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If A is in the III quadrant, 3 tan A –4 = 0 then 5 sin 2A + 3 sin A + 4 cos A=

Which of the following is the graph for identity function?

For the equation of ellipse, $\frac{x^2}{4}+\frac{y^2}{9}=1,$ what does $S_1$ correspond to

The number of roots of the equation log(-2x) = 2 log(x+1) are

A and B are two non-singular square matrices of order $3\times 3$ such that AB = A and BA = B then

If R = {(x, y) : x, y $ϵ$ Z, $x^2+y^2\le 4$ } is a relation is Z, then domain of R is

A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that

(i) all the three balls are blue balls

(ii) all the balls are of different colours.

Match the following. Equation of the parabola is $y^2=4ax$

$\begin{array}{cc}\text{Column 1}& \text{Column 2}\\ \text{P) Focal distance}& \text{T) Focal chord perpendicular to axis}\\ \text{Q) Double ordinate}& \text{U) A chord perpendicular to axis}\\ \text{R) Latus rectum}& \text{V) Distance of a point on parabola from directrix}\\ \text{S) Vertex}& \text{W) Meeting point of axis and parabola}\end{array}$

Let R be the real line. Consider the following sub-sets of the plane $R\times R$ S = {x,y}:y = x + 1 and 0 < x < 2, T = {(x,y):x - y} is an integer. Which of the following is true

Find the value of $\theta$ and p, if the equation $xcos\theta +ysin\theta =p$ is the normal form of the line $\sqrt{3}x+y+2=0.$

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?

If rth term is the middle term in the expansion of ${(x^2-\frac{1}{2x})}^{20}$, then $(r+3{)}^{th}$ term is

Equation of the line on which the length of the perpendicular from origin is 5 and the angle which this perpendicular makes with the x axis is ${60}^{\circ }$.

Let A be a non singular, symmetric matrix of order three such that $A=adj(A+A^T)$, then

The sum of the series ${31}^3+{32}^3+\dots \dots +{50}^3$ is

The number of common tangents to the circles $x^2+y^2=4$ and $x^2+y^2-6x-8y=24$ is

Prove that:

$\frac{sin\theta +sin2\theta }{1+cos\theta +cos2\theta }=tan\theta$

$\underset{x\to 0}{lim}\frac{x{.2}^x-x}{1-cosx}$

The set of all points of discontinuity of $f\left(x\right)=\frac{x-1}{x^3+6x^2+11x+6}$ is

Six boys and six girls sit in a row randomly.

The probability that all girls sit together is

If A is a square matrix of order n such that |adj (adj A)|$=|A{|}^9$, then the value of n can be

Five different marbles are placed in 5 different boxes randomly. Then the probability that exactly two boxes remain empty is (each box can hold any number of marbles).

Find the equation of lines through the point of intersection of the lines $x-y+1=0$ and $2x-3y+5=0$ whose distance from the point $(3,2)is\frac{7}{5}$.

Period of the function 2 sin⁴x + 3 cos⁴x is

Suppose $z$ is any root of $11z^8+20i{z}^7+10iz–22=0$, where $i=\sqrt{-1}$ . Then $S=|z{|}^2+|z|+1$ satisfies

If $\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{C}+\overrightarrow{D}$, then select the correct alternative:

If A and B are two events associated with a random experiment such that $P\left(A\right)=0.3,P\left(B\right)=0.4$ and $P(A\cup B)$ = 0.5, find $P(A\cap B)$

If ${}^n{C}_2+{}^n{C}_3={}^{n+1}{C}_r$, then the minimum possible value of $r$ is

Domain of $\frac{1}{\ln (x-4)}$ is

If $\sin x=\frac{2t}{1+t^2},\tan y=\frac{2t}{1-t^2}$
then $\frac{dy}{dx}$ is equal to

What is the mean of $f\left(x\right)=3x+2$ where $x$ is a random variable with probability distribution
$\begin{array}{ccccc}X=x& 1& 2& 3& 4\\ P(X=x)& \frac{1}{6}& \frac{1}{3}& \frac{1}{3}& \frac{1}{6}\end{array}$

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
both balls are red.

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
first ball is black and second is red.

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability. that
one of them is black and other is red

There are $8$ events that can be scheduled in a week, then total number of ways that these $8$ events are scheduled on exactly $6$ days of a week is given by $266\times k!$ where $k\in N$, then $k$ is

There are $4$ candidates for the post of a professor in Mathematics and one is to be selected by a opinion of $5$ subject experts. The number of the way in which the experts opinion can be expressed is

Verify that the points (3, -2, 4), (1, 0, -2) and (-1, 2, -8) are collinear.

The coordinates of a point common to a directrix and an asymptote of the hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$ are