NDA Mathematics 4 September 2022
Paper was held on Sun, Sep 4, 2022 8:30 AM
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Mathematics

How many four-digit natural numbers are there such that all of the digits are odd ?
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What is&nbsp;$\displaystyle\sum_{r=0}^n$2r&nbsp;C(n, r) equal to ?
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If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with o
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Consider the following statements : 1. If f is the subset of Z × Z defined by f = {(xy, x − y); x, y ∈ Z}, then f is a
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Consider the determinant Δ =&nbsp;$\left|\begin{array}{lll}\text{a}_{11} &amp; \text{a}_{12} &amp; \text{a}_{13} \\ \te View Question If A =&nbsp;$\left(\begin{array}{ccc}1 &amp; 0 &amp; 0 \\ 0 &amp; \cos \theta &amp; \sin \theta \\ 0 &amp; \sin \theta &
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If X is a matrix of order 3 × 3, Y is a matrix of order 2 × 3 and Z is a matrix of order 3 × 2, then which of the follow
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For how many quadratic equations, the sum of roots is equal to the product of roots?
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Consider the following statements : 1. The set of all irrational numbers between&nbsp;$\sqrt{2}$ and&nbsp;$\sqrt{5}$ is
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Consider the following statements : 1. 2 + 4 + 6 + ........ + 2n = n2&nbsp;+ n 2. The expression n2&nbsp;+ n + 41 alwa
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Let p, q(p &gt; q) be the roots of the quadratic equation x2&nbsp;+ bx + c = 0 where c &gt; 0. If p2&nbsp;+ q2&nbsp;− 11
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What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm ?
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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
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Let R be a relation from N to N defined by R = {(x, y): x, y ∈ N and x2&nbsp;= y3}. Which of the following are not corre
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Consider the following : 1. A ∩ B = A ∩ C ⇒ B = C 2. A ∪ B = A ∪ C ⇒ B = C Which of the above is/are correct ?
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What is the modulus of z?
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What is angle θ such that z is purely real ? where n is an integer
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What is angle θ such that z is purely imaginary ? where n is an integer
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What is the ratio of the first term of A to that of B ?
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What is the ratio of their 10th&nbsp;terms ?
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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
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What is the value of q if the coefficients of x3&nbsp;and x6&nbsp;are equal ?
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What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x)?
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Under what condition the coefficients of x2&nbsp;and x4&nbsp;are equal ?
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How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed ?
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How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate position
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How many 8-letter words with or without meaning, can be formed so that all consonants are together?
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What is the value of a11C11&nbsp;+ a12C12&nbsp;+ a13C13&nbsp;?
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What is the value of $a_{21}C_{11}+a_{22}C_{12}+a_{23}C_{13}$?
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What is the value of&nbsp;$\left|\begin{array}{lll}\text{a}_{21} &amp; \text{a}_{31} &amp; \text{a}_{11} \\ \text{a}_{23 View Question If&nbsp;$\displaystyle\sum_{x=2}^n$​f(x) = 2044, then what is the value of n ? View Question What is&nbsp;$\displaystyle\sum_{x=1}^5$f(2x − 1) equal to ? View Question What is&nbsp;$\displaystyle\sum_{x=1}^6$2x f(x) equal to ? View Question How many received medals in exactly two of the three sports ? View Question How many received medals in at least two of three sports ? View Question How many received medals in exactly one of three sports ? View Question What is P equal to ? View Question What is Q equal to ? View Question What is the minimum value of determinant of A ? View Question What is the height of the lamp post ? View Question What is&nbsp;$\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)$&nbsp;? View Question What is the value of&nbsp;$\cos \left(\frac{5 \pi}{17}\right)+\cos \left(\frac{7 \pi}{17}\right)+2 \cos \left(\frac{11 \
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What is the value of tan$\left(\frac{3\pi}{8}\right)$&nbsp;?
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What is tan−1&nbsp;cot(cosec−1&nbsp;2) equal to ?
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In a triangle ABC, a = 4, b = 3, c = 2. What is cos 3C equal to ?
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What is cos 36° − cos 72° equal to ?
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If sec x =&nbsp;$\frac{25}{24}$&nbsp;and x lies in the fourth quadrant, then what is the value of tan x + sin x ?
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What is the value of tan2&nbsp;165° + cot2&nbsp;165° ?
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What is the value of&nbsp;$\sin\left(2\text{n}\pi+\frac{5\pi}{6}\right)\sin\left(2\text{n}\pi−\frac{5\pi}{6}\right)$&nbs
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If 1 + 2(sin x + cos x)(sin x − cos x) = 0 where 0 &lt; x &lt; 360°, then how many values does x take ?
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Consider the following statements in respect of the line passing through origin and inclining at an angle of 75° with th
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If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?
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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
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The centre of the circle passing through the origin and making positive intercepts 4 and 6 on the coordinate axes, lies
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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
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An equilateral triangle is inscribed in a parabola x2&nbsp;=&nbsp;$\sqrt{3}$y where one vertex of the triangle is at the
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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
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Consider the equation of a sphere x2&nbsp;+ y2&nbsp;+ z2&nbsp;− 4x − 6y − 8z − 16 = 0. Which of the following statement
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A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?
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Consider the following statements : 1. The direction ratios of y-axis can be &lt;0, 4, 0&gt; 2. The direction ratios o
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PQRS is a parallelogram. If&nbsp;$\overrightarrow{\text{PR}}=\vec{\text{a}}$&nbsp;and&nbsp;$\overrightarrow{\text{QS}}=\ View Question Let&nbsp;$\vec{\text{a}}$&nbsp;and&nbsp;$\vec{\text{b}}$&nbsp;are two unit vectors such that&nbsp;$\vec{\text{a}}+2 \vec
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Let&nbsp;$\vec{\text{a}}$,&nbsp;$\vec{\text{b}}$&nbsp;and&nbsp;$\vec{\text{c}}$&nbsp;be unit&nbsp;vectors lying on the s
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What are the values of x for which the angle between the vectors 2x2$\hat{\text{i}}$&nbsp;+ 3x$\hat{\text{j}}$&nbsp;+&nb
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The position vectors of vertices A, B and C of triangle ABC are respectively&nbsp;$\hat{\text{j}}+\hat{\text{k}}, 3\hat{ View Question Let z = [y] and y = [x] − x, where [.] is the greatest integer function. If x is not an integer but positive, then what View Question ​If f(x) = 4x + 1 and g(x) = kx + 2 such that fog(x) = gof(x), then what is the value of k ? View Question What is the minimum value of the function f(x) = log10(x2&nbsp;+ 2x + 11) ? View Question What is ∫(xx)2&nbsp;(1 + ln x)dx equal to ? View Question What is ∫ex{1 + ln x + x ln x}dx equal to ? View Question What is&nbsp;$\int\frac{(\cos x)^{1.5}−(\sin x)^{1.5}}{\sqrt{\sin x⋅\cos x}}$dx equal to ? View Question If y =&nbsp;$\frac{x \sqrt{x^2−16}}{2} − 8 \ln\left|x + \sqrt{x^2−16}\right|$, then what is&nbsp;$\frac{\text{dy}}{\text
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If y = (xx)x, then which one of the following is correct ?
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What is the maximum value of 3(sin x − cos x) + 4(cos3&nbsp;x − sin3&nbsp;x) ?
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What is the area of the region (in the first quadrant) bounded by y =&nbsp;$\sqrt{1−\text{x}^2}$, y = x and y = 0 ?
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What is the area of the region bounded by x − |y| = 0 and x − 2 = 0 ?
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If f(α) =&nbsp;$\sqrt{\sec^2\alpha−1}$, then what is&nbsp;$\frac{f(\alpha)+f(\beta)}{1−f(\alpha) f(\beta)}$&nbsp;equal t
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If f(x) = ln (x +&nbsp;$\sqrt{1+\text{x}^2}$), then which one of the following is correct ?
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What is&nbsp;$\displaystyle\lim_{x \rightarrow 0} \frac{x}{\sqrt{1−\cos 4x}}$&nbsp;equal to ?
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What is&nbsp;$\displaystyle\lim_{x\rightarrow \frac{\pi}{2}} \frac{4x−2\pi}{\cos x}$&nbsp;equal to ?
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If f(x) =&nbsp;$\frac{x^2+x+|x|}{x}$, then what is&nbsp;$\displaystyle\lim_{x \rightarrow 0}$&nbsp;f(x) equal to ?
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What is&nbsp;$\displaystyle\lim_{h \rightarrow 0} \frac{\sin^2(x+h)−\sin^2x}{h}$&nbsp;equal to ?
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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
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If y = ln2$\left(\frac{x^2−x+1}{x^2+x+1}\right)$, then what is&nbsp;$\frac{\text{dy}}{\text{dx}}$&nbsp;at x = 0 equal to
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If&nbsp;$\frac{d}{d x}\left(\frac{1+x^4+x^8}{1−x^2+x^4}\right)$&nbsp;= ax + bx3, then which one of the following is corr
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Under which one of the following conditions does the function f(x) = (p sec x)2&nbsp;+ (q cosec x)2&nbsp;attain minimum
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Where does the function f(x) =&nbsp;$\displaystyle\sum_{j=1}^7$(x − j)2&nbsp;attain its minimum value ?
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Consider the following statements in respect of the function f(x) =&nbsp;$\left\{\begin{array}{rc}|x|+1, &amp; 0&lt;|x| View Question What is&nbsp;$\displaystyle\int_0^1 \ln \left(\frac{1}{x}−1\right)$dx equal to ? View Question If&nbsp;$\displaystyle\int_0^{\pi/2}$(sin4&nbsp;x + cos4&nbsp;x)dx = k, then what is the value of&nbsp;$\displaystyle\in
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What is&nbsp;$\displaystyle\int_{−\pi/2}^{\pi/2}$(ecos x&nbsp;sin x + esin x&nbsp;cos x)dx equal to ?
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What is the area of the region enclosed in the first quadrant by x2&nbsp;+ y2&nbsp;= π2, y = sin x and x = 0 ?
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Consider the following statements: 1. The degree of the differential equation&nbsp;\$\frac{\text{dy}}{\text{dx}} + \cos
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What is the differential equation of the family of parabolas having a vertex at origin and axis along positive y-axis?
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What is the solution of the differential equation (dy − dx) + cos x(dy + dx) = 0 ?
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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&nbsp;
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What is the probability of getting a composite number in the list of natural numbers from 1 to 50?
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If n &gt; 7, then what is the probability that C(n, 7) is a multiple of 7?
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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
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A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies x
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Three fair dice are tossed once. What is the probability that they show different numbers that are in AP?
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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') ?
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Five coins are tossed once. What is the probability of getting at most four tails ?
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Three fair dice are thrown. What is the probability of getting a total greater than or equal to 15 ?
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The probability that a person hits a target is 0.5. What is the probability of at least one hit in 4 shots ?
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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
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During war, one ship out of 5 was sunk on an average in making a certain voyage. What is the probability that exactly 3
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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
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The coefficient of correlation between ages of husband and wife at the time of marriage for a given set of 100 couples w
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The completion of a construction job may be delayed due to strike. The probability of strike is 0.6. The probability tha
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Which one of the following subjects shows highest variability of marks ?
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What is the coefficient of variation of marks in Mathematics ?
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What is the median of the distribution ?
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What is mean deviation about the median ?
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What is the mean deviation about the mean ?
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