Mathematics
1. If ω is a non-real cube root of 1, then what is the value of $\left|\frac{1-\omega}{\omega+\omega^2}\rig 2. What is the number of 6-digit numbers that can be formed only by using 0, 1, 2, 3, 4 and 5 (each once); and divisi 3. What is the binary number equivalent to decimal number 1011 ? 4. Let A be a matrix of order 3 × 3 and |A| = 4. If |2adj(3A)| = 2α 3β, then what is the value of (α + β)? 5. If α and β are the distinct roots of equation x2 - x + 1 = 0, then what is the value of $\left| 6. Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (AB - BA) ?
1. It 7. Consider the following statements in respect of square matrices A, B, C each of same order n :
1. AB = AC ⇒ B = C 8. The system of linear equations
x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has
9. Let AX = B be a system of 3 linear equations with 3-unknowns. Let X1 and X2 be its two distinct solutions. If 10. What is the sum of the roots of the equation $\left|\begin{array}{ccc} 0 & x-a & x-b \\ 0 & 0 & x-c 11. If 2 - i√3 where i = √-1 is a root of the equation x2 + ax + b = 0, then what is the value of (a + b)? 12. If $z=\frac{1+i √{3}}{1-i √{3}}$ where i = √-1 then what is the argument of z ? 13. If a, b, c are in AP, then what is $\left|\begin{array}{lll} x+1 & x+2 & x+3 \\ x+2 & x+3 & x+4 \\ 14. If logxa, ax and logbx are in GP, then what is x equal to ? 15. If $2^{\frac{1}{c}}, 2^{\frac{b}{a c}}, 2^{\frac{1}{a}}$ are in GP, then which one of the following is correct ? 16. The first and the second terms of an AP are $\frac{5}{2}$ and $\frac{23}{12}$ respectively. If nth term is the larg 17. For how many integral values of k, the equation x2 - 4x + k = 0, where k is an integer has real roots and both of them l 18. In an AP, the first term is x and the sum of the first n terms is zero. What is the sum of next m terms ? 19. Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above 20. If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then what is |z| equal to ? 21. How many real numbers satisfy the equation |x - 4| + |x - 7| = 15 ? 22. A mapping f : A → B defined as $f(x)=\frac{2 x+3}{3 x+5}, x \in A$ If f is to be onto, then what are A an 23. α and β are distinct real roots of the quadratic equation x2 + ax + b = 0. Which of the following statements is/are 24. If the sixth term in the binomial expansion of $\left(x^{-\frac{8}{3}}+x^2 \log _{10} x\right)^8$ is 5600, the 25. How many terms are there in the expansion of (3x - y)4(x + 3y)4 ? 26. p, q, r and s are in AP such that p + s = 8 and qr = 15. What is the difference between largest and smallest numbers ?&n 27. Consider the following statements for a fixed natural number n:
1. C(n, r) is greatest if n = 2r
2. C(n, r) is gr 28. m parallel lines cut n parallel lines giving rise to 60 parallelograms. What is the value of (m + n) ? 29. Let x be the number of permutations of the word ‘PERMUTATIONS’ and y be the number of permutations of the word ‘COMBINAT 30. 5-digit numbers are formed using the digits 0, 1, 2, 4, 5 without repetition. What is the percentage of numbers which ar 31. What is cos 2β equal to ? 32. What is the value of sec2γ? 33. If x is the distance of P from the bottom of the pillar, then consider the following statements :
1. x can take two val 34. What is a possible value of tan θ ? 35. What is the perimeter of the triangle ? 36. Consider the following statements :
1. ABC is right angled triangle
2. The angles of the triangle are in AP
Which of 37. What is the minimum value of x ? 38. At what value of A does x attain the minimum value ? 39. What is the nature of the triangle ? 40. If c = 8, what is the area of the triangle ? 41. At what value of x does the function attain minimum value ? 42. What is the minimum value of the function ? 43. If the sum S is divided by 8, what is the remainder ? 44. If the sum S is divided by 60, what is the remainder ? 45. What is the value of n ? 46. What is the length of the smallest side ? 47. The given equation can be reduced to 48. If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ?  49. What is the HM of the roots of the equation ? 50. What is the GM of the roots of the equation ? 51. If Δ(a, b, c, α) = 0 for every α > 0, then which one of the following is correct ? 52. If Δ(7, 4, 2, α) = 0, then α is a root of which one of the following equations ? 53. What is the least value of m(θ) ? 54. Under what condition does m attain the least value ? 55. What is the equation of diagonal through origin ? 56. What is the equation of other diagonal ? 57. What is PE + PF equal to ? 58. Consider the following points :
1. $\left(\frac{\sqrt{3}}{2}, 0\right)$
2. $\left(\frac{\sqrt{3}}{2}, \frac{ 59. What is the area of minor segment ? 60. What is the area of major segment ? 61. What is u + v + w equal to ? 62. P(x, y, z) is any point on the sphere, then what is PA2 + PB2 equal to ? 63. What is the value of k? 64. What are the direction ratios of a line which is perpendicular to both the lines ? 65. What is $\vec{b}$ equal to ? 66. What is the angle between $(\vec{a}+\vec{b})$ and $\vec{c}$ ? 67. What is cosα equal to ? 68. What is cos2β + cos2γ equal to ? 69. Consider the following points :
1. (-1, -3, 1)
2. (-1, 3, 2)
3. (-2, 5, 3)
Which of the above points 70. What is the magnitude of $\overrightarrow{A B}$ ? 71. ‘What is the value of Q ? 72. What is the value of R ? 73. What is f'(0) equal to ? 74. What is the order of the differential equation ? 75. What is the degree of the differential equation ? 76. What is f(0) equal to ? 77. What is $\lim _{x \rightarrow 0} \frac{f(x)}{x}$ equal to ? 78. What is $\lim _{x \rightarrow 0} \frac{f(x)}{x^2}$ equal to ? 79. What is $f\left(\frac{\pi}{2}\right)$ equal to ? 80. What is $f\left(\frac{\pi}{4}\right)$ equal to ? 81. What is the value of $\frac{I_1+I_2}{I_1-I_2} $ ? 82. What is the value of $8 I_1^2$ 83. What is the value of I2 ? 84. What is l equal to when a < 0 < b ? 85. What is l equal to when a < b < 0 ? 86. What is the derivative of f(x) at x = 0.5 ? 87. What is the derivative of f(x) at x = 2 ? 88. What is the derivative of fof(x), where 1 < x < 2 ? 89. What is the value of p ? 90. What is the value of q ? 91. Consider the following statements :
1. f(x) = In x is increasing in (0, ∞)
2. $g(x)=e^x+e^{\frac{1}{x}} $ is decreasin 92. What is the derivative of sin2 x with respect to cos2x ? 93. For what value of m with m < 0, is the area bounded by the lines y = x, y = mx and x = 2 equal to 3 ? 94. What is the derivative of cosec(x°) ? 95. A solution of the differential equation
$\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0 $ is
96. If f(x) = x2 + 2 and g(x) = 2x - 3, then what is (fog)(1) equal to ? 97. What is the range of the function f(x) = x + |x| if the domain is the set of real numbers ? 98. If f(x) = x(4x2 - 3), then what is f(sinθ) equal to ? 99. What is $\lim\limits_{x \rightarrow 5} \frac{5-x}{|x-5|}$ equal to ? 100. What is $\lim\limits_{x \rightarrow 1} \frac{x^9-1}{x^3-1}$ equal to ? 101. The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 2 102. Let A and B be two independent events such that
P(A̅) = 0.7, P(B̅) = k, P(A ∪ B) = 0.8, what is the value of k ?
103. A biased coin with the probability of getting head equal to $\frac{1}{4}$ is tossed five times. What is the probabi 104. A coin is biased so that heads comes up thrice as likely as tails. In four independent tosses of the coin, what is proba 105. Let X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 an 106. If two lines of regression are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y = -3 ? 107. The central angles p, q, r and s (in degrees) of four sectors in a Pie Chart satisfy the relation 9p = 3q = 2r = 6s. Wha 108. The observations 4, 1, 4, 3, 6, 2, 1, 3, 4, 5, 1, 6 are outputs of 12 dices thrown simultaneously. If m and M are means 109. A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ? 110. A die is thrown 10 times and obtained the following outputs :
1, 2, 1, 1, 2, 1, 4, 6, 5, 4
What will be the 111. Consider the following frequency distribution :
x
1
2
3
5
f
4
6
9
7
W 112. For data -1, 1, 4, 3, 8, 12, 17, 19, 9, 11; if M is the median of first 5 observations and N is the median of last five 113. Let P, Q, R represent mean, median and mode. If for some distribution $5 P=4 Q=\frac{R}{2}$ then what is 114. If G is the geometric mean of numbers 1, 2, 22, 23,.....2n-1, then what is the value of 1 + 2log2G ? 115. If H is the harmonic mean of numbers 1, 2, 22, 23, ......2n-1 what is n/H equal to ? 116. Let P be the median, Q be the mean and R be the mode of observations x1, x2, x3, .....xn. Let $S=\su 117. One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the 118. Three dice are thrown. What is the probability that each face shows only multiples of 3 ? 119. What is the probability that the month of December has 5 Sundays ? 120. A natural number n is chosen from the first 50 natural numbers. What is the probability that $n+\frac{50}{n}<50
1
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
2
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then what is |z| equal to ?
A
$\frac{1}{2}$
B
$\frac{2}{3}$
C
1
D
2
3
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
How many real numbers satisfy the equation |x - 4| + |x - 7| = 15 ?
A
Only one
B
Only two
C
Only three
D
Infinitely many
4
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
A mapping f : A → B defined as $f(x)=\frac{2 x+3}{3 x+5}, x \in A$ If f is to be onto, then what are A and B equal to ?
A
$A=R \backslash\left\{-\frac{5}{3}\right\} \text { and } B=R \backslash\left\{-\frac{2}{3}\right\}$
B
$A=R \text { and } B=R \backslash\left\{-\frac{5}{3}\right\}$
C
$A=R \backslash\left\{-\frac{3}{2}\right\} \text { and } B=R \backslash\{0\}$
D
$A=R \backslash\left\{-\frac{5}{3}\right\} \text { and } B=R \backslash\left\{\frac{2}{3}\right\}$
Paper analysis
Total Questions
Mathematics
120
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