NDA Mathematics 3 September 2023
Paper was held on Sun, Sep 3, 2023 8:30 AM
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Mathematics

If z z̅ = |z + z̅ |, where z = x + iy, i = $\sqrt{-1}$,&nbsp;then the locus of z is a pair of:
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If 1! + 3! + 5! + 7! + ... + 199! is divided by 24,&nbsp;what is the remainder?
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What is the value of&nbsp;$\sqrt{12+5 i}+\sqrt{12-5 i}$ where $i=\sqrt{-1}$ ?
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If $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then what is the value of&nbsp;det(I + AA'), where I is the
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If A, B and C are square matrices of order 3 and det(BC) = 2 det(A), then what is the value of det(2A-1BC)?
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If the nth&nbsp;term of a sequence is $\frac{2 n+5}{7}$,&nbsp;then&nbsp;what is the sum of its first 140 terms?&nbsp;
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Let A be a skew-symmetric matrix of order 3. What is the value of&nbsp;det(4A4) - det(3A3) + det(2A2) - det(A) + det(-I
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If $A=\left[\begin{array}{rrr} 0 &amp; 3 &amp; 4 \\ -3 &amp; 0 &amp; 5 \\ -4 &amp; -5 &amp; 0 \end{array}\right]$, then
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If $A=\left[\begin{array}{lll} 2 &amp; 0 &amp; 0 \\ 0 &amp; 3 &amp; 0 \\ 0 &amp; 0 &amp; 4 \end{array}\right]$,&nbsp;the
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If (a + b), 2b, (b + c) are in HP, then which one of the following is correct?
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Let t1, t2, t3&nbsp;...&nbsp;be in GP. What is&nbsp;$\rm \left(t_1 t_3 \ldots t_{21}\right)^{\frac{1}{11}}$ equal to ?
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Which one of the following is a square root of&nbsp;$-\sqrt{-1}$?
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What is the maximum number of points of intersection of 10 circles?
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A set S contains (2n + 1) elements. There are 4096 subsets of S which contain at most n elements. What is n equal to?
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If&nbsp;$\left|\begin{array}{ccc} x^2+3 x &amp; x-1 &amp; x+3 \\ x+1 &amp; -2 x &amp; x-4 \\ x-3 &amp; x+4 &amp; 3 x \en View Question If all elements of a third order determinant are equal to 1 or -1, then the value of the&nbsp;determinant is: View Question If$A=\left[\begin{array}{rrr} 2 &amp; -1 &amp; 0 \\ -1 &amp; 3 &amp; 0 \\ 1 &amp; 0 &amp; 1 \end{array}\right]$, then w View Question If$A=\left[\begin{array}{lll}1 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 1\end{array}\right]$,&nbsp;then View Question The value of the determinant of a matrix A of&nbsp;order 3 is 3. If C is the matrix of cofactors of&nbsp;the matrix A, t View Question If$A_k=\left[\begin{array}{cc} k-1 &amp; k \\ k-2 &amp; k+1 \end{array}\right] $,&nbsp;then what is&nbsp;det(A1) + det( View Question The Cartesian product A&nbsp;×&nbsp;A has 16 elements among which are (0, 2) and (1, 3). Which of the&nbsp;following sta View Question Let A = {1, 2, 3, ..., 20}. Define a relation R from A to A by R = {(x, y) : 4x - 3y = 1}, where&nbsp;x, y ∈&nbsp;A. Whi View Question Consider the following statements:&nbsp; 1.&nbsp;The relation f defined by&nbsp;$f(x)= \begin{cases}x^3, &amp; 0 \leq x
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Consider the following statements&nbsp; 1.&nbsp;A = (A&nbsp;∪&nbsp;B)&nbsp;∪&nbsp;(A - B), 2.&nbsp;A&nbsp;∪&nbsp;(B -
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A function satisfies&nbsp;$f(x-y)=\frac{f(x)}{f(y)}$, where f(y) ≠ 0. If f(1) = 0.5, then what is&nbsp;f(2) + f(3) + f(4
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What is 2 cot&nbsp;$\left(\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right)$ equal to ?
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If sec-1&nbsp;p - cosec-1q = 0, where p &gt; 0, q &gt; 0; then what is the value of p-2&nbsp;+ q-2&nbsp;?
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What is&nbsp;$1+\sin ^2\left(\cos ^{-1}\left(\frac{3}{\sqrt{17}}\right)\right)$ equal to ?
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If tan (π&nbsp;cos θ) = cot (π&nbsp;sin&nbsp;θ),&nbsp;$0&lt;\theta&lt;\frac{\pi}{2}$; then what is the value of&nbsp;$8 View Question If$\tan \alpha=\frac{1}{7}$,$\sin \beta=\frac{1}{\sqrt{10}}$;$0&lt;\alpha, \beta&lt;\frac{\pi}{2}$, then what is the View Question What is the number of real roots of the&nbsp;equation? View Question What is the sum of all the roots of the&nbsp;equation? View Question What are the roots of equation-I ? View Question Which one of the following is a root of&nbsp;equation-II? View Question What is the number of common roots of&nbsp;equation-I and equation-II? View Question If&nbsp;$\rm {k}=\frac{{c}}{2},({c} \neq 0)$, then the roots of the equation&nbsp;are : View Question If k = c, then the roots of the equation are: View Question What is T1&nbsp;+ 2T2&nbsp;+ 3T3&nbsp;+ ... + nTn&nbsp;equal to ? View Question What is 1 - T1&nbsp;+ 2T2&nbsp;- 3T3&nbsp;+ ... + (-1)nnTn&nbsp;equal to ?&nbsp; View Question What is T1&nbsp;+ T2&nbsp;+ T3&nbsp;+ ... + Tn&nbsp;equal to ? View Question Which one of the following is a possible&nbsp;expression for g(x)? View Question What is g(15) equal to ? View Question What is f(0.5) equal to ? View Question If f is differentiable, then what is f'(0.5) equal to? View Question The function is decreasing on : View Question The function attains local minimum value at : View Question What is the maximum value of y? View Question What is the maximum value of xy ? View Question What is the range of the function? View Question What is the period of the function? View Question What is the directrix of the parabola ? View Question What is the length of latus rectum of the&nbsp;parabola? View Question What is&nbsp;$\displaystyle \lim _{x \rightarrow 1} \frac{f(x)-1}{g(x)}$equal to? View Question What is&nbsp;$\displaystyle \lim _{x \rightarrow 1} f(x)^{\frac{1}{g(x)}}$equal to? View Question What is the domain of the function? View Question What is the greatest value of the function? View Question What is&nbsp;$\displaystyle \lim _{x \rightarrow 0+}$&nbsp;h(x) equal to ? View Question What is&nbsp;$\displaystyle \lim _{x \rightarrow 0-}$&nbsp;h(x) equal to ? View Question What is the value of a ? View Question What is the value of b? View Question What is&nbsp;$\displaystyle \int_0^\pi\left(\sin ^4 x+\cos ^4 x\right) d x$equal to? View Question What is I equal to? View Question If the function f(x) is differentiable at x = 1,&nbsp;then what is the value of (a + b)? View Question What is$\displaystyle \lim _{x \rightarrow 0} $&nbsp;f(x) equal to ? View Question If f(x) = |ln|x||&nbsp;where 0 &lt; x &lt; 1, then what is&nbsp;f'(0.5) equal to ? View Question If f'(x) = cos (In x) and$y=f\left(\frac{2 x-3}{x}\right)$, then&nbsp;what is&nbsp;$\frac{d y}{d x}$equal to ? View Question What is&nbsp;$\displaystyle \rm \int_0^{8 \pi}|\sin x| d x$equal to? View Question What is the area between the&nbsp;curve&nbsp;f(x) = x |x|&nbsp;and x-axis for x = [-1, 1]? View Question What are the order and the degree&nbsp;respectively of the differential equation&nbsp;$\rm x^2\left(\frac{d^3 y}{d x^3}\
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What is the differential equation of all&nbsp;parabolas of the type y2&nbsp;= 4a (x - b)?
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What is&nbsp;a1&nbsp;+ a5&nbsp;-&nbsp;a10&nbsp;- a15&nbsp;- a20&nbsp;- a25&nbsp;+ a30&nbsp;+ a34&nbsp;equal to ?
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What is&nbsp;$\displaystyle \sum_{n=1}^{34} a_n$&nbsp;equal to ?
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What is the value of p + q?
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What is the value of pq?
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What is pq equal to ?
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For how many values of x does&nbsp;$\frac{1}{p}$&nbsp;become&nbsp;zero?
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What is a value of sin 3x + sin 3y?
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What is a value of cos3 x + cos3 y?
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What is the value of a + b + √2 c equal to ?
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What is the ratio of a2&nbsp;∶&nbsp;b2&nbsp;∶&nbsp;c2&nbsp;?
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What is the equation of directrix of parabola y2&nbsp;= 4bx, where b &lt; 0 and b2&nbsp;+ b - 2 = 0?
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The points (-a, -b), (0, 0), (a, b) and (a2, ab)&nbsp;are:
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Given that 16p2&nbsp;+ 49q2&nbsp;- 4r2&nbsp;- 56pq&nbsp;= 0.&nbsp;Which one of the following is a point on a pair of str
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If 3x + y - 5 = 0 is the equation of a chord of&nbsp;the circle x2&nbsp;+ y2&nbsp;- 25 = 0, then what are the coordinate
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Consider the following in respect of the&nbsp;equation&nbsp;$\frac{x^2}{24-k}+\frac{y^2}{k-16}=2$. 1. The equation repr
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Consider the following statements in respect&nbsp;of hyperbola&nbsp;$\frac{x^2}{\cos ^2 \theta}-\frac{y^2}{\sin ^2 \thet View Question Consider the following in respect of the circle 4x2&nbsp;+ 4y2&nbsp;- 4ax - 4ay + a2&nbsp;= 0: 1.&nbsp;The circle touch View Question For&nbsp;what values&nbsp;of k is the line&nbsp;(k - 3)x - (5 - k2) y + k2&nbsp;- 7k + 6 = 0 parallel&nbsp;to the line x View Question The line x + y = 4 cuts the line joining P(-1, 1) and Q(5, 7) at R. What is PR&nbsp;∶&nbsp;RQ equal to ? View Question What is the sum of the intercepts of the line whose perpendicular distance from origin is 4 units and the angle which th View Question What is the length of projection of the vector&nbsp;$\rm \hat{i}+2 \hat{j}+3 \hat{k}$on the vector&nbsp;$\rm2 \hat{i}+3
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If&nbsp;$\rm (\vec{a} \times \vec{b})^2+(\vec{a} \cdot \vec{b})^2=144$ and&nbsp;$\rm|\vec{b}|=4$,&nbsp;then what is the
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If θ&nbsp;is the angle between vectors $\vec{a}$ and $\vec{b}$ such that&nbsp;$\vec{a} \cdot \vec{b} \geq 0$, then whic
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The vectors&nbsp;$\rm 60 \hat{i}+3 \hat{j}, 40 \hat{i}-8 \hat{j}$ and&nbsp;$\rm \beta \hat{i}-52 \hat{j}$ are collinear
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Consider the following in respect of the vectors&nbsp;$\rm \vec{a}=(0,1,1)$ and&nbsp;$\rm \vec{b}=(1,0,1)$&nbsp;: 1.&n
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If L is the line with direction&nbsp;ratios&nbsp;&lt; 3, -2, 6 &gt; and passing through (1, -1, 1),&nbsp;then what are t
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Which one of the planes is parallel to the line&nbsp;$\rm \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ ?
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What is the angle between the lines 2x = 3y = -z and 6x = -y = -4z?
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What is the&nbsp;equation&nbsp;of&nbsp;the&nbsp;sphere&nbsp;concentric&nbsp;with the&nbsp;sphere&nbsp;x2&nbsp;+ y2&nbsp;
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A point P lies on the line joining A(1, 2, 3) and&nbsp;B(2, 10, 1). If z-coordinate of P is 7, what is the&nbsp;sum of o
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The sum of deviations of n numbers from 10 and 20 are p and q respectively. If (p - q)2&nbsp;= 10000, then what is the v
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If X̅&nbsp;= 20 is the mean of 10 observations x1, x2, ... x10; then what is the value of&nbsp;$\displaystyle \sum_{i=1} View Question If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation View Question Three dice are thrown. What is the probability of getting a sum which is a perfect square? View Question A, B, C and D are mutually exclusive and&nbsp;exhaustive events. If 2P(A) = 3P(B) = 4P(C) = 5P(D),&nbsp;then what is 77 View Question Two distinct natural numbers from 1 to 9 are&nbsp;picked at random. What is the probability that their product has 1 in View Question Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ? View Question What is the mean of the numbers 1, 2, 3, ...&nbsp;10&nbsp;with frequencies&nbsp;9C0,&nbsp;9C1,&nbsp;9C2&nbsp;...,&nbsp;9 View Question The probability that a person recovers from a&nbsp;disease is 0.8. What is the probability that exactly 2 persons out of View Question Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The ch View Question If r is the coefficient of correlation between x&nbsp;and&nbsp;y,&nbsp;then what is the correlation coefficient&nbsp;bet View Question A fair coin is tossed 6 times. What is the&nbsp;probability of getting a result in the 6th&nbsp;toss&nbsp;which is diffe View Question If H is the Harmonic Mean of three numbers&nbsp;10C4,&nbsp;10C5, and&nbsp;10C6, then what is the value&nbsp;of&nbsp;$\fr
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In a class, there are n students including the students P and Q. What is the probability that&nbsp;P and Q sit together
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In a Binomial distribution B(n, p), n = 6 and&nbsp;9P(X = 4) = P(X = 2). What is p equal to ?
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What is the probability that all three boys sit&nbsp;together?
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What is the probability that boys and girls sit&nbsp;alternatively?
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What is the probability that no two girls sit&nbsp;together?
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What is the probability that P and Q take the&nbsp;two end positions?
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What is the probability that Q and U sit&nbsp;together?
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