The particular solution of differential equation $\left(1+y^2\right)(1+\log x) d x+x d y=0$ at $x=1,

The general solution of the differential equation $\frac{1}{x} \frac{d y}{d x}=\tan ^{-1} x$ is

The general solution of the differential equation $x \cos y \mathrm{dy}=\left(x \mathrm{c}^x \log x+

If $(2+\sin x) \frac{d y}{d x}+(y+1) \cos x=0$ and $y(0)=1$, then $y\left(\frac{\pi}{2}\right)$ is e

If $y=y(x)$ is the solution of the differential equation $\left(\frac{5+e^x}{2+y}\right) \frac{d y}{

Truth values of $p \rightarrow r$ is $F$ and $p \leftrightarrow q$ is $F$. Then the truth values of

If $(p \wedge \sim r) \rightarrow(\sim p \vee q)$ has truth value False, then truth values of $\math

If $p \rightarrow(\sim p \vee \sim q)$ is false, then the truth values of $p$ and q are respectively

Let $\mathrm{p}, \mathrm{q}, \mathrm{r}$ be three statements such that the truth value of $(p \wedge

If the statements p q and r have the truth values F, T, F respectively, then the truth values of the

If $(p \wedge \sim q) \wedge(p \wedge r) \rightarrow \sim p \vee q$ is false, then the truth values

If the statement $\mathrm{p} \vee \sim(\mathrm{q} \wedge \mathrm{r})$ is false, then the truth value

Let $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in \mathbb{R}^{+}$and $A^4=\left[

Let A and B be $3 \times 3$ real matrices such that A is symmetric matrix and $B$ is skew-symmetric

If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & a & 3 \\ 3 & 2 & 2\end{array}\right]$ and $B=\left[\b

Let $\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]$ and $\mathrm{A}^{-1}=\math

Suppose A is any $3 \times 3$ non-singular matrix and $(A-31)(A-5 I)=0$ where $I=I_3$ and $O=O_3$. H

Let $\mathrm{X}=\left[\begin{array}{l}\mathrm{a} \\ \mathrm{b} \\ \mathrm{c}\end{array}\right], \mat

Let $\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]$ and $\mathrm{A}^{-1}=\alph

For the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$,

If $\mathrm{A}=\left[\begin{array}{cc}5 \mathrm{a} & -\mathrm{b} \\ 3 & 2\end{array}\right]$ and $\m

If $A=\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]$ then $\left(A^2-5 A\right)^{-1}$ is

Inverse of the matrix $\left[\begin{array}{cc}0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$ is

If $A=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$, then $A^{-1}=$

If $A=\left[\begin{array}{ll}3 & -1 \\ -4 & 2\end{array}\right]$, then $A^{-1}$ is

Suppose that the points $(h, k),(1,2)$ and $(-3,4)$ lie on the line $l_1$. If a line $l_2$ passing t

Let $P \equiv(-5,0), Q \equiv(0,0)$ and $R \equiv(2,2 \sqrt{3})$ be three points. Then the equation

If the length of the perpendicular to a line from the origin is $2 \sqrt{2}$ units, which makes an a

Let a line intersect the co-ordinate axes in points A and B such that the area of the triangle OAB i

If $\theta$ denotes the acute angle between the curves $y$ $=10-x^2$ and $y=2+x^2$, at a point of th

If two sides of a square are $4 x+3 y-20=0$ and $4 x+3 y+15=0$, then the area of the square is

A straight line $L$ through the point $(3,-2)$ is inclined at an angle of $60^{\circ}$ to the line $

The straight line, $2 x-3 y+17=0$ is perpendicular to the line passing through the points $(7,17)$ a

The acute angle between the lines $x \cos 30^{\circ}+y$ $\sin 30^{\circ}=3$ and $x \cos 60^{\circ}+y

The equation of the line passing through the point of intersection of the lines $3 x-y=5$ and $x+3 y

The line $L$ given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line k is

The area (in sq.units) bounded by the curves $y=(x+1)^2, y=(x-1)^2$ and the line $y=\frac{1}{4}$ is

The area of the region bounded by hyperbola $x^2-y^2=9$ and its latus rectum is

The area (in sq. units) bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9 y$ and the line $

The area of the region bounded by curves $\mathrm{y}=3 x+1, \mathrm{y}=4 x+1$ and $x=2$ is

The area of the region bounded by the parabola $y=x^2+2$ and the lines $y=x, x=0$ and $x=3$, is

The area of the region lying in the first quadrant bounded by $\mathrm{y}=4 x^2, x=0, \mathrm{y}=2,

Area (in sq. units ) lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and the lines

The area bounded between the curves $y=a x^2$ and $x=a y^2(agreater than0)$ is 1 sq.units then the v

The area (in sq. units) of the region described by $\left\{(x, y) / y^2 \leq 2 x\right.$ and $\left.

The area enclosed between the parabola $y^2=4 x$ and the line $y=2 x-4$ is

The area (in sq. units) of the region bounded by $y-x=2$ and $x^2=y$ is equal to

The value of $\mathrm{I}=\int_{\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\mathrm{x}^2 \cos \mathrm{x}}{1+

The value of $\int_{-\pi / 2}^{\pi / 2} \frac{\sin ^2 x}{1+2^x} d x$ is

$$I=\int_{\sqrt{\cos 2} 2}^{\sqrt{\log 2} 3} \frac{x \sin x^2}{\sin x^2+\sin \left(\log _c 6-x^2\r$$

The value of integral $\int_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{\sqrt{1+\cos x}}{(1-\cos x)^{5 / 2

The integral $\int_{\text {-/2 }}^{1 / 2}\left([x]+\log _c\left(\frac{1+x}{1-x}\right)\right) d x$,

The value of integral$\int_{-2}^0 (x^3+3 x^2+3 x+3+(x+1)\cos (x+1) dx.$is equal to

$$\int_{0.2}^{35}[x] d x=$$

$\int_b^{\frac{\pi}{2}}|\sin x-\cos x| d x$ has the value

The integral $\int_{\% / 6}^{\pi / 6} \frac{d x}{\sin 2 x\left(\tan ^5 x+\cot ^5 x\right)}$ is equal

let $f$ and $g$ be continuous functions on $[0, a]$ such that $\mathrm{f}(x)=\mathrm{f}(a-x)$ and $\

If $\int_0^{3 / 2} \frac{\tan \theta}{\sqrt{2 k \sec \theta}} d \theta=1-\frac{1}{\sqrt{2}},(kMORETH

$$\int_0^{\frac{\pi}{4}} \log \left(\frac{\sin x+\cos x}{\cos x}\right) d x=$$

The value of the integral $\oint_b^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x+\sqrt{\tan x}}}