NDA Mathematics 10 April 2022

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Sun, Apr 10, 2022 8:30 AM

## Mathematics

If $Δ_1 = \begin{vmatrix} 1 & p & q \\ 1 & q & r \\ 1 & r & 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 $\begin{vmatrix}a & b & c \\ a^2 &

View Question Under which of the following conditions does the determinant $\begin{vmatrix}a & b & c \\ b & c & a

View Question Consider the following in respect of the matrices:
A = [m n], B = [-n -m] & $ C = \begin{bmatrix} m \\ -m\end{

View Question If $A = \begin{bmatrix} 2 \sin \theta & \cos \theta & 0 \\ -2\cos \theta & \sin \theta & 0 \\ -1 &a

View Question For what value of k is the matrix $\begin{bmatrix} 2\cos 2\theta & 2\cos 2\theta & 6 \\ 1 -2 \sin^2\theta &

View Question 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

View Question Consider the following statements in respect of square matrices A and B of same order :
1. If AB is a null matrix, then

View Question 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

View Question 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

View Question How many terms are there in the expansion of $\left(1 + \frac{2}{x}\right)^9\left(1-\frac{2}{x}\right)^9 ? $

View Question Consider the following statements in respect of the expansion of (x + y)10
1. Among all the coefficients of the terms,

View Question If C(3n, 2n) = C(3n, 2n - 7), then what is the value of C(n, n - 5)?

View Question 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(

View Question How many odd numbers between 300 and 400 are there in which none of the digits is repeated ?

View Question How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even p

View Question 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 + mx + n =

View Question Let α and β be the roots of the equation x2 - ax - bx + ab - c = 0. What is the quadratic equation whose roots are

View Question If the roots of the equation x2 - ax - bx - cx + bc + ca = 0 are equal, then which one of the following is correct?

View Question Let α and β (α > β) be the roots of the equation x2 - 8x + q = 0. If α2 - β2 = 16, then what is t

View Question What is the maximum value of n such that 5n divides (30! + 35!), where n is a natural number?

View Question What is the value of 2(2 × 1) + 3(3 × 2 × 1) + 4(4 × 3 × 2 × 1) + 5(5 × 4 × 3 ×

View Question If A = {{1, 2, 3}}, then how many elements are there in the power set of A?

View Question If a, b, c are in GP where a > 0, b > 0, c > 0, then which of the following are correct?
1. a2, b2, c2 ar

View Question If $\frac{a+b}{2}, b, \frac{b+c}{2}$ are in HP, then which one of the following is correct?

View Question What is value of cot2 15° + tan2 15° ?

View Question In a triangle ABC, sin A - cos B - cos C = 0. What is angle B equal to?

View Question If $α + β = \frac{\pi}{4}$ and 2tan α = 1, then what is tan 2β equal to?

View Question If tan (45° + θ) = 1 + sin 2θ, where $-\frac{\pi}{4}< θ <\frac{\pi}{4},$ then what is the value of cos 2

View Question Let sin 2θ = cos 3θ, where θ is acute angle. What is the value of 1 + 4 sin θ? (given that $\sin 18^\circ =\fr

View Question If $\tan θ = - \frac{5}{12},$ then what can be the value of sin θ?

View Question What is the value of $\cos^4\frac{7\pi}{8}+\cos^4\frac{5\pi}{8}?$

View Question What is $\sin^2\left(\frac{\pi}{4}+\theta\right)-\sin^2\left(\frac{\pi}{4}-\theta\right)$ 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 $\tan^{-1} \left(\frac{1}{2}\right)+\tan^{-1} \left(\frac{x}{3}\right)=\frac{\pi}{4},$ where 0 < x <

View Question If 3 sin-1x + cos-1x = π, then what is x equal to?

View Question If tan α + tan β = 1 - tan α.tan β, where tan α tan β ≠ 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° + ⋯ + 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 ∉ (A ∪ B) ⇒ x ∉ A or x

View Question Consider the following statements in respect of two non-empty sets A and B :
1. A ∪ B = A ∩ B if 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 is also

View Question What is the principal argument of $\frac{1}{1 + i}$ where $i = \sqrt{-1}?$

View Question What is the modulus of $\left(\frac{\sqrt{-3}}{2}-\frac{1}{2}\right)^{200}?$

View Question Consider the following statements:
1. $\frac{n!}{3!}$ is divisible by 6, where n > 3
2. $\frac{n!}{3

View Question In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players ?

View Question 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

View Question 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

View Question If the 5th term of an AP is $\frac{1}{10}$ and its 10th term is $\frac{1}{5},$ then what is the sum of first 5

View Question What is (1110011)2 ÷ (10111)2 equal to ?

View Question If x3 + y3 = (100010111)2 and x + y = (11111)2, then what is (x - y)2 + xy equal to ?

View Question Consider the inequations 5x - 4y + 12 < 0, x + y < 2, x < 0 and y > 0. Which one of the following points lie

View Question Consider the following statements in respect of the function y = [x], x ∈ (-1, 1) where [.] is the greatest integer

View Question What is the degree of the differential equation? $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 $f(x) =\sqrt{1 - (x-1)^2} \ ?$

View Question The area of the region bounded by the parabola y2 = 4kx, where k > 0 and its latus rectum is 24 square units. What is

View Question What is $\int\limits^{\frac{\pi}{4}}_0 \frac{dx}{(\sin x + \cos x)^2}$ equal to?

View Question What is $\int (\sin x)^{-1/2} (\cos x)^{-3/2}dx$ equal to?

View Question If $I_1 =\int\frac{e^x dx}{e^x + e^{-x}}$ and $I_2 =\int\frac{dx}{e^{2x} + 1},$then what is I1 + I2 equal

View Question What is $\int\limits^{-1}_{-2}\frac{x}{|x|}dx$ equal to?

View Question How many extreme values does sin4x + 2x, where $0 < x < \frac{\pi}{2} $ have ?

View Question What is the maximum value of the functions $f(x) = \frac{1}{\tan x+\cot x},$ where $0 < x < \frac{\

View Question If $4f(x) - f \left(\frac{1}{x}\right)=\left(2x+\frac{1}{x}\right)\left(2x-\frac{1}{x}\right),$ then what is f

View Question If f(x) = 4x + 3, then what is f o f o f(-1) equal to?

View Question If xyyx = 1, then what is $\frac{dy}{dx}$ at (1, 1) equal to?

View Question If y = (xx)x, then what is the value of $\frac{dy}{dx}$ at x = 1?

View Question Let y = [x + 1], -4 < x < -3 where [.] is the greatest integer function. What is the derivative of y with respect

View Question If $\frac{dy}{dx} = (\ln 5)y $ with y(0) = ln 5, then what is y(1) equal to?

View Question Consider the following in respect of the function f(x) = 10x :
1. Its domain is (-∞, ∞)
2. It is a continuous function

View Question What is $\lim\limits_{x \to 0}x^3(\text{cosec} \ x)^2$ equal to ?

View Question What is $\lim\limits_{x \to 1}\frac{x^3 - 1}{\sqrt x - 1}$ equal to?

View Question In which one of the following intervals is the function $f(x) = \frac{x^3}{3}-\frac{7x^2}{2} + 6x + 5$ decreas

View Question If the derivative of the function$f(x) =\frac{m}{x} +2nx + 1$ vanishes at x = 2, then what is the value of m + 8n ?

View Question What is the area included in the first quadrant between the curves y = x and y = x3 ?

View Question If xy = 4225 where x, y are natural numbers, then what is the minimum value of x + y ?

View Question What does the equation $x \frac{dy}{dx}-2y= 0$ represent ?

View Question If the points with coordinates (-5, 0), (5p2, 10p) and (5q2, 10q) are collinear, then what is the value of pq where p ≠

View Question What is the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from the

View Question What is the equation of the circle which touches both the axes in the first quadrant and the line y - 2 = 0?

View Question What is the equation of the parabola with focus (-3, 0) and directrix x - 3 = 0 ?

View Question What is the distance between the foci of the ellipse x2 + 2y2 = 1 ?

View Question 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

View Question A straight line passes through the point of intersection of x + 2y + 2 = 0 and 2x - 3y - 3 = 0. It cuts equal intercepts

View Question Under which one of the following conditions are the lines ax + by + c = 0 and bx + ay + c = 0 parallel (a ≠ 0, b ≠ 0)?

View Question 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

View Question If the point (x, y) is equidistant from the points (2a, 0) and (0, 3a) where a > 0, then which one of the following i

View Question What is the value of k?

View Question If p is the perpendicular distance from the centre of the sphere to the plane, then which one of the following is correc

View Question What is the equation of the line through the origin and the centre of the sphere ?

View Question What are the direction ratios of the normal to the plane ?

View Question 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

View Question If $4\hat i + \hat j - 3\hat k$ and $p\hat i + q\hat j - 2\hat k$ are collinear vectors, then what are the possible

View Question 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

View Question Consider the following statements :
1. Dot product over vector addition is distributive
2. Cross product over vector a

View Question Let $\vec{a}, \vec{b}, \vec{c}$ be three non-zero vectors such that $\vec{a}\times \vec{b} = \vec{c} $.

View Question Let $\vec a$ and $\vec b$ be two unit vectors such that $|\vec a - \vec b|<2.$ 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 $P (G \cap \overline T)$ equal to?

View Question What is $P(G | \overline T) $ equal to?

View Question What is $P(\overline T | \overline G)$ equal to?

View Question What is the probability that exactly 3 out of 6 workers suffer from a disease?

View Question What is the probability that no one out of 6 workers suffers from a disease?

View Question What is the probability that at least one out of 6 workers suffer from a disease ?

View Question What is the value of p ?

View Question What is the value of q ?

View Question If the frequency of each class is doubled, then what would be the mean?

View Question