Mathematics
1. If $p ^ x = q ^ y = r ^ z$ where x, y and z are in GP, then consider the following statements:
I. p, q and rare in 2. If A and B are non-empty subsets of a set, and $A ^ c$ and $ B ^ c$ represent their complements, then which of the follo 3. Let y=x! and z = (2x)! If (z / y) = 120 then what is the value of (3x)!? 4. Let n be a natural number. The number of consecutive zeros at the end of the expansion of n! is exactly 2. How many valu 5.
If and $ (10+\log _{10}x), (10+\log _{10}y)$ are $(10 + log_{10}z)$ in AP, then consider the following stat 6. How many terms of the series 1 + 3 + 5 + 7 +... amount to a sum equal to 12345678987654321? 7. How many terms are identical in the two APs 19, 21, 23,... up to 110 terms and 19, 22, 25, 28,... up to 75 terms? 8. If $\alpha =\frac{-1+\sqrt{-3}}{2}$ then what is the value of $(1+\alpha ^{19}-\alpha ^{35})^{100}-(1-3\alpha ^{25} 9. What is the remainder when $5 ^ {99}$ is divided by 13? 10. What is the value of the determinant of the inverse of the matrix $\begin{bmatrix} -4 & -5 \\ 2 & 2 \end{bm 11. In a class of 45 students, 34 like to play cricket and 26 like to play football. Further, each student likes to play at 12. The system of equations 15y - 10x + 50 = 0, 2x - 3y - 5 = 0 13. If $(\frac{1-i}{1+i})^{2m}(\frac{1+i}{1-i})^{2n}=1$where $i=\sqrt{-1}$ then what is the smallest positive val 14. In obtaining the solution of the system of equations x + y + z = 7 x + 2y + 3z = 16 and x + 3y + 4z = 22 by Cramer's rul 15. Consider the following in respect of non-singular matrices A and B:
I. $(AB) ^ {- 1} = A ^ {- 1} B ^ {- 1}$
II. $ (BA) 16.
The value of the determinant $\left|\begin{matrix}a&b&c\\ l&m&n\\ p&q&r\end{matrix}\right 17. Let 1, ω, $\omega ^ 2$ be three cube roots of unity. If x = a + b $y=a\omega +b\omega ^{2}, z=a\omega ^{2}+b\omega$ then 18. How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is n 19. If a, b, c are the sides of a triangle ABC and p is the perimeter of the triangle, then what is equal to? det $\left|\be 20. Which one of the following is the greatest coefficient in the expansion of $(1 + x) ^ {100}$ ? 21. What is ẞ equal to? 22. What is the relation between α and β 23. If p + q = 66 then which one of the following is correct? 24. If p + q = 15 then what is equal to? q - p 25. What is p/q equal to? 26. What is $\frac{p^{2}-q^{2}}{p^{2}+q^{2}}$ equal to? 27. What is $(\frac{\sqrt{3}p}{4}-\frac{q}{4})$ equal to? 28. What is $\frac{p^{2}+q^{2}}{p^{2}q^{2}}$ equal to? 29. How many values does (x + y) have? 30. How many values does (y-x) have? 31. If the roots of the equation are equal, then which one of the following is correct? 32. If the roots of the equation are equal, then a, b, c are in 33. What is the relation between m and n? 34. How many values of m are possible? 35. How many triangles can be formed by joining these points? 36. How many quadrilaterals can be formed by joining these points? 37. What is the other root of f(x) = 0 38. What is (a + b + c) equal to? 39. What is the value of the determinant of the matrix $A ^ 4$ 40. What is $[adj A ]^ {-1}$ equal to? 41. What is the sum of the binary numbers $(10110110) _2$ and $( 10001 1) _2$
42. Set X contains 3n elements and set Y contains 2n elements, and they have n elements in common. How many elements does (X 43. Let A = {- 3, - 2, - 1, 0, 1, 2, 3} and B = {0, 1, 4, 9} How many elements does the subset of AB corresponding to the re 44. Consider the following statements:
Statement-l: If X is an nn matrix, then det(mX) = $m ^ n$ det(X), where m is a scala 45. Consider the following statements about
the matrix $M=\left[\begin{matrix}71&23&48\\ 57&28&29\\ 65& 46. What is$\cot ^{-1}9+\>\mathrm{cosec}\>{}^{-1}\left(\frac{\sqrt{41}}{4}\right)$
equal to?
47. How many values of $\theta $, where$- \pi < \theta < \pi$ satisfy both the equations $\cot \theta =-\sqrt{3}$ and 48. If $x+\frac{1}{x}=2\cos \theta$ then what is $x^{3}+\frac{1}{x^{3}}$ equal to? 49. If $0\le x\le \frac{\pi }{2}$ then what is the number of values of x satisfying the equation $\tan x+\sec x=2\cos x 50. What is the value of $\tan \left[\frac{1}{2}\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)\right]?$ 51. Which of the following are the direction ratios of the line of intersection of the given planes? 52. What is the equation of the plane P? 53. What is the radius of S? 54. On which one of the following planes does the centre of S lie? 55. What is the fourth vertex D? 56. If angle BCD is $\theta $ then what is $ cos^2 \theta$ equal to? 57. For different values of m, the equation 4y=mx-m+ 2 represents 58. The equation of the locus of a point equidistant from the points (a, b) and (c, d) is (a - c) x + (b - d) y 59. Consider the following statements in respect of the equation $x ^ 2 + 3y = 0$
I. The equation represents the equation t 60. What is the sum of the intercepts of the line
$\frac{x}{a^{2}}+\frac{y}{b^{2}}=\frac{2}{a^{2}+b^{2}} $ on the coord 61. Which one of the following is the perpendicular form of the straight line $\sqrt{3}x+2y=7$ ? 62. If the vertices Band D of a square ABCD are (2, 3) and (4, 1) respectively, then what is the area of the square? 63. What is the value of sin $\theta $ if $\theta $ is the acute angle between the lines whose equations are px + 64. The circle $ x ^ 2 + y ^ 2 - 2kx - 2ky + k ^ 2 = 0$ touches the x-axis at P and y-axis at Q. What is PQ equal to? 65. What is the distance between the foci of the hyperbola $x ^ 2 - 4y ^ 2 = 1$ 66. Let $\vec{p}=\vec{a}-\vec{b},\vec{q}=\vec{a}+\vec{b}$. If $|\vec{a}|=|\vec{b}|=2$ and $\vec{a}\cdot \vec{b}=2$, then wha 67. How many of the following can be a vector perpendicular to both the vectors $2\hat{i} - \hat{j} + \hat{k}$ and $\ha 68. What is the area of the parallelogram whose sides are represented by the vectors $\hat{i}+2\hat{j}+3\hat{k}$ and $2\hat{ 69. The position vectors of the vertices A, B, Cand D of a quadrilateral ABCD are given by $3\hat{i}+4\hat{j}-2\hat{k}$ , $4 70. A force$\vec{F} = 2\hat{i} - \lambda\hat{j} + 5\hat{k}$ is applied at the point A(1, 2, 5) If its moment about the point 71. What is $\lim _{x\rightarrow 0^{-}}f(x)$ equal to? 72. What is $\lim _{x\rightarrow 0^{-}}f(x)$ equal to? 73. What is $\lim _{x\rightarrow -1}f(x)$ equal to? 74. What is the area bounded by the curve f(x) the x-axis and the lines x = - 2 and x = 1 75. Consider the following statements:
I. The function is increasing in the interval (-∞,∞),
II. The function is different 76. What is $\frac{f(x)}{f(x+1)}$ equal to? 77. What is $ (1-x)f(\sqrt{x})+xf(\sqrt{x}+1)$ equal to?
78. What is the slope of the tangent to the curve y = f(x) at x = 0.5 79. What is $\frac{d^{2}y}{dx^{2}}$ at x = 0 equal to? 80. If x = sin $\theta$ then what is $\frac{dy}{dx}$ equal to?
81. What is the domain of the function? 82. The function has 83. If the function is continuous, then what is the value of k? 84. What is f'(-1) equal to? 85. What is u + v equal to? 86. Consider the following:
I. $\frac{du}{dx}=-v $
II. $\frac{dv}{dx}=-u$
Which of the above is/are correct? 87. What is $\frac{dy}{dx}$ at x = 3.5 equal to? 88. Consider the following statements:
I. The function is differentiable at x = 3
II. The function is differentiable at x 89. What is$f\circ f\circ f\circ f\circ f(0)$ equal to? 90. What is the inverse of the function? 91. What is the degree of the differential equation
$(\frac{d^{2}y}{dx^{2}})^{\frac{3}{2}}=(\frac{dy}{dx})^{\frac{5}{2}}$ 92. What is $\int _{n}^{n+1}(x-[x])dx$, where [.] is the greatest integer function and n is natural number? 93. Consider the following statements:
I. $y=xe^{2x}$ is the solution of $\frac{dy}{dx}=y(2+\frac{1}{x})$
II. $y=x\ln |x|+ 94. If k is an arbitrary constant, then what is the general solution of the equation $(x+y)^{2}\frac{dy}{dx}=k^{2}$ 95. What is $\int \frac{dx}{10^{x}+10^{-x}}$ equal to? 96. A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct?
I. The rectang 97. If $I_{1}=\int _{e}^{e^{2}}\frac{dx}{ln~x}$ and $I_{2}=\int _{1}^{2}\frac{e^{x}}{x}dx$ then which 98. What is the area of the region bounded by |x| <= 2k and |y| <= k where k is a positive real number? 99. Consider the following statements regarding the function f(x) = 1/(x - 5)
Statement-I: f(x) is decreasing on the interv 100. Consider the following statements:
Statement-I: The function $f(x)=\frac{x^{3}+128}{x}$ has a minimum value 101. What is the harmonic mean of the numbers C(10,3) C(10,4) C(10,5) C(10,6) and C(10,7) ? 102. In a sample survey of a village, the probability that a farmer is in debt is 0.60. What is the probability that three ra 103. The probability that a family owns a laptop is 0.68; that it also owns a desktop is 0.56. If the probability that it own 104. An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is the probability that both the b 105. An urn contains 5 white, 6 red and 4 blue balls. Three balls are drawn at random. What is the probability that a white b 106. Under which of the following conditions may binomial distribution be used?
I. The number of trials is infinite and not 107. A person X speaks the truth 4 out of 5 times and person Y speaks the truth 5 out of 6 times. What is the probability tha 108. The probability that a student passes Physics test is 2/3 and the probability that he passes both Physics test and Engli 109. An event X can happen with probability pand event Y can happen with probability q. Further, X and Y are independent even 110. Three faces of a die are black, two faces are white and one face is red. The die is tossed three times. What is the prob 111. A fair coin is tossed 4 times. What is the probability that two heads do not occur consecutively? 112. In a throw of three dice, what is the probability of getting one prime number, one composite number and one number which 113. An integer is chosen at random from the first 50 integers. What is the probability that the integer is neither divisible 114. Out of 50 consecutive natural numbers, two integers are chosen at random. What is the probability that their sum is odd? 115. The standard deviation of 100 observations is 10. If 20 is added to each observation, then what will be the new standard 116. Let X be a random variable following binomial distribution with parameters n = 5 and p = k Further, P(X = 1) = 0.40 117. The frequency distribution of the marks obtained by students in a Science examination is given below:
Ma 118. If P(A) = 0.3 , P(B) = 0.4 and P( A |B)=0.5, then what is the value P( B |A) ?
119. If P(A) = 1/3 , P(B) = 1/2 and $ P(A\cap B)=1/4$ , then what is the value of $P(\overline{A}\cup B)$ ? 120. Consider the following statements:
I. Mean and variance have the same unit of measurement.
II. Mean deviation and stan
1
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Consider the following statements:
I. Mean and variance have the same unit of measurement.
II. Mean deviation and standard deviation have the same unit of measurement.
Which of the statements given above is/are correct?
1
I only
2
II only
3
Both I and II
4
Neither I nor II
Paper Analysis
Total Questions
Mathematics 120
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