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If $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$ are the vertices of a triangle, then the excentre opposite to B is

Using binomial theorem, prove that $2^{3n}-7n-1$ is divisible by 49, where $n\in N.$

Number of $2$-digit numbers (having different digits), which are divisible by $5$ is

If $y={\log }_{\cos x}\left(\tan x\right)$, then $\frac{dy}{dx}{|}_{x=\frac{\pi }{4}}$ is equal to

The angular points of a triangle are $A(–1,–7),B(5,1)$ and $C(1,4)$. The equation of the bisector of the angle $\angle ABC$ is

If $f\left(x\right)=cos\left(logx\right)$, then value of $f\left(x\right)$
$f\left(4\right)-\frac{1}{2}\{f\left(\frac{x}{4}\right)+f(4x\left)\right\}$ is

If $f:R\to R$ is a function such that $f\left(x\right)=x^3+x^2{f}^{\prime }\left(1\right)+x{f}^{\prime \prime }\left(2\right)+f^{\prime \prime \prime }\left(3\right)$ $\forall x\in R,$ then $f\left(2\right)-f\left(1\right)=$

$I={\int }_0^{a}ln(cota+tanx)dx$, where $aϵ(0,\frac{\pi }{2})$, then I is equal to

If the coefficient of the middle term in the expansion of $(1+x{)}^{2n+2}$ is $\alpha$ and the coefficients of middle terms in the expansion of $(1+x{)}^{2n+1}$ are $\beta$ and $\gamma$, then relation between $\alpha ,\beta$ and $\gamma$ is-

If $U=\{1,3,5,7,9,11,13\}$, then which of the following is/are the subsets of $U$?

The probability that a student is not a swimmer is 1/5. The probability that out of five students, four are swimmers is

(a) ${}^5{C}_4{\left(\frac{4}{5}\right)}^4\frac{1}{5}\left(b\right){\left(\frac{4}{5}\right)}^4\frac{1}{5}\left(c\right){}^5{C}_1\frac{1}{5}{\left(\frac{4}{5}\right)}^4$

(d) None of these

Find the equation of the plane through the points (2,1,0), (3,-2,-2) and (3,1,7).

The value of the integral ${\int }_0^{\infty }\frac{x\mathrm{dx}}{\left(1+x\right)\left(1+x^2\right)}$ is equal to

The function is defined by f(x)=$\{\begin{array}{c}k{x}^2,ifx\le 2\\ 3,ifx>2\end{array}$

Find the particular solution of the differential equation $\frac{dy}{dx}=1+x+y+xy$, given that $y=0$ when $x=1$

If A and B are square matrices of the same order such that AB=BA, then prove by induction that A$B^n$=$B^n$A. Further, prove that $(AB{)}^n$ =$A^n$$B^n$ for all $n\in N$.

The value of Sin(2tan^-11/3)+cos(tan^-12√2) is?

I am not understanding this question:if A={5,7,9,11},B={9,10} let a R b means a<b.a belongs to A ,(a,b) belongs to R,b belongs to b .Then

Sir I am not able to understand the topic 'singleton/unit set'. Please help me to understand this topic.

The period of the function $y={\sin }^{-1}\left(\sin x\right)$ is

Sin(n+1)A sin(n+2)A + cos(n+1)A cos(n+2)A=

Let $(1+x+x^2{)}^{2014}=a_0+a_{1}x+a_2{x}^2+a_3{x}^3+...+a_{4028}{x}^{4028},$ and let

$A=a_0-a_3+a_6-...+a_{4026},B=a_1-a_4+a_7-...-a_{4027},C=a_2-a_5+a_8-...+a_{4028}.$

Then

The family of curves satisfying the differential equation $\frac{dy}{dx}+\frac{1}{x}\sin 2y=x^3{\cos }^{2}y,$ is
(where $C$ is an arbitrary constant)

The differentiation of ${\cos }^{-1}\left(\frac{1-x^2}{1+x^2}\right)$ w.r.t. x is

The straight line $y=2x+\lambda$ does not meet the parabola $y^2=2x$, if

Let R be relation defined on the set of natural number N as follows, $R=\left\{\right(x,y):x\in N,2x+y=41\}$, Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

The feasible region for a LPP is shown in the following figure. Evaluate Z=4x +y at each of the corner points of this region. Find the minimum value of Z, if it exists.

In a survey of 100 students, the number of students studying the various languages were found to be : English only 18, English but not Hindi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and Hindi 8, no language 24. Find :

(i) How many students were studying Hindi ?

(ii) How many students were studying English and Hindi ?

The maximum value of $3\cos \theta +5\sin (\theta -\frac{\pi }{6})$ for any real value of $\theta$ is:

If $y={\log }_{\sin x}\left(\tan x\right)$, then ${\left(\frac{dy}{dx}\right)}_{x=\frac{\pi }{4}}$ is

If P and Q are two sets such that P has 40 elements, $P\cup Q$ has 60 elements and $P\cap Q$ has 10 elements, how many elements does Q have ?

The number of divisor of $2^5{.3}^4{.5}^2{.7}^3.11$ is equal to:

Find the no.of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that:

(a)All vowels occur together.

(b)All vowels do not occur together.

Let $f:[-2,2]\to R$ defined by $f\left(x\right)=\{\begin{array}{c}-1,-2\le x<0\\ x-1,0\le x\le 2\end{array}$
then, $\{x|x\in [-2,2]:x\le 0\text{and}f(|x|)=x\}$ is equal to

The equation of the normals to the curve $y=2x^3+2x$ which are parallel to $2x+16y=7$ is

Tangents to the ellipse $b^2{x}^2+a^2{y}^2=a^2{b}^2$ makes angles ${\theta }_1$ and ${\theta }_2$ with major axis such that $cot{\theta }_1+cot{\theta }_2=k$.Then the locus of the point of intersection is

A bag contains 4 white, 3 red and 2 blue balls. A ball is drawn at random. Find the probability of the event 'the ball drawn is white or red'.