTRUCTIONS
More informationCAREER POINT PRE FOUNDATION DIVISON CLASS-9. IMO Stage-II Exam MATHEMATICS Date :
CAREER POINT PRE FOUNDATION DIVISON IMO Stage-II Exam.-07 CLASS-9 MATHEMATICS Date : -0-07 Q. In the given figure, PQR is a right angled triangle, right angled at Q. If QRST is a square on side QR and
More informationR1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member
Chapter R Review of basic concepts * R1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member Ex: Write the set of counting numbers
More informationI 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 informationANSWERS 1.3 EXERCISE. 1. (i) {2} (ii) {0, 1} (iii) {1, p}
ANSWERS. EXERCISE. (i) {} (ii) {0, } (iii) {, p}. (i) {0,, } (ii). {,,,,... P,( p } (iii) {,,, } 4. (i) True (ii) False (iii) True (iv) True 7. (i) {, 4, 6, 8,..., 98} (ii) (,4, 9, 6, 5, 6, 49, 64, 8,}
More informationGiven that m A = 50 and m B = 100, what is m Z? A. 15 B. 25 C. 30 D. 50
UNIT : SIMILARITY, CONGRUENCE AND PROOFS ) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of. The dilation is centered at ( 4, ). ) Which transformation results in a figure that is similar
More informationNATIONAL BOARD FOR HIGHER MATHEMATICS. M. A. and M.Sc. Scholarship Test. September 22, Time Allowed: 150 Minutes Maximum Marks: 30
NATIONAL BOARD FOR HIGHER MATHEMATICS M. A. and M.Sc. Scholarship Test September 22, 2012 Time Allowed: 150 Minutes Maximum Marks: 30 Please read, carefully, the instructions on the following page 1 INSTRUCTIONS
More informationa Write down the coordinates of the point on the curve where t = 2. b Find the value of t at the point on the curve with coordinates ( 5 4, 8).
Worksheet A 1 A curve is given by the parametric equations x = t + 1, y = 4 t. a Write down the coordinates of the point on the curve where t =. b Find the value of t at the point on the curve with coordinates
More informationMCPS Algebra 2 and Precalculus Standards, Categories, and Indicators*
Content Standard 1.0 (HS) Patterns, Algebra and Functions Students will algebraically represent, model, analyze, and solve mathematical and real-world problems involving functional patterns and relationships.
More informationCOMPLEX NUMBERS AND QUADRATIC EQUATIONS
Chapter 5 COMPLEX NUMBERS AND QUADRATIC EQUATIONS 5. Overview We know that the square of a real number is always non-negative e.g. (4) 6 and ( 4) 6. Therefore, square root of 6 is ± 4. What about the square
More informationAP Calculus Free-Response Questions 1969-present AB
AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions
More informationVKR Classes TIME BOUND TESTS 1-7 Target JEE ADVANCED For Class XI VKR Classes, C , Indra Vihar, Kota. Mob. No
VKR Classes TIME BOUND TESTS -7 Target JEE ADVANCED For Class XI VKR Classes, C-9-0, Indra Vihar, Kota. Mob. No. 9890605 Single Choice Question : PRACTICE TEST-. The smallest integer greater than log +
More informationTEST CODE: MIII (Objective type) 2010 SYLLABUS
TEST CODE: MIII (Objective type) 200 SYLLABUS Algebra Permutations and combinations. Binomial theorem. Theory of equations. Inequalities. Complex numbers and De Moivre s theorem. Elementary set theory.
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 informationQ.1 If a, b, c are distinct positive real in H.P., then the value of the expression, (A) 1 (B) 2 (C) 3 (D) 4. (A) 2 (B) 5/2 (C) 3 (D) none of these
Q. If a, b, c are distinct positive real in H.P., then the value of the expression, b a b c + is equal to b a b c () (C) (D) 4 Q. In a triangle BC, (b + c) = a bc where is the circumradius of the triangle.
More informationPURE 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 informationADVANCED MATHS TEST - I PRELIMS
Model Papers Code : 1101 Advanced Math Test I & II ADVANCED MATHS TEST - I PRELIMS Max. Marks : 75 Duration : 75 Mins. General Instructions : 1. Please find the Answer Sheets (OMR) with in the envelop
More information