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In a group of 65 people 40 like cricket, 10 like both cricket and tennis, how like tennis only and not cricket?

${lim}_{x\to 0}\frac{2x^2+3x+4}{x^2+3x+2}$

Find the roots of the equation $2x^2+4x+6=0$

The Value of ${}^{14}{C}_2+{}^{14}{C}_3+{}^{14}{C}_4+.....+{}^{14}{C}_{14}$ is

Consider a plane x + y - z = 1 and the point A(1, 2, -3). A line L has the equation x = 1 + 3r, y = 2 – r, z = 3 + 4r.
The coordinate of a point B of line L, such that AB is parallel to the plane, is

The vertices of an acute angled triangle are $A(x_1,x_1\tan \alpha ),B(x_2,x_2\tan \beta )$ and $C(x_3,x_2\tan \gamma ).$ If origin is the circumcentre of $△ABC$ and $H(a,b)$ be its orthocentre, then $\frac{b}{a}$ equals to
(where $x_1,x_2,x_3$ are positive)

If the inclination of the line joining the points $(x,-3)$ and $(2,5)$ is ${135}^{\circ }$, then the value of $x$ is

Find all the points on x+y=2, which are at a distance of $\frac{4}{5}$ units from 4x+3y=7.

If $x_1$ and $x_2$ are two real solutions of the equation $(x{)}^{\ln x^2}=e^{18},$ then the product $(x_1.x_2)$ equals

Equations to the sides of a triangle are $x-3y=0$, $4x+3y=5$ and $3x+y=0$. The line $3x-4y=0$ passes through the

Column – 1 represents equation of straight lines
Column – 2 represents position of points A $\equiv$ (1, 4) and B(4, 3) w.r.t. equation of line in Column - 1
Column – 3 represents the sum of length of perpendiculars from points A and B to the lines in Column-1
$\begin{array}{ccc}Column1& Column2& Column3\\ \left(I\right)L_1:y-x+1=0& \left(i\right)Bothpointslieonthesamesideoftheline& \left(p\right)\frac{7\sqrt{5}}{5}units\\ \left(II\right)L_2:6y+x-11=0& \left(ii\right)Bothpointslieontheoppositesideoftheline& \left(Q\right)2\sqrt{2}units\\ \left(III\right)L_3:y-2x+2=0& \left(iii\right)Bothpointslieontheline& \left(R\right)\frac{25\sqrt{37}}{37}units\\ \left(IV\right)L_4:3y+x-13=0& \left(iv\right)Onepoint(outofA,B)lieontheline& \left(S\right)0units\end{array}$
Which of the following options is the only INCORRECT combination?

If $x\frac{dy}{dx}=y(logy-logx+1)$, then the solution of the equation is

Find $\frac{dy}{dx}$of the functions given in question.

$y^x=x^y.$

Round the following numbers to 2 significant digits

(a) 3472,

(b) 84.16,

(c) 2.55 and

(d) 28.5.

The square root of $3-4i$ is

Write the value of $\sqrt{-25}\times \sqrt{-9}.$

The line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{0}$ is parallel to

The solution of the equation $8\sin x=\frac{\sqrt{3}}{\cos x}+\frac{1}{\sin x}$ is/are given by

Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7)

The pole of $3x+4y-45=0$ with respect to the circle $x^2+y^2-6x-8y+5=0$ is

Let f(n) = $[\frac{1}{2}+\frac{(n-1)}{50}]\left(n^2\right)$, where [n] denotes the greatest integer less than or equal to n, then ${\sum }_{n=1}^{100}f\left(n\right)$ is equal to;

Let $A$ be the set of first $10$ natural numbers and $R$ be a relation on $A$ defined by $(x,y)\in R\iff x+2y=10.$ Then the range of $R$ is

A wheel make 360 revolutions in one minute .Through how many radians does it turn in one second

The slope of the line formed by joining the points A(1, 3) and B(4, 7) is .

Ravi and Fathima have two kids - Tina and Bobby. Fathima is Bobby's _____.

For the differential equation given in the question find a particular solution satisfying the given condition.

$(1+x^2)\frac{dy}{dx}+2xy=\frac{1}{1+x^2},$where y=0 and x=1.

${lim}_{x\to 1}\frac{sin\pi x}{x-1}$ is equal to

(i) A company is having a current ratio of 3 : 1. Its current liabilities are Rs 90,000. The accountant of the firm is interested in maintaining it to its standard ratio by purchasing certain assets on credit. Find out the value of asset to be purchased.

(ii) A company is having its operating ratio equals to 80$\%$. Find out its operating profit ratio.

$$\begin{array}{cc}TrigonometricEquations& GeneralSolutions\\ 1.tanx=2& P.2n\pi \pm \frac{2\pi }{3},n\in I\\ 2.sinx=\frac{\sqrt{3}}{2}& Q.n\pi -\frac{\pi }{4},n\in I\\ 3.cosx=\frac{-1}{2}& R.n\pi +(-1{)}^n\frac{\pi }{3},n\in I\\ 4.cotx=-1& S.n\pi +ta{n}^{-1}\left(2\right),n\in I\end{array}$$

There are 25 railway stations between Nellore and Hyderabad. The number of different kinds of single second class tickets to be printed so as to enable a passenger to travel from one station to another is

Prove that:

$\frac{cos\theta }{1-sin\theta }=tan(\frac{\pi }{4}+\frac{\theta }{2})$

If $(p\wedge \sim q)\wedge (p\wedge r)\to \sim p\vee q$ is false, then the truth values of $p,q$ and $r$ are, repectively :

Consider three functions, $f\left(x\right)=x^3+x^2+x+1,g\left(x\right)=\frac{2x}{x^2+1}andh\left(x\right)=si{n}^{-1}x-co{s}^{-1}x+ta{n}^{-1}x-co{t}^{-1}x$ and let p(x) be a differentiable function on R defined as $p\left(x\right)=\{\begin{array}{c}a{\int }_0^x\sqrt{p\left(t\right)}dt+b;x>0\\ x^2+4x+1;x\le 0\end{array}where,a,bϵ(0,\infty )$ and tangent drawn to the graph of p(x) at x = 1 is y = mx + c
$\begin{array}{cccccc}& Column1& & Column2& & Column3\\ \left(I\right)& Ifrangeoff\left(g\right(x\left)\right)is[l,m],& \left(i\right)& a=& \left(P\right)& 1\\ & then(l+m)=& & & & \\ \left(II\right)& Thenumberofintegersinthe& \left(ii\right)& b=& \left(Q\right)& 3\\ & rangeofg\left(f\right(x\left)\right)isequalto& & & & \\ \left(III\right)& Themaximumvalueof& \left(iii\right)& |c|=& \left(R\right)& 4\\ & g\left(h\right(x\left)\right)isequalto& & & & \\ \left(IV\right)& Iftheminimumvalueof& \left(iv\right)& (m-7)=& \left(S\right)& 5\\ & h\left(g\right(f\left(x\right)\left)\right)is\frac{k\pi }{2},then|k|isequalto& & & & \end{array}$
Which of the following option is the only correct combination?

For natural numbers m, n if ${(1-y)}^m{(1+y)}^n=1+a_{1}y+a_2{y}^2+...and{a}_1=a_2=10,then(m,n)$ is

Find the equation of the line mid - way between the parallel lines $9x+6y-7=0$ and $3x+2y+6=0$.

Show that the Signum function $f:R\to R,$ given by $f\left(x\right)=\{\begin{array}{c}1,ifx>0\\ 0,ifx=0\\ -1,ifx<0\end{array}$ is neither one-one nor onto.

$f\left(x\right)=2\left|\frac{x-1}{x-1}\right|\forall x\&x\ne 1$, What should be the value of f(x) at x=1 so that it is differentiable from $(-\infty ,\infty )$

If $P\left(B\right)$ = 0.5 and $P(A\cap B)=0.32$, find $P\left(\frac{A}{B}\right)$ .

The number of possible outcomes in a throw of $5$ ordinary dice in which at least one of the dice shows an odd number is

If $ln=\int (1+x+x^{-1})e^{x+x^{-1}}dx=$

Find the cube of $a+3b$.

Find the value ${\left(tan\right(22\frac{1}{2})}^{\circ }\times (\sqrt{2}+1)$

Show that the given differential equation is homogeneous and then solve it.

$(x^2-y^2)dx+2xydy=0$