NDA Mathematics 4 September 2022

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Sun, Sep 4, 2022 8:30 AM

## Mathematics

How many four-digit natural numbers are there such that all of the digits are odd ?

View Question What is $\displaystyle\sum_{r=0}^n$2r C(n, r) equal to ?

View Question If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with o

View Question Consider the following statements :
1. If f is the subset of Z × Z defined by f = {(xy, x − y); x, y ∈ Z}, then f is a

View Question Consider the determinant
Δ = $\left|\begin{array}{lll}\text{a}_{11} & \text{a}_{12} & \text{a}_{13} \\ \te

View Question If A = $\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \cos \theta & \sin \theta \\ 0 & \sin \theta &

View Question If X is a matrix of order 3 × 3, Y is a matrix of order 2 × 3 and Z is a matrix of order 3 × 2, then which of the follow

View Question For how many quadratic equations, the sum of roots is equal to the product of roots?

View Question Consider the following statements :
1. The set of all irrational numbers between $\sqrt{2}$ and $\sqrt{5}$ is

View Question Consider the following statements :
1. 2 + 4 + 6 + ........ + 2n = n2 + n
2. The expression n2 + n + 41 alwa

View Question Let p, q(p > q) be the roots of the quadratic equation x2 + bx + c = 0 where c > 0. If p2 + q2 − 11

View Question What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm ?

View Question Let A = {7, 8, 9, 10, 11, 12, 13; 14, 15, 16} and let f ∶ A → N be defined by f(x) = the highest prime factor of x.
How

View Question Let R be a relation from N to N defined by R = {(x, y): x, y ∈ N and x2 = y3}. Which of the following are not corre

View Question Consider the following :
1. A ∩ B = A ∩ C ⇒ B = C
2. A ∪ B = A ∪ C ⇒ B = C
Which of the above is/are correct ?

View Question What is the modulus of z?

View Question What is angle θ such that z is purely real ?
where n is an integer

View Question What is angle θ such that z is purely imaginary ?
where n is an integer

View Question What is the ratio of the first term of A to that of B ?

View Question What is the ratio of their 10th terms ?

View Question If d is the common difference of A, and D is the common difference of B, then which one of the following is always corre

View Question What is the value of q if the coefficients of x3 and x6 are equal ?

View Question What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x)?

View Question Under what condition the coefficients of x2 and x4 are equal ?

View Question How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed ?

View Question How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate position

View Question How many 8-letter words with or without meaning, can be formed so that all consonants are together?

View Question What is the value of a11C11 + a12C12 + a13C13 ?

View Question What is the value of $a_{21}C_{11}+a_{22}C_{12}+a_{23}C_{13}$?

View Question What is the value of $\left|\begin{array}{lll}\text{a}_{21} & \text{a}_{31} & \text{a}_{11} \\ \text{a}_{23

View Question If $\displaystyle\sum_{x=2}^n$f(x) = 2044, then what is the value of n ?

View Question What is $\displaystyle\sum_{x=1}^5$f(2x − 1) equal to ?

View Question What is $\displaystyle\sum_{x=1}^6$2x f(x) equal to ?

View Question How many received medals in exactly two of the three sports ?

View Question How many received medals in at least two of three sports ?

View Question How many received medals in exactly one of three sports ?

View Question What is P equal to ?

View Question What is Q equal to ?

View Question What is the minimum value of determinant of A ?

View Question What is the height of the lamp post ?

View Question What is $\frac{\text{AB}}{\sin \text{C}}$ equal to ?

View Question What is cos A + cos B + cos C equal to ?

View Question At what height is the top of the tower above the ground level ?

View Question If θ is the inclination of the tower to the horizontal, then what is cot θ equal to ?

View Question What is the length of the tower ?

View Question What is the value of cosec$\left(−\frac{73 \pi}{3}\right)$ ?

View Question What is the value of $\cos \left(\frac{5 \pi}{17}\right)+\cos \left(\frac{7 \pi}{17}\right)+2 \cos \left(\frac{11 \

View Question What is the value of tan$\left(\frac{3\pi}{8}\right)$ ?

View Question What is tan−1 cot(cosec−1 2) equal to ?

View Question In a triangle ABC, a = 4, b = 3, c = 2. What is cos 3C equal to ?

View Question What is cos 36° − cos 72° equal to ?

View Question If sec x = $\frac{25}{24}$ and x lies in the fourth quadrant, then what is the value of tan x + sin x ?

View Question What is the value of tan2 165° + cot2 165° ?

View Question What is the value of $\sin\left(2\text{n}\pi+\frac{5\pi}{6}\right)\sin\left(2\text{n}\pi−\frac{5\pi}{6}\right)$&nbs

View Question If 1 + 2(sin x + cos x)(sin x − cos x) = 0 where 0 < x < 360°, then how many values does x take ?

View Question Consider the following statements in respect of the line passing through origin and inclining at an angle of 75° with th

View Question If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?

View Question The base AB of an equilateral triangle ABC with side 8 cm lies along the y-axis such that the mid-point of AB is at the

View Question The centre of the circle passing through the origin and making positive intercepts 4 and 6 on the coordinate axes, lies

View Question The centre of an ellipse is at (0, 0), major axis is on the y-axis. If the ellipse passes through (3, 2) and (1, 6), the

View Question An equilateral triangle is inscribed in a parabola x2 = $\sqrt{3}$y where one vertex of the triangle is at the

View Question Consider the points A(2, 4, 6), B(−2, −4, −2), C(4, 6, 4), and D(8, 14, 12). Which of the following statements is/are co

View Question Consider the equation of a sphere x2 + y2 + z2 − 4x − 6y − 8z − 16 = 0.
Which of the following statement

View Question A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?

View Question Consider the following statements :
1. The direction ratios of y-axis can be <0, 4, 0>
2. The direction ratios o

View Question PQRS is a parallelogram. If $\overrightarrow{\text{PR}}=\vec{\text{a}}$ and $\overrightarrow{\text{QS}}=\

View Question Let $\vec{\text{a}}$ and $\vec{\text{b}}$ are two unit vectors such that $\vec{\text{a}}+2 \vec

View Question Let $\vec{\text{a}}$, $\vec{\text{b}}$ and $\vec{\text{c}}$ be unit vectors lying on the s

View Question What are the values of x for which the angle between the vectors 2x2$\hat{\text{i}}$ + 3x$\hat{\text{j}}$ +&nb

View Question The position vectors of vertices A, B and C of triangle ABC are respectively $\hat{\text{j}}+\hat{\text{k}}, 3\hat{

View Question Let z = [y] and y = [x] − x, where [.] is the greatest integer function. If x is not an integer but positive, then what

View Question If f(x) = 4x + 1 and g(x) = kx + 2 such that fog(x) = gof(x), then what is the value of k ?

View Question What is the minimum value of the function f(x) = log10(x2 + 2x + 11) ?

View Question What is ∫(xx)2 (1 + ln x)dx equal to ?

View Question What is ∫ex{1 + ln x + x ln x}dx equal to ?

View Question What is $\int\frac{(\cos x)^{1.5}−(\sin x)^{1.5}}{\sqrt{\sin x⋅\cos x}}$dx equal to ?

View Question If y = $\frac{x \sqrt{x^2−16}}{2} − 8 \ln\left|x + \sqrt{x^2−16}\right|$, then what is $\frac{\text{dy}}{\text

View Question If y = (xx)x, then which one of the following is correct ?

View Question What is the maximum value of 3(sin x − cos x) + 4(cos3 x − sin3 x) ?

View Question What is the area of the region (in the first quadrant) bounded by y = $\sqrt{1−\text{x}^2}$, y = x and y = 0 ?

View Question What is the area of the region bounded by x − |y| = 0 and x − 2 = 0 ?

View Question If f(α) = $\sqrt{\sec^2\alpha−1}$, then what is $\frac{f(\alpha)+f(\beta)}{1−f(\alpha) f(\beta)}$ equal t

View Question If f(x) = ln (x + $\sqrt{1+\text{x}^2}$), then which one of the following is correct ?

View Question What is $\displaystyle\lim_{x \rightarrow 0} \frac{x}{\sqrt{1−\cos 4x}}$ equal to ?

View Question What is $\displaystyle\lim_{x\rightarrow \frac{\pi}{2}} \frac{4x−2\pi}{\cos x}$ equal to ?

View Question If f(x) = $\frac{x^2+x+|x|}{x}$, then what is $\displaystyle\lim_{x \rightarrow 0}$ f(x) equal to ?

View Question What is $\displaystyle\lim_{h \rightarrow 0} \frac{\sin^2(x+h)−\sin^2x}{h}$ equal to ?

View Question Let f(x) be a function such that f'(x) = g(x) and f''(x) = −f(x). Let h(x) = {f(x)}2 + {g(x)}2. Then consider the follow

View Question If y = ln2$\left(\frac{x^2−x+1}{x^2+x+1}\right)$, then what is $\frac{\text{dy}}{\text{dx}}$ at x = 0 equal to

View Question If $\frac{d}{d x}\left(\frac{1+x^4+x^8}{1−x^2+x^4}\right)$ = ax + bx3, then which one of the following is corr

View Question Under which one of the following conditions does the function f(x) = (p sec x)2 + (q cosec x)2 attain minimum

View Question Where does the function f(x) = $\displaystyle\sum_{j=1}^7$(x − j)2 attain its minimum value ?

View Question Consider the following statements in respect of the function f(x) = $\left\{\begin{array}{rc}|x|+1, & 0<|x|

View Question What is $\displaystyle\int_0^1 \ln \left(\frac{1}{x}−1\right)$dx equal to ?

View Question If $\displaystyle\int_0^{\pi/2}$(sin4 x + cos4 x)dx = k, then what is the value of $\displaystyle\in

View Question What is $\displaystyle\int_{−\pi/2}^{\pi/2}$(ecos x sin x + esin x cos x)dx equal to ?

View Question What is the area of the region enclosed in the first quadrant by x2 + y2 = π2, y = sin x and x = 0 ?

View Question Consider the following statements:
1. The degree of the differential equation $\frac{\text{dy}}{\text{dx}} + \cos

View Question What is the differential equation of the family of parabolas having a vertex at origin and axis along positive y-axis?

View Question What is the solution of the differential equation (dy − dx) + cos x(dy + dx) = 0 ?

View Question Let x be the mean of squares of first n natural numbers and y be the square of mean of first n natural numbers. If

View Question What is the probability of getting a composite number in the list of natural numbers from 1 to 50?

View Question If n > 7, then what is the probability that C(n, 7) is a multiple of 7?

View Question Two numbers x and y are chosen at random from a set of the first 10 natural numbers. What is the probability that (x + y

View Question A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies x

View Question Three fair dice are tossed once. What is the probability that they show different numbers that are in AP?

View Question If P(A) = 0.5, P(B) = 0.7 and P(A ∩ B) = 0.3, then what is the value of P(A' ∩ B') + P(A' ∩ B) + P(A ∩ B') ?

View Question Five coins are tossed once. What is the probability of getting at most four tails ?

View Question Three fair dice are thrown. What is the probability of getting a total greater than or equal to 15 ?

View Question The probability that a person hits a target is 0.5. What is the probability of at least one hit in 4 shots ?

View Question A box contains 2 white balls, 3 black balls, and 4 red balls. What is the number of ways of drawing 3 balls from the box

View Question During war, one ship out of 5 was sunk on an average in making a certain voyage. What is the probability that exactly 3

View Question A card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace. The odds against his winnin

View Question The coefficient of correlation between ages of husband and wife at the time of marriage for a given set of 100 couples w

View Question The completion of a construction job may be delayed due to strike. The probability of strike is 0.6. The probability tha

View Question Which one of the following subjects shows highest variability of marks ?

View Question What is the coefficient of variation of marks in Mathematics ?

View Question What is the median of the distribution ?

View Question What is mean deviation about the median ?

View Question What is the mean deviation about the mean ?

View Question