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List of top Mathematics Questions

The points on the curve $\frac{x^2}{9} + \frac{y^2}{16} = 1$ at which the tangents are parallel to x-axis:

If $e^y(x+2)=10$, then $\frac{d^2y}{dx^2}$ is equal to:

If, $f(x) = \begin{bmatrix}0 & x-a & x-b \\[0.3em]x+a&o & x-c \\[0.3em]x+b & x+c & 0\\[0.3em] \end{bmatrix}$, then $f(0)$ is:

If, A is a square matrix of order 3 and |A| = -2 then. $|-2 \ A^{-1}|$ is:

A. $\begin{bmatrix}1& 2& 3 \\[0.3em]2 & 4 & 5 \\[0.3em]3 & 5&6 \\[0.3em] \end{bmatrix}$ is a Symmetric matrix.
B. $\begin{bmatrix}0 &0 &0 \\[0.3em]0& 0&0 \\[0.3em] \end{bmatrix}$ is a Null matrix.
C. $\begin{bmatrix}1& 0& 0 \\[0.3em]0 & 2 & 0\\[0.3em]0 & 0&3\\[0.3em] \end{bmatrix}$ is an Identity matrix.
D. $\begin{bmatrix}0& 1&2 \\[0.3em]-1 & 0 & 3 \\[0.3em]-2 & 3&0\\[0.3em] \end{bmatrix}$ is a Skew symmetric matrix.
E. $\begin{bmatrix}\sqrt{3} &0& 0\\[0.3em]0 & \sqrt{3} & 0 \\[0.3em]0 & 0&\sqrt{3} \\[0.3em] \end{bmatrix}$ is a Scalar matrix
Choose the correct answer from the options given below:

If, A is a square matrix of order $3 \times 3$ such that $A^2 = A$ and I is the unit matrix of order $3 \times 3$, then the value of $(I-A)^3+A^2+I$ is:

A random variable X has the following probability distribution

X	0	1	2	3	4	5	6	7
P(X)	0	k	2k	2k	3k	k²	2k²	7k²+k

then value of E(X) is:

If $A$ and $B$ are two non-zero $n \times n$ matrics such that $A ^2+ B = A ^2 B$, then

Let$\overrightarrow{ a }=2 \hat{i}-7 \hat{j}+5 \hat{k}, \overrightarrow{ b }=\hat{i}+\hat{k} and \overrightarrow{ c }=\hat{i}+2 \hat{j}-3 \hat{k}$ be three given vectors If $\overrightarrow{ r }$ is a vector such that$ \vec{r} \times \vec{a}=\vec{c} \times \vec{a} \ and \ \vec{r} \cdot \vec{b}=0,$ then $|\vec{r}|$ is equal to :

The value of b for which the function f(x) = sinx - bx + C, where b and e are constants is decreasing for $x \in R$ is given by

The radius of a spherical ball is increasing at the rate of 1 m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by:

The absolute maximum value of the function f(x)=sinx + cosx, x $\in$[0, $\pi$] is:

$\int \frac{cos x - sin x}{1 + sin2x} dx$ is equal to:

The value of $\int_0^{\frac{\pi}{2}} log (\frac{5 + 4 sinx}{5 + 4 cosx})dx$ is:

The area of the region enclosed between the parabolas $y^2 = x + 1$ and $y^2 = x + 1$ is:

The area of the region bounded by the curves $x^2=4y$, the line x = 3 and x axis is:

The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is:

For any two non zero vectors $\vec{a}$ and $\vec{b}$
A. If $|\vec{a}| = |\vec{b}|$then $\vec{a} = \vec{b}$
B. If $\vec{a} = \vec{b}$ then $|\vec{a}| = |\vec{b}|$
C. $\vec{a} . \vec{b}=\vec{b} . \vec{a}$
D. $\vec{a} \times \vec{b}=\vec{b} \times \vec{a}$
E. area of the parallelogram = $\frac{1}{2} |\vec{a} \times \vec{b}|$. where $\vec{a}$ and $\vec{b}$ represent resent the diagonals of the parallelogram.
Choose the correct answer from the options given below:

The value of $\lambda$, for which the projection of $\vec{a} = \lambda \hat{i} + \hat{j} +4 \hat{k}$ on $\vec{b} =2\hat{i} +6 \hat{j} +3\hat{k}$ is 4 units

The straight line $ \frac{x+2}{3} = \frac{z-3}{ -2}, y-2 $ is

If the lines $\frac{x-1}{-3} = \frac{y-2}{2 \lambda} = \frac{z-3}{2}$ and $\frac{x-1}{3 \lambda} = \frac{y-1}{2} = \frac{z-6}{-5}$ are perpendicular. Then the value of $\lambda$ is:

Two tailors A and B earn ₹150 and ₹200 per day respectively. A can stitch 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. If the tailors A and B work for x and y days respectively. To maximize the earning for producing at least 60 shirts and 32 pants, the LPP is:

Match List I with List II

List I	List II
A. The region represented by $x \geq 0, y \geq 0$	I. no feasible region
B. The region represented by the inequalities $2x + y \geq 3, x + 2y \geq 6, x,y \geq 0$	II. 1st quadrant
C. The region represented by the inequalities $x + 2y \leq 8, 3x + 2y \leq 12, x,y \geq 0$	III. unbounded
D. The region represented by the inequalities $x + y \leq 2, 3x + 5y \geq 15, x,y \geq 0$	IV. bounded

Choose the correct answer from the options given below:

Let a pair of dice be thrown and the random variable X be the sum of numbers on the two dice. Then.
Match List I with List II.

List I	List II
A. P (X = 2)	I. $\frac{4}{36}$
B. P (X = 4)	II. $\frac{5}{36}$
C. P (X - 5)	III. $\frac{1}{36}$
D. P (X - 6)	IV. $\frac{3}{36}$

Choose the correct answer from the options given below:

For two events A and B
Match List I with List II

List I	List II
A. $P (\bar{\bigwedge} \cap \bar{B}) = P(\bar{\bigwedge}) . P(\bar{B})$	I. $P(A/B) \geq P(A)$
B. $A \subset B $ and $P(B) \neq0$	II. $P(A) = P(B)$
C. $P(A \bigcup B) = P(A) + P(B)$	III. A and B are independent events
D. $P(A\|B) = P (B\|A)$	IV. A and B are mutually exclusive events

Choose the correct answer from the options given below:

List I	List II
A. \(P (\bar{\bigwedge} \cap \bar{B}) = P(\bar{\bigwedge}) . P(\bar{B})\)	I. \(P(A/B) \geq P(A)\)
B. \(A \subset B \) and \(P(B) \neq0\)	II. \(P(A) = P(B)\)
C. \(P(A \bigcup B) = P(A) + P(B)\)	III. A and B are independent events
D. \(P(A\|B) = P (B\|A)\)	IV. A and B are mutually exclusive events

List I	List II
A. The region represented by \(x \geq 0, y \geq 0\)	I. no feasible region
B. The region represented by the inequalities \(2x + y \geq 3, x + 2y \geq 6, x,y \geq 0\)	II. 1st quadrant
C. The region represented by the inequalities \(x + 2y \leq 8, 3x + 2y \leq 12, x,y \geq 0\)	III. unbounded
D. The region represented by the inequalities \(x + y \leq 2, 3x + 5y \geq 15, x,y \geq 0\)	IV. bounded

List I	List II
A. P (X = 2)	I. \(\frac{4}{36}\)
B. P (X = 4)	II. \(\frac{5}{36}\)
C. P (X - 5)	III. \(\frac{1}{36}\)
D. P (X - 6)	IV. \(\frac{3}{36}\)