NDA Mathematics 10 April 2022
Paper was held on Sun, Apr 10, 2022 8:30 AM
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## Mathematics

If&nbsp;$Δ_1 = \begin{vmatrix} 1 &amp; p &amp; q \\ 1 &amp; q &amp; r \\ 1 &amp; r &amp; p\end{vmatrix} \ \text{and} \ Δ View Question If (a - b) (b - c) (c - a) = 2 and abc = 6, then what is the value of&nbsp;$\begin{vmatrix}a &amp; b &amp; c \\ a^2 &amp
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Under which of the following conditions does the determinant&nbsp;$\begin{vmatrix}a &amp; b &amp; c \\ b &amp; c &amp; a View Question Consider the following in respect of the matrices: A = [m n], B = [-n -m] &amp;&nbsp;$ C = \begin{bmatrix} m \\ -m\end{
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If&nbsp;$A = \begin{bmatrix} 2 \sin \theta &amp; \cos \theta &amp; 0 \\ -2\cos \theta &amp; \sin \theta &amp; 0 \\ -1 &a View Question For what value of k is the matrix&nbsp;$\begin{bmatrix} 2\cos 2\theta &amp; 2\cos 2\theta &amp; 6 \\ 1 -2 \sin^2\theta &
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Let A be a non-singular matrix and B = adj A. Which of the following statements is/are correct? 1. AB = BA 2. AB is a
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Consider the following statements in respect of square matrices A and B of same order : 1. If AB is a null matrix, then
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If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C
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Let A and B be non-singular matrices of the same order such that AB = A and BA = B. Which of the following statements is
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How many terms are there in the expansion of&nbsp;$\left(1 + \frac{2}{x}\right)^9\left(1-\frac{2}{x}\right)^9 ?$
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Consider the following statements in respect of the expansion of (x + y)10 1. Among all the coefficients of the terms,
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If C(3n, 2n) = C(3n, 2n - 7), then what is the value of C(n, n - 5)?
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What is the value of C(51, 21) - C(51, 22) + C(51, 23) - C(51, 24) + C(51, 25) - C(51, 26) + C(51, 27) - C(51, 28) + C(
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How many odd numbers between 300 and 400 are there in which none of the digits is repeated ?
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How many permutations are there of the letters of the&nbsp;word 'TIGER' in which the vowels should not occupy the even p
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Let α and β be the roots of the equation x2 + px + q = 0. If α3 and β3 are the roots of the equation x2&nbsp;+ mx + n =
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Let α and β be the roots of the equation x2&nbsp;- ax - bx + ab - c = 0. What is the quadratic equation whose roots are
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If the roots of the equation x2 - ax - bx - cx + bc + ca = 0 are equal, then which one of the following is correct?
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Let&nbsp;α and&nbsp;β (α &gt; β) be the roots of the equation x2 - 8x + q = 0. If&nbsp;α2 -&nbsp;β2 = 16, then what is t
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What is the maximum value of n such that 5n divides (30! + 35!), where n is a natural number?
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What is the value of 2(2 × 1) + 3(3 ×&nbsp;2 × 1) + 4(4 ×&nbsp;3 ×&nbsp;2 ×&nbsp;1) + 5(5 ×&nbsp;4 ×&nbsp;3&nbsp;×&nbsp;
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If A = {{1, 2, 3}}, then how many elements are there in the power set of A?
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If a, b, c are in GP where a &gt; 0, b &gt; 0, c &gt; 0, then which of the following&nbsp;are correct? 1. a2, b2, c2 ar
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If&nbsp;$\frac{a+b}{2}, b, \frac{b+c}{2}$&nbsp;are in HP, then which one of the following is correct?
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What is value of cot2 15° + tan2 15° ?
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In a triangle ABC, sin A - cos B - cos C = 0. What is angle B equal to?
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If&nbsp;$α + β = \frac{\pi}{4}$&nbsp;and 2tan α = 1, then what is tan 2β equal to?
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If tan (45° + θ) = 1 + sin 2θ, where&nbsp;$-\frac{\pi}{4}&lt; θ &lt;\frac{\pi}{4},$&nbsp;then what is the value of cos 2
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Let sin 2θ = cos 3θ, where&nbsp;θ is acute angle. What is the value of 1 + 4 sin&nbsp;θ? (given that $\sin 18^\circ =\fr View Question If$\tan θ = - \frac{5}{12},$&nbsp;then what can be the value of sin θ? View Question What is the value of&nbsp;$\cos^4\frac{7\pi}{8}+\cos^4\frac{5\pi}{8}?$View Question What is&nbsp;$\sin^2\left(\frac{\pi}{4}+\theta\right)-\sin^2\left(\frac{\pi}{4}-\theta\right)$&nbsp;equal to? View Question A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the p View Question The shadow of a tower becomes x metre longer, when the angle of elevation of sun changes from 60° to θ. If the height of View Question If&nbsp;$\tan^{-1} \left(\frac{1}{2}\right)+\tan^{-1} \left(\frac{x}{3}\right)=\frac{\pi}{4},$&nbsp;where 0 &lt; x &lt; View Question If 3 sin-1x + cos-1x =&nbsp;π, then what is x equal to? View Question If tan&nbsp;α + tan&nbsp;β = 1 - tan&nbsp;α.tan β, where tan&nbsp;α tan&nbsp;β&nbsp;≠ 1, then which of the following is View Question If (1 + tan θ) (1 + tan 9θ) = 2, then what is the value of tan(10θ)? View Question What is the value of sin 0° + sin 10° + sin 20° + sin 30° +&nbsp;⋯ + sin 360°? View Question Consider all the subsets of the set A = {1, 2, 3, 4}. How many of them are supersets of the set {4}? View Question Consider the following statements in respect of two non-empty sets A and B : 1. x&nbsp;∉ (A ∪ B)&nbsp;⇒ x&nbsp;∉ A or x View Question Consider the following statements in respect of two non-empty sets A and B : 1. A&nbsp;∪ B = A&nbsp;∩ B if&nbsp;A = B View Question Consider the following statements in respect of the relation R in the set IN of natural numbers defined by xRy if x2 - 5 View Question Consider the following statements in respect of any relation R on a set A : 1. If R is reflexive, then R-1&nbsp;is also View Question What is the principal argument of&nbsp;$\frac{1}{1 + i}$&nbsp;where$i = \sqrt{-1}?$View Question What is the modulus of&nbsp;$\left(\frac{\sqrt{-3}}{2}-\frac{1}{2}\right)^{200}?$View Question Consider the following statements: 1.&nbsp;$\frac{n!}{3!}$&nbsp;is divisible by 6, where n &gt; 3 2.&nbsp;$\frac{n!}{3
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In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players ?
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In the expansion of $\left(x + \frac{1}{x}\right)^{2n}$, what is the (n + 1)th term from the end (when arranged in desc
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If the sum of the first 9 terms of an AP is equal to sum of the first 11 terms, then what is the sum of the first 20 ter
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If the 5th term of an AP is $\frac{1}{10}$&nbsp;and its 10th term is $\frac{1}{5},$&nbsp;then what is the sum of first 5
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What is (1110011)2 ÷ (10111)2 equal to ?
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If x3&nbsp;+ y3 = (100010111)2 and x + y = (11111)2, then what is (x - y)2&nbsp;+ xy equal to ?
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Consider the inequations 5x - 4y + 12 &lt; 0, x + y &lt; 2, x &lt; 0 and y &gt; 0. Which one of the following points lie
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Consider the following statements in respect of the function y = [x], x&nbsp;∈ (-1, 1) where [.] is the greatest integer
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What is the degree of the differential equation?&nbsp;$1+\left(\frac{dy}{dx}\right)^2 =\left(\frac{d^2y}{dx^2}\right)^{\ View Question A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decay View Question What is the domain of the function&nbsp;$f(x) =\sqrt{1 - (x-1)^2} \ ?$View Question The area of the region bounded by the parabola y2 = 4kx, where k &gt; 0 and its latus rectum is 24 square units. What is View Question What is&nbsp;$\int\limits^{\frac{\pi}{4}}_0 \frac{dx}{(\sin x + \cos x)^2}$&nbsp;equal to? View Question What is&nbsp;$\int (\sin x)^{-1/2} (\cos x)^{-3/2}dx$&nbsp;equal to? View Question If&nbsp;$I_1 =\int\frac{e^x dx}{e^x + e^{-x}}$&nbsp;and&nbsp;$I_2 =\int\frac{dx}{e^{2x} + 1},$then what is I1 + I2 equal View Question What is&nbsp;$\int\limits^{-1}_{-2}\frac{x}{|x|}dx$&nbsp;equal to? View Question How many extreme values does sin4x + 2x, where$0 &lt; x &lt; \frac{\pi}{2} $have ? View Question What is the maximum value of the functions&nbsp;$f(x) = \frac{1}{\tan x+\cot x},$&nbsp;where&nbsp;$0 &lt; x &lt; \frac{\
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If&nbsp;$4f(x) - f \left(\frac{1}{x}\right)=\left(2x+\frac{1}{x}\right)\left(2x-\frac{1}{x}\right),$&nbsp;then what is f
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If f(x) = 4x + 3, then what is f o f o f(-1) equal to?
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If xyyx = 1, then what is&nbsp;$\frac{dy}{dx}$&nbsp;at (1, 1) equal to?
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If y = (xx)x, then what is the value of&nbsp;$\frac{dy}{dx}$&nbsp;at x = 1?
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Let y = [x + 1], -4 &lt; x &lt; -3 where [.] is the greatest integer function. What is the derivative of y with respect
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If&nbsp;$\frac{dy}{dx} = (\ln 5)y$&nbsp; with y(0) = ln 5, then what is y(1) equal to?
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Consider the following in respect of the function f(x) = 10x : 1. Its domain is (-∞, ∞) 2. It is a continuous function
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What is&nbsp;$\lim\limits_{x \to 0}x^3(\text{cosec} \ x)^2$&nbsp;equal to ?
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What is&nbsp;$\lim\limits_{x \to 1}\frac{x^3 - 1}{\sqrt x - 1}$&nbsp;equal to?
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In which one of the following intervals is the function&nbsp;$f(x) = \frac{x^3}{3}-\frac{7x^2}{2} + 6x + 5$&nbsp;decreas
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If the derivative of the function$f(x) =\frac{m}{x} +2nx + 1$&nbsp;vanishes at x = 2, then what is the value of m + 8n ?
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What is the area included in the first quadrant between the curves y = x and y = x3&nbsp;?
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If xy = 4225 where x, y are natural numbers, then what is the minimum value of x + y ?
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What does the equation $x \frac{dy}{dx}-2y= 0$ represent ?
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If the points with coordinates (-5, 0), (5p2, 10p) and (5q2, 10q) are collinear, then what is the value of pq where p ≠
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What is the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from the
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What is the equation of the circle which touches both the axes in the first quadrant and the line y - 2 = 0?
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What is the equation of the parabola with focus (-3, 0) and directrix x - 3 = 0 ?
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What is the distance between the foci of the ellipse x2 + 2y2 = 1 ?
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Let a, b, c be the lengths of sides BC, CA, AB respectively of a triangle ABC. If p is the perimeter and q is the area o
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A straight line passes through the point of intersection of x + 2y + 2 = 0 and 2x - 3y - 3 = 0. It cuts equal intercepts
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Under which one of the following conditions are the lines ax + by + c = 0 and bx + ay + c = 0 parallel (a ≠ 0, b ≠ 0)?
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What is the equation of the locus of the mid-point of the line segment obtained by cutting the line x + y = p, (where p
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If the point (x, y) is equidistant from the points (2a, 0) and (0, 3a) where a &gt; 0, then which one of the following i
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What is the value of k?
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If p is the perpendicular distance from the centre of the sphere to the plane, then which one of the following is correc
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What is the equation of the line through the origin and the centre of the sphere ?
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What are the direction ratios of the normal to the plane ?
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If p, q and r are the intercepts made by the plane on the coordinate axes respectively, then what is (p + q + r) equal t
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If $4\hat i + \hat j - 3\hat k$&nbsp;and $p\hat i + q\hat j - 2\hat k$ are collinear vectors, then what are the possible
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If $\vec a, \vec b, \vec c$, are the position vectors of the vertices A, B, C respectively of a triangle ABC and G is th
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Consider the following statements : 1. Dot product over vector addition is distributive 2. Cross product over vector a
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Let &nbsp;$\vec{a}, \vec{b}, \vec{c}$ be three non-zero vectors such that&nbsp;&nbsp;$\vec{a}\times \vec{b} = \vec{c}$.
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Let $\vec a$ and $\vec b$ be two unit vectors such that $|\vec a - \vec b|&lt;2.$&nbsp;If 2θ is the angle between $\vec View Question Two digits out of 1, 2, 3, 4, 5 are chosen at random and multiplied together. What is the probability that the last digi View Question The frequency curve (assuming unimodal) corresponding to the data obtained in an experiment is skewed to the left. What View Question The variance of five positive observations is 3.6. If four of the observations are 2, 2, 4, 5 then what is the remaining View Question What is the arithmetic mean of 50 terms of an AP with first term 4 and common difference 4 ? View Question What is the coefficient of mean deviation of 21, 34, 23, 39, 26, 37, 40, 20, 33, 27 (taken from mean)? View Question What is the mean of the values? View Question What is the algebraic sum of the deviations of the same set of values measured from 99? View Question If the algebraic sum of the deviations of the same set of values measured from y is 180, then what is the value of y ? View Question What is the mean of the marks ? View Question What is the median of the marks? View Question What is the sum of the deviations measured from the median? View Question What is$P (G \cap \overline T)$&nbsp;equal to? View Question What is&nbsp;$P(G | \overline T) $&nbsp;equal to? View Question What is&nbsp;$P(\overline T | \overline G)\$&nbsp;equal to?
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What is the probability that exactly 3 out of 6 workers suffer from a disease?
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What is the probability that no one out of 6 workers suffers from a disease?
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What is the probability that at least one out of 6 workers suffer from a disease ?
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What is the value of p ?
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What is the value of q ?
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If the frequency of each class is doubled, then what would be the mean?
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