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cosec A - 2cot 2A cos A =

If z is a complex number, then the minimum value of |z|+|z-1| is

The function $f\left(x\right)=x^2(x-2{)}^2$

The standard deviation of 4 consecutive numbers which are in A.P is $\sqrt{5}$. The common difference (d) of this A.P is

If $a_1$, $a_2$, $a_3$, ........$a_{24}$ are in arithmetic progression and $a_1$ + $a_5$ + $a_{10}$ + $a_{15}$ + $a_{20}$ + $a_{24}$ = 225, then find the value of

$a_1$ + $a_2$ + $a_3$ + ..........+ $a_{23}$ + $a_{24}$

If the area of the pentagon formed by the vertices $A(1,3),B(-2,5),C(-3,-1),D(0,-2)$ and $E=(2,t)$ is $\frac{45}{2}\text{sq. units}$, then possible value(s) of $t$ is/are

If $1+sinx+si{n}^{2}x+.......\infty =4+2\sqrt{3}$, 0< x< $\pi ,x\ne \frac{\pi }{2}$, then x =

Let $A_n=[a_{ij}{]}_{n\times n}$ be a $(n\times n)$ determinant with the following conditions

$a_{ij}=\left\{\begin{array}{cc}9,& i=j\\ 3,& |i-j|=1\\ 0,& \text{other wise}\end{array}\right\}$ then

In a cricket match, the runs scored by $11$ players are as follows:





Find the mode of this data.

The number of Goals scored by Messi in Laliga for the past 7 years are as follows. 23, 34, 31, 50, 46, 28, 43. What is the Range of his Goals for past 7 seasons?

Evaluate the integral ${\int }_0^{\frac{\pi }{2}}\sin xdx$

If $1,\omega$ and ${\omega }^2$ are the cube roots of unity, then $\Delta =\left|\begin{array}{ccc}1& {\omega }^n& {\omega }^{2n}\\ {\omega }^n& {\omega }^{2n}& 1\\ {\omega }^{2n}& 1& {\omega }^n\end{array}\right|$ is equal to

In the expansion of $(1+x+x^3+x^4{)}^{10},$ the coefficient of $x^4$ is

In $8$ people, there are more girls than boys. How many girl could be there?

If $\frac{1}{(1-\frac{y}{x}{)}^{\frac{1}{2}}}$ = $1+\frac{1}{k}\frac{y}{x}$,find the value of k(x>>y)

Area enclosed by curve $y^3-9y+x=0$ and Y - axis is -

If $0\le x<\frac{\pi }{2}$, then the number of values of $x$ for which $\sin x-\sin 2x+\sin 3x=0$, is :

Find the value of $\underset{x\to a}{lim}\frac{x^n-a^n}{x-a}$

In a triangle $ABC,a^{3}cos(B-C)+b^{3}cos(C-A)+c^{3}cos(A-B)=$

Find the sum of the GP \((1+x)^{21}+(1+x)^{22}+......(1+x)^{30}

Find the sum of the series 0.6 + 0.66 + 0.666 + ... .

Or

The product of the three numbers in GP is 216. If 2, 8 and 6 be added to them, then the results are in Al, find the numbers.

The equations of tangents drawn from the point (2,3) to the ellipse $9x^2+16y^2=144$ are:

A box $B_1$ contains $1$ white ball, $3$ red balls, and $2$ black balls. Another box $B_2$ contains $2$ white balls, $3$ red balls, and $4$ black balls. A third box $B_3$ contains $3$ white balls, $4$ red balls, and $5$ black balls.

If 1 ball is drawn from each of the boxes $B_1,B_2$ and $B_3$ the probability that all $3$ drawn balls are of the same colour is

The vectors $\overrightarrow{x}$ and $\overrightarrow{y}$ satisfy the equation $p\overrightarrow{x}+q\overrightarrow{y}=\overrightarrow{a}$ (where $p,q$ are scalar constants and $\overrightarrow{a}$ is a known vector). It is given that $\overrightarrow{x}.\overrightarrow{y}\ge \frac{|\overrightarrow{a}{|}^2}{4pq}$, then $\frac{|\overrightarrow{x}|}{|\overrightarrow{y}|}$ is equal to ($pq>0$)

The sides of a rectangle are $x=0,y=0,x=4,y=3$. The equation of the straight line having slope $\frac{1}{2}$ that divides the rectangle into two equal halves, is

The solution set of the inequality ${\log }_3\left(\right(x+2\left)\right(x+4\left)\right)+{\log }_{1/3}(x+2)<\frac{1}{2}{\log }_{\sqrt{3}}7$ is

Sum of coefficients of the following expansion $(x+2y+3z{)}^8$ is ____

If $f\left(x\right)=30-2x-x^3$, then the number of positive integral value(s) of $x$ satisfying $f\left(f\right(f\left(x\right)\left)\right)>f\left(f\right(-x\left)\right)$ is

(correct answer + 1, wrong answer - 0.25)

What are the points on the y - axis whose distance from the line $\frac{x}{3}+\frac{y}{4}=1$ is 4 units.

There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84$, then the value of $m$ is :

The roots of the equation $a(x^2+1)-(a^2+1)x$ = 0 are

If ${\cos }^{-1}x+{\cos }^{-1}y+{\cos }^{-1}z=\pi$, then

If x is real, then the minimum value of $x^2-8x+17$ is……

If a function $f:[-2,\infty )\to R$ is such that $f\left(x\right)=x^2+4x-|x^2-4|,$ then the value(s) $f\left(x\right)$ can have is (are)

The angle between pair of tangents drawn from any point on the circle $x^2+y^2=a^2$ upon the circle $x^2+y^2=b^2$ is $\frac{\pi }{3}$. Then, the locus of mid point of chord of contact is

The distance of the point $(1,3,–7)$ from the plane passing through the point $(1,–1,–1),$ having normal perpendicular to both the lines $\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}$ and $\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1}$, is:

If 2|3x+9|<36, then the number of integral values of x is

Solution of the inequality |3 - ${\log }_{2}x$| < 2 is ______.

If $arg\left(z\right)<0$, then $arg(-z)-arg\left(z\right)$ equals

$li{m}_{x\to a}$$\frac{\left(\sqrt{3x-a}\right)-\left(\sqrt{x+a}\right)}{x-a}$ =

Consider the curve $\sin x+\sin y=1$, lying in the first quadrant , then

$\begin{array}{cccc}& \text{List- I}& & \text{List-II}\\ \text{(I)}& \underset{x\to \pi /2}{lim}\frac{d^{2}y}{d{x}^2}=& \text{(P)}& 0\\ \text{(II)}& \underset{x\to 0^{+}}{lim}{x}^{3/2}\frac{d^{2}y}{d{x}^2}=& \text{(Q)}& 1\\ \text{(III)}& \underset{x\to 0^{+}}{lim}{x}^2\frac{d^{2}y}{d{x}^2}=& \text{(R)}& \frac{1}{\sqrt{2}}\\ \text{(IV)}& \underset{x\to \pi /2}{lim}\frac{dy}{dx}=& \text{(S)}& \frac{1}{2\sqrt{2}}\\ & & \text{(T)}& \sqrt{2}\\ & & \text{(U)}& 3\end{array}$



Which of the following is the only CORRECT combination?

Let $\omega$ be a complex cube root of unity with $\omega \ne 0$ and $P=\left[p_{ij}\right]$ be an $n\times n$ matrix with $P_{ij}={\omega }^{i+j}$. Then $P^2=0$ when n is equal to