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Which of the following is the correct relation between kWh and Joule?

The domain of the function ${\cos }^{-1}(3x-2)$ is

If $1-p$ is a root of the equation $x^2+px+1-p=0$, then the roots of the equation are

Let $A=\{1,4,9,25\}$ and $B=\{-5,-3,-2,-1,1,2,3,5\}$, if relation from $A$ to $B$ is $R=\left\{\right(1,1),(1,-1),(4,2),(4,-2),(9,3),(9,-3),(25,5),(25,-5\left)\right\}$, then the set builder form of relation is

A contest consists of predicting the results win, draw or defeat of 7 foot ball matches. A sent his entry by predicting at random. The probability that his entry will contain exactly 4 correct predictions is:

If ${\tan }^2(x+y)+{\cot }^2(x+y)=1+2x-x^2,$ then the correct option(s) is/are

If $A=\{1,2,3\}$ and $B=\{4,5\},$ then $A\times B=$ ___.

The number of ways of choosing $10$ objects out of $31$ objects of which $10$ are identical and the remaining $21$ are distinct, is

If $z_1=2-i$ and $z_2=1+i$, find $\left|\frac{z_1+z_2+1}{z_1-z_2+1}\right|$

For the complex number z, which of the following is true?

The orthocenter of the triangle formed by the lines $xy=0$ and $x+y=1$ is

The probability that randomly selected positive integer is relatively prime to 6

$n^{th}$ term of the series 2 + 4 + 7 + 11 + ...... will be

Match the following (a > 0)
(1) | x| $\le$ a (P) -a $\le$ x $\le$ a
(2) | x| $\ge$ a (Q) x $\le$ -a or x $\ge$ a
(3) | x| - a = 0 (R) x = a or x = -a
(4) $|x-a|$ = 0 (S) x = a
(5) $x^2$ $\le$ $a^2$

Let $z=cos\theta +isin\theta$. The value of ${\sum }_{m=1}^{15}Im\left(z^{2m-1}\right)$ at $\theta =2^{\circ }$

If the centroid and a vertex of an equilateral triangle are $(2,3)$ and $(4,3)$ respectively, then the other two vertices of the triangle are

The trigonometric form of $z=(1-icot8{)}^3$ (where $i=\sqrt{-1}$) is

If $T_r$ denotes the rth term in the expansion of ${(x+\frac{1}{y})}^{23}$ then

Find the value of $\frac{co{s}^{3}A-cos3A}{cosA}$ + $\frac{si{n}^{3}A-sin3A}{sinA}$

Given $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$ Find the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Vertex of the parabola whose parametric equation is $x=t^2-t+1,y=t^2+t+1;t\in R,$ is

Which of the following can be the parametric equation of

$(x-1{)}^2=-36(y-4)$

The logical statement $(p\Rightarrow q)\wedge (q\Rightarrow \sim p)$ is equivalent to

The minimum value of $|z-1|+|z-3|$ is

If $x$ satisfies the inequality ${\log }_{x+3}(x^2-x)<1,$ then

If the mapping $f\left(x\right)=ax+b,a>0$ maps $[-1,1]$ onto $[0,2]$ then $\cot [{\cot }^{-1}7+{\cot }^{-1}8+{\cot }^{-1}18]$ is equal to

If the distance of the point P (1, -2, 1) from the plane $x+2y-2z=\alpha$ where $\alpha >0$, is 5, then the foot of the perpendicular form P to the plane is

The value of $\underset{x\to 0}{lim}\frac{(1+x{)}^{1/x}-e+\frac{1}{2}ex}{x^2}$ is

Given n observations x₁, x₂ ......x_n and their central tendency a. Find the mean deviation about a.

If $U=\{11,12,13,14,15,16\},$ and $A=\{12,14,16\}$, then $A^{\prime }$ is:

The value of $\int \frac{1}{\sqrt{{(x-1)}^2+{\left(\sqrt{2}\right)}^2}}dx$ is

${\left(\frac{cos\theta +isin\theta }{sin\theta +icos\theta }\right)}^4$ equals

The number of points in the rectangle $\left\{\right(x,y)|-12\le x\le 12\text{and}-3\le y\le 3\}$ which lie on the curve $y=x+\sin x$ and at which the tangent to the curve is parallel to the $x$ - axis is