NDA Mathematics 3 September 2023

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Sun, Sep 3, 2023 8:30 AM

## Mathematics

If z z̅ = |z + z̅ |, where z = x + iy, i = $\sqrt{-1}$, then the locus of z is a pair of:

View Question If 1! + 3! + 5! + 7! + ... + 199! is divided by 24, what is the remainder?

View Question What is the value of $\sqrt{12+5 i}+\sqrt{12-5 i}$ where $i=\sqrt{-1}$ ?

View Question If $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then what is the value of det(I + AA'), where I is the

View Question 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)?

View Question If the nth term of a sequence is $\frac{2 n+5}{7}$, then what is the sum of its first 140 terms?

View Question Let A be a skew-symmetric matrix of order 3.
What is the value of det(4A4) - det(3A3) + det(2A2) - det(A) + det(-I

View Question If $A=\left[\begin{array}{rrr} 0 & 3 & 4 \\ -3 & 0 & 5 \\ -4 & -5 & 0 \end{array}\right]$, then

View Question If $A=\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{array}\right]$, the

View Question If (a + b), 2b, (b + c) are in HP, then which one of the following is correct?

View Question Let t1, t2, t3 ... be in GP. What is $\rm \left(t_1 t_3 \ldots t_{21}\right)^{\frac{1}{11}}$ equal to ?

View Question Which one of the following is a square root of $-\sqrt{-1} $?

View Question What is the maximum number of points of intersection of 10 circles?

View Question A set S contains (2n + 1) elements. There are 4096 subsets of S which contain at most n elements. What is n equal to?

View Question If $\left|\begin{array}{ccc} x^2+3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x \en

View Question If all elements of a third order determinant are equal to 1 or -1, then the value of the determinant is:

View Question If $A=\left[\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 3 & 0 \\ 1 & 0 & 1 \end{array}\right]$, then w

View Question If $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$, then

View Question The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, t

View Question If $A_k=\left[\begin{array}{cc} k-1 & k \\ k-2 & k+1 \end{array}\right] $, then what is det(A1) + det(

View Question The Cartesian product A × A has 16 elements among which are (0, 2) and (1, 3). Which of the 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 x, y ∈ A. Whi

View Question Consider the following statements:
1. The relation f defined by $f(x)= \begin{cases}x^3, & 0 \leq x

View Question Consider the following statements
1. A = (A ∪ B) ∪ (A - B),
2. A ∪ (B -

View Question A function satisfies $f(x-y)=\frac{f(x)}{f(y)}$, where f(y) ≠ 0. If f(1) = 0.5, then what is f(2) + f(3) + f(4

View Question What is 2 cot $\left(\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right)$ equal to ?

View Question If sec-1 p - cosec-1q = 0, where p > 0, q > 0; then what is the value of p-2 + q-2 ?

View Question What is $1+\sin ^2\left(\cos ^{-1}\left(\frac{3}{\sqrt{17}}\right)\right)$ equal to ?

View Question If tan (π cos θ) = cot (π sin θ), $0<\theta<\frac{\pi}{2}$; then what is the value of $8

View Question If $\tan \alpha=\frac{1}{7}$, $\sin \beta=\frac{1}{\sqrt{10}}$; $0<\alpha, \beta<\frac{\pi}{2}$, then what is the

View Question What is the number of real roots of the equation?

View Question What is the sum of all the roots of the equation?

View Question What are the roots of equation-I ?

View Question Which one of the following is a root of equation-II?

View Question What is the number of common roots of equation-I and equation-II?

View Question If $\rm {k}=\frac{{c}}{2},({c} \neq 0)$, then the roots of the equation are :

View Question If k = c, then the roots of the equation are:

View Question What is T1 + 2T2 + 3T3 + ... + nTn equal to ?

View Question What is 1 - T1 + 2T2 - 3T3 + ... + (-1)nnTn equal to ?

View Question What is T1 + T2 + T3 + ... + Tn equal to ?

View Question Which one of the following is a possible 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 parabola?

View Question What is $\displaystyle \lim _{x \rightarrow 1} \frac{f(x)-1}{g(x)}$ equal to?

View Question What is $\displaystyle \lim _{x \rightarrow 1} f(x)^{\frac{1}{g(x)}}$ 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 $\displaystyle \lim _{x \rightarrow 0+}$ h(x) equal to ?

View Question What is $\displaystyle \lim _{x \rightarrow 0-}$ h(x) equal to ?

View Question What is the value of a ?

View Question What is the value of b?

View Question What is $\displaystyle \int_0^\pi\left(\sin ^4 x+\cos ^4 x\right) d x$ equal to?

View Question What is I equal to?

View Question If the function f(x) is differentiable at x = 1, then what is the value of (a + b)?

View Question What is $\displaystyle \lim _{x \rightarrow 0} $ f(x) equal to ?

View Question If f(x) = |ln|x|| where 0 < x < 1, then what is f'(0.5) equal to ?

View Question If f'(x) = cos (In x) and $y=f\left(\frac{2 x-3}{x}\right)$, then what is $\frac{d y}{d x}$ equal to ?

View Question What is $\displaystyle \rm \int_0^{8 \pi}|\sin x| d x$ equal to?

View Question What is the area between the curve f(x) = x |x| and x-axis for x = [-1, 1]?

View Question What are the order and the degree respectively of the differential equation $\rm x^2\left(\frac{d^3 y}{d x^3}\

View Question What is the differential equation of all parabolas of the type y2 = 4a (x - b)?

View Question What is a1 + a5 - a10 - a15 - a20 - a25 + a30 + a34 equal to ?

View Question What is $\displaystyle \sum_{n=1}^{34} a_n$ equal to ?

View Question What is the value of p + q?

View Question What is the value of pq?

View Question What is pq equal to ?

View Question For how many values of x does $\frac{1}{p}$ become zero?

View Question What is a value of sin 3x + sin 3y?

View Question What is a value of cos3 x + cos3 y?

View Question What is the value of a + b + √2 c equal to ?

View Question What is the ratio of a2 ∶ b2 ∶ c2 ?

View Question What is the equation of directrix of parabola y2 = 4bx, where b < 0 and b2 + b - 2 = 0?

View Question The points (-a, -b), (0, 0), (a, b) and (a2, ab) are:

View Question Given that 16p2 + 49q2 - 4r2 - 56pq = 0. Which one of the following is a point on a pair of str

View Question If 3x + y - 5 = 0 is the equation of a chord of the circle x2 + y2 - 25 = 0, then what are the coordinate

View Question Consider the following in respect of the equation $\frac{x^2}{24-k}+\frac{y^2}{k-16}=2$.
1. The equation repr

View Question Consider the following statements in respect of hyperbola $\frac{x^2}{\cos ^2 \theta}-\frac{y^2}{\sin ^2 \thet

View Question Consider the following in respect of the circle 4x2 + 4y2 - 4ax - 4ay + a2 = 0:
1. The circle touch

View Question For what values of k is the line (k - 3)x - (5 - k2) y + k2 - 7k + 6 = 0 parallel 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 ∶ 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 $\rm \hat{i}+2 \hat{j}+3 \hat{k}$ on the vector $\rm2 \hat{i}+3

View Question If $\rm (\vec{a} \times \vec{b})^2+(\vec{a} \cdot \vec{b})^2=144$ and $\rm|\vec{b}|=4 $, then what is the

View Question If θ is the angle between vectors $\vec{a}$ and $ \vec{b}$ such that $\vec{a} \cdot \vec{b} \geq 0$, then whic

View Question The vectors $\rm 60 \hat{i}+3 \hat{j}, 40 \hat{i}-8 \hat{j}$ and $\rm \beta \hat{i}-52 \hat{j}$ are collinear

View Question Consider the following in respect of the vectors $\rm \vec{a}=(0,1,1)$ and $\rm \vec{b}=(1,0,1) $ :
1.&n

View Question If L is the line with direction ratios < 3, -2, 6 > and passing through (1, -1, 1), then what are t

View Question Which one of the planes is parallel to the line $\rm \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ ?

View Question What is the angle between the lines 2x = 3y = -z and 6x = -y = -4z?

View Question What is the equation of the sphere concentric with the sphere x2 + y2

View Question A point P lies on the line joining A(1, 2, 3) and B(2, 10, 1). If z-coordinate of P is 7, what is the sum of o

View Question The sum of deviations of n numbers from 10 and 20 are p and q respectively. If (p - q)2 = 10000, then what is the v

View Question If X̅ = 20 is the mean of 10 observations x1, x2, ... x10; then what is the value of $\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 exhaustive events.
If 2P(A) = 3P(B) = 4P(C) = 5P(D), then what is 77

View Question Two distinct natural numbers from 1 to 9 are 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, ... 10 with frequencies 9C0, 9C1, 9C2 ..., 9

View Question The probability that a person recovers from a 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 and y, then what is the correlation coefficient bet

View Question A fair coin is tossed 6 times. What is the probability of getting a result in the 6th toss which is diffe

View Question If H is the Harmonic Mean of three numbers 10C4, 10C5, and 10C6, then what is the value of $\fr

View Question In a class, there are n students including the students P and Q. What is the probability that P and Q sit together

View Question In a Binomial distribution B(n, p), n = 6 and 9P(X = 4) = P(X = 2). What is p equal to ?

View Question What is the probability that all three boys sit together?

View Question What is the probability that boys and girls sit alternatively?

View Question What is the probability that no two girls sit together?

View Question What is the probability that P and Q take the two end positions?

View Question What is the probability that Q and U sit together?

View Question