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In a college of 300 students, every student reads 5 news paper and every newspaper is read by 60 students. The no. of newspaper is

If $p\Rightarrow (q\vee r)$ is false, then the truth values of p,q,r are respectively

The minimum value of the function $f\left(x\right)=|2-|1-x||-1,$ where $|x|$ denotes the absolute value of $x,$ is

Consider the function $f\left(x\right)$ and $g\left(x\right)$ on $R,$ defined as $f\left(x\right)=2x-x^2$ and $g\left(x\right)=x^n$ where $n\in N.$ If the area between $y=f\left(x\right)$ and $y=g\left(x\right)$ in the first quadrant is $\frac{1}{2}$ sq. unit, then $n$ is a divisor of

Let $z$ be a unimodular complex number having the argument $\theta$, $0<\theta <\frac{\pi }{2}$ and satisfying the relation $|z-3i|=3,$ then $\arg (\cot \theta -\frac{6}{z})$ is

9th term of the expansion $(4x-\frac{1}{2\sqrt{x}}{)}^{12}$is

The number of values of $\theta$ in the interval (- $\frac{\pi }{2}$, $\frac{\pi }{2}$) satisfying the eqautions

(1 - tan$\theta$)(1 + tan$\theta$)$se{c}^2$$\theta$ + $2^{ta{n}^2\theta }$ = 0

If the orthocenter of a triangle is $(6,3)$ and centroid is $(2,5)$, then find the circumcenter of the triangle.

In a triangle coordinates of orthocenter and circumcenter are $(-3,5,2)$ and $(6,2,5)$. Find the coordinates of centroid of the triangle.

Find the ratio in which the YZ-plane divides the line segment formed by joining the points $(-2,4,7)$ and $(3,-5,8).$

If $(h,k)$ is the centre of $x^2+y^2-2x-4y+11=0$, find the value of $h^2+k^2+hk$.

Let $p\left(x\right)$ be a polynomial such that $\frac{p(x+1)}{p\left(x\right)}=\frac{x^2+x+1}{x^2-x+1}$ and $p\left(2\right)=3$, then ${\int }_0^1{\tan }^{-1}\left(p\right(x\left)\right)\cdot {\tan }^{-1}\sqrt{\frac{x}{1-x}}dx$ is

Find the equation of a straight line which passes through the point (3, 4) and sum of its intercepts on the x and y axis is 14.

If every pair of the equations $x^2+px+qr=0,x^2+qx+rp=0,x^2+rx+pq=0$ have a common root, then the sum of three common roots is

Find the number of dissimilar terms in the expansion of $(x+y{)}^{32}$

If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg \left(\frac{1+z}{1+\overline{z}}\right)$ equals :

If $\exp \left[\right({\sin }^{2}x+{\sin }^{4}x+{\sin }^{6}x+....\infty ){\log }_{e}2$, satisfies the equation $x^2-9x+8=0$, then the value of $\frac{\cos x}{\cos x+\sin x},0<x<\frac{\pi }{2}$ is

Let $f\left(x\right)=\left|{\sin }^{-1}\right(\sin x\left)\right|-\left(\frac{\pi -x}{2}\right)$. Then number of solutions of equation $f\left(x\right)=0$ in $x\in [-\pi ,\pi ]$ is

The centre of the circle passing through (0, 0) and (1, 0) and touching the circle $x^2+y^2=9$ is

If the equation $2x^4+7x^3+ax+b=0$ has four roots (All real roots) then find the value of a and b. Given that (x - 3) and (x - 1) may exactly divide the above given expression.

The equation(s) of standard ellipse which passes through the point $(-3,1)$ and has eccentricity $\sqrt{\frac{2}{5}}$, is/are

The graph of a quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is shown below. Then which of the following option(s) is/are correct ?

If $\alpha$ is a root of $4x^2+2x-1$ = 0. then root is:

An element has a body-centered cubic unit cell. If one of the atom from the corner is removed. Calculate the packing fraction.

Solve the inequalities: $6\le -3(2x-4)<12$

Let the mean of $n$ terms be $\overline{x}$, if the first term is increased by $1$, second term is increased by $2$ and so on, then the new mean is

If $(1+ax{)}^n$ = 1 + 8x + 24 $x^2$ + ......, then the value of a

and n is

A hen lays eight eggs. Each egg was weighed and recorded as, 60g, 56g, 61g, 68g, 51g, 53g, 69g and 54g. Find the mean and standard deviation.

If $A$ and $B$ are square matrices of the same order and $A$ is non-singular, then for a positive integer $n,(A^{-1}BA{)}^n$ is equal to

If |$z_1|=|z_2|=|z_3|=|z_4|=1$ and $z_1+z_2+z_3+z_4=0$

then least value of the expression

$E=|z_1-z_2{|}^2+|z_2-z_3{|}^2+|z_3-z_4{|}^2+|z_4-z_1{|}^2$ is

In the above figure first derivative (f’(x)) of the function y = f(x) at point P will be equal to

If the equation $4\sin (x+\frac{\pi }{3})\cos (x-\frac{\pi }{6})=a^2+\sqrt{3}\sin 2x-\cos 2x$ has a solution, then the value of $a$ can be

If $\alpha ,\beta$ are the roots of $a{x}^2+bx+c=0$ and $\alpha +\beta ,{\alpha }^2+{\beta }^2,{\alpha }^3+{\beta }^3$ are in G.P., where $△=b^2-4ac$, then

Let $|A|=|a_{ij}{|}_{3\times 3}\ne 0$. Each element $a_{ij}$ multiplied by $k^{i-j}$. Let |B| be the resulting determinant, where $k_1|A|+k_2|B|=0.Then{k}_1+k_2=$

The number of solutions of ${16}^{{\sin }^{2}x}+{16}^{{\cos }^{2}x}=10$ in the interval $x\in [0,\pi ]$ is

If the line x+2by+7=0 is a diameter of the circle $x^2+y^2-6x+2y=0$, then b=

The sum of the series $1+3x+5x^2+7x^3+\dots$ upto $n$ terms is

Match the lines given on the left side with their corresponding slopes on the right..
$\begin{array}{cc}Linepassesthroughthepoints& Slopeoftheline\\ p.\left)\right(1,6\left)and\right(-4,2)& 1.)0\\ q.\left)\right(5,9\left)and\right(2,9)& 2.)-3\\ r.\left)\right(-2,-1\left)and\right(-3,2)& 3.)\frac{4}{5}\\ s.\left)\right(4,0\left)and\right(3,3)& 4.)\frac{5}{3}\end{array}$

The equation of the directrix of the parabola $x^2-4x-3y+10=0$ is

Let $S_n=1+q+q^2+\cdots +q^n$ and $T_n=1+\left(\frac{q+1}{2}\right)+{\left(\frac{q+1}{2}\right)}^2+\cdots +{\left(\frac{q+1}{2}\right)}^n$ where $q$ is a real number and $q\ne 1$. If ${}^{101}{C}_1{+}^{101}{C}_2\cdot S_1+\cdots +{}^{101}{C}_{101}\cdot S_{100}=\alpha T_{100}$, then $\alpha$ is equal to :

A,B and C are events such that $P\left(A\right)=0.3,P\left(B\right)=0.4,P\left(C\right)=0.8,P(A\cap B)=0.08,P(A\cap C)=0.28$and $A\cup B\cup C)\ge 0.75$ show that $P(B\cap C)$ lies in the interval [0.23, 0.48]

Or

An integer is chosen random from 1 to 50, what is the probability that the integer chosen, is a multiple of 2 or 3 or 10?

If $ta{n}^{2}A=2ta{n}^{2}B+1$ then the value of $cos2A+si{n}^{2}B$.

In throwing a pair of dice, find the probability of getting a total of 8.

Complete solution set $\left[{\cot }^{-1}x\right]+2\left[{\tan }^{-1}x\right]=0$, where $[.]$ denotes the greatest integer function, is

If $y=\sqrt{(a-x)(x-b)}-(a-b)ta{n}^{-1}\sqrt{\left(\frac{a-x}{x-b}\right)}$, then $\frac{dy}{dx}$ is equal to

The lines $\frac{x-a+d}{\alpha -\delta }=\frac{y-a}{\alpha }=\frac{z-a-d}{\alpha +\delta }$ and $\frac{x-b+c}{\beta -\gamma }=\frac{y-b}{\beta }=\frac{z-b-c}{\beta +\gamma }$ are coplanar and then equation to the plane in which they lie, is