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a2=31/4 a31=1/2 an =-30/2 find n

A line $x+1=y$ meets the curve $2x^3+10x^2+x-4=y$ at $A,B$ and $C$. If point $P\equiv (-1,0)$, then $|PA.PB.PC|$ is equal to

The general solution of the differential equation $dy-\left(\sin x\sin y\right)dx=0,$ where $c$ is a constant of integration, is

$Theequationofcircum-circleofa\Delta ABCis{x}^2+y^2+3x+y-6=0.IfA=(1,-2),B(-3,2)andthevertexCvariesthenthelocusofortho-centreof\Delta ABCisa$

The equation of the circle passsing through $(1,0)$ and $(0,1)$ and having the smallest possible radius is

If $a_1,a_2,a_3,\dots \dots a_n$ are in A.P., with common difference d, then the sum of the series $sind[cosec{a}_{1}cosec{a}_2+cosec{a}_{1}cosec{a}_3+\dots \dots +cosec{a}_n-1cosec{a}_n]$ is

The solution set of $x-2>0,x-9<0$ and $x^2-9\ge 0$ is

The number of solution(s) for $\text{sgn}(x+1)=2x^2-x$ is

Let $E_1$ and $E_2$ be two independent events such that $P\left(E_1\right)=P_1$ and $P\left(E_2\right)=P_2$. Describe in words of the events whose probabilities are

$1-(1-P_1)(1-P_2)$

This doubt is regarding every chapter. How we have to answer the conceptual questions in exams ??

Prove

sin²72° - sin²60° = √5 -1/8

If the coefficient of $5^{\text{th}}$ term is numerically the greatest coefficient in the expansion of $(1-x{)}^n,$ then the positive integral value of $n$ is

Range of rational expression $y=\frac{x^2-x+4}{x^2+x+4},x\in R$ is

Let $f\left(x\right)=\frac{{(27-2x)}^{1/3}-3}{9-3{(243+5x)}^{1/5}},x\ne 0.$ If $f\left(x\right)$ is continuous at $x=0$, then the value of $f\left(0\right)$ is

If tan $\alpha =2$,then the values of x which satisfy the relation

$tanx=\frac{1}{2}are$ $0<x<$$2\pi and$$0<\alpha <$$\frac{\pi }{2}$

Evaluate : ${\int }_0^{\pi }\frac{xtanx}{secx+tanx}dx.$ OR Evaluate : ${\int }_1^4\text{{|x-1|+|x-2|+|x-4|}dx.}$

The positive value of $\lambda$ for which the co-efficient of $x^2$ in the expression $x^2{(\sqrt{x}+\frac{\lambda }{x^2})}^{10}$ is $720$, is :

सवैया के आधार पर बताओ कि दो कदम चलने के बाद सीता का ऐसा हाल क्यों हुआ?

If the maximum and the minimum values of $1+\sin (\frac{\pi }{4}+\theta )+2\cos (\frac{\pi }{4}-\theta )$ for all real values of $\theta$ are $\lambda$ and $\mu$ respectively, then $\lambda -\mu$ is

Find
the inverse of each of the matrices, if it exists.

${lim}_{x\to 0}\frac{log|1+x^3|}{si{n}^{3}x}$

The total number of arrangements of letter $a^5{b}^4{c}^6$ when written at full length is

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{The least positive integral value of}x\text{satisfying the inequality}& \text{(P)}& 1\\ & {\tan }^{-1}(x^3+5x-2)>{\tan }^{-1}(4-6x+6x^2),\text{is}& & \\ \text{(B)}& \text{If}f\left(x\right)=\frac{a\cos x-\cos bx}{x^2},x\ne 0\text{and}f\left(0\right)=4\text{is continuous at}x=0,\text{then}& \text{(Q)}& 2\\ & |a+b|\text{can be}& & \\ \text{(C)}& \text{Let}f\left(x\right)=\underset{n\to \infty }{lim}\frac{x^n(a+\sin (x^n\left)\right)+(b-\sin (x^n\left)\right)}{(1+x^n)\sec \left({\tan }^{-1}\right(x^n+x^{-n}\left)\right)}\text{be continuous at}x=1.& \text{(R)}& 3\\ & \text{Then}(a+b+1)\text{is}& & \\ \text{(D)}& \text{Let}f\left(x\right)=\underset{t\to 0}{lim}{\sin }^{-1}\left(\frac{e^{xt}-1}{t}\right).\text{Then}\underset{t\to 0}{lim}6\left(\frac{f\left(x\right)-x}{x^3}\right)\text{is}& \text{(S)}& 4\\ & & \text{(T)}& 6\end{array}$



Which of the following is the only CORRECT combination?

Find A, B, C in the adjacent multiplication table.

If R is a relation on a finite set having n elements, then the number of relations on A is

The area of an equilateral triangle with the equation of base as x+y-2=0 and the opposite vertex with the coordinates (2, -1) is sq. units.

If circle $x^2+y^2-6x-10y+c=0$ does not touch (or) intersect the coordinates axes and the point $(1,4)$ is inside the circle, then the range of $c$ is

Let $P$ be the image of the point $(3,1,7)$ with respect to the plane $x-y+z=3$. Then the equation of the plane passing thorugh $P$ and containing the straight line $\frac{9}{1}=\frac{Y}{2}=\frac{z}{1}$ is

The negation of $(p\vee q)\wedge (q\vee \sim r)$ is