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The sum of an infinite GP is 57 and the sum of their cubes is 9747, find the GP.

If P is a prime number, then $n^p$ - n is divisible by p when n is a

The equation of the lines joining the vertex of the parabola $y^2=6x$ to the point on it whose abscissa is 24 , is

If $f\left(x\right)=\left|\begin{array}{ccc}\cos (x+x^2)& \sin (x+x^2)& -\cos (x+x^2)\\ \sin (x-x^2)& \cos (x-x^2)& \sin (x-x^2)\\ \sin 2x& 0& \sin \left(2x^2\right)\end{array}\right|,$ then

If a function $f:[-2,\infty )\to R$ is such that $f\left(x\right)=x^2+4x-|x^2-4|$, then the value(s) $f\left(x\right)$ can have is (are)

If both sum of roots and product of roots of $x^2-({\lambda }^2-5\lambda +5)x+(2{\lambda }^2-3\lambda -4)=0$ are less than $1,$ then the range of $\lambda$ is

If $z$ is a non-zero complex number, then the area of the quadrilateral formed by the points $z,\overline{z},-z$ and $-\overline{z}$ is

The number of solutions of the equation $\cos x=\sqrt{1-\sin 2x}$ where $x\in [0,2\pi ]$ is

The value of $\left\{\sin \frac{25\pi }{3}\right\}$ is

(where $\{.\}$ is fractional part function)

If $a,b$ and $c$ are the integers that satisfy the domain of ${\sin }^{-1}\left[x\right]$, where $[.]$ is the greatest integer function, then

If in a triangle ABC, a = 15, b = 36, c = 39, then sin C/2 is equal to

A variable force $F=3x^2$ is applied on an object. What is the work done to move the object from x = 0m to x = 5m?

(Assume the displacement is in the direction of force applied at all points)

If, in a $G.P.$ of $3n$ terms, $S_1$ denotes the sum of the first $n$ terms, $S_2$ the sum of the second block of $n$ terms and $S_3$ the sum of the last $n$ terms, then $S_1,S_2,S_3$ are in

Let R be a relation from N to N defined by
R = {(a, b):a, b ϵ N and a = b² }
Then which of the following is not true?

If $\underset{x\to a}{lim}$[f(x) + g(x)] = 10 and $\underset{x\to a}{lim}$ f(x)=2, then find the value of $\underset{x\to a}{lim}$ g(x), provided the limit

Let $z$ be a complex number satisfying $|z-3|\le |z-2|,$ $|z-3|\le |z-6|,$ $|z-i|\le |z+i|$ and $|z-i|\le |z-5i|$. Then the area of region in sq. units in which $z$ lies is

The fifth of the H.P. 2,$\frac{5}{2}$,$\frac{10}{3}$,................. will be

The number of real roots of the equation $(x+1)(x+2)(x+3)(x+4)=120$ is

The solution set of $\left|\frac{3x}{x-3}\right|+|x|=\frac{x^2}{|x-3|}$ is

What can be shape of the graph if $(m-2)x^2+8x+(m+4)$ > 0 $\forall$ x $ϵ$ R

Write the negation of sets A and B are equal if and only if ($A\subseteq B$ and $B\subseteq A$).

The value of $\sum _{k=1}^{10}(\sin \frac{2k\pi }{11}-i\cos \frac{2k\pi }{11})$ is

${}_7^{14}N$ weighs 14.003074 g and weighs 15.000 g. If average mass of Nitrogen is 14.0067, calculate the relative abundance of both isotopes ( ${}^{14}N$ and ${}^{15}N$ respectively).

If the 2nd, 5th and 9th terms of a non-constant AP are in GP, then the common ratio of this GP is

If $(1+x{)}^n=C_0+C_{1}x+C_2{x}^2+...+C_n{x}^n,then{C}_0^2+C_1^2+C_2^2+.....+C_n^2$ is equal to :

The value of ${}^{10}{C}_1+{}^{10}{C}_3+{}^{10}{C}_5+{}^{10}{C}_7+{}^{10}{C}_9$ is

The one which does not represent a hyperbola is

If $f:R\to R$ satisfies f(x+y) = f(x) + f(y), for all x, y $\in R$ and f(1) = 7, then ${\sum }_{r=1}^{n}f\left(r\right)$ is equal to

Let $f_k\left(x\right)=\frac{1}{k}(si{n}^{k}x+co{s}^{k}x)$ where $xϵR$ and $k⩾1$

Then $f_4\left(x\right)-f_6\left(x\right)$ equals

The number of ways in which the letters of the word PERSON can be placed in the squares of the given figure so that no row remains empty is

Let $I_n={\int }_0^{\infty }{e}^{-x}(sinx{)}^{n}dx,nϵN,n>1$ then $\frac{I_{2008}}{I_{2006}}$ equals

For universal set U, and sets A, B which are subsets of U, the following information is given -

n(U) = 47

n(A) = 18

n(B) = 11

n(A ∩ B) = 10

Then, the number of elements that neither in A nor B are __

A dice is rolled and two events P and Q are given as
P = {1, 4, 3, 5}, Q = {2, 6}

Which of the following describes the relation between P and Q?

The number of numbers between $3000$ and $4000$ which are divisible by $5$, without repetition using digits $3,4,5,6,7,8$ is

Which of the following set of values of $x$ satisfies the equation $2^{2{\sin }^{2}x-3\sin x+1}+2^{2-2{\sin }^{2}x+3\sin x}=9$

(where $n\in Z$)

Each coefficient in the equation $a{x}^2+bx+c=0$ is determined by throwing an ordinary die. Find the probability that the equation will have equal roots.

Six boys and six girls sit in a row alternatively in x ways and at a round table (again alternatively) in y ways. Then

The integral $\underset{\pi /6}{\overset{\pi /3}{\int }}{\sec }^{2/3}x{cosec}^{4/3}xdx$ is equal to :

A function f(x) is defined on [a,b]. What should be the condition for the function to be a strictly decreasing function at x = b ?

If $x=-1$ and $x=2$ are extreme points of $f\left(x\right)=\alpha \log |x|+\beta x^2+x$ then :

If a tan$\theta$= b then a cos 2$\theta$ + b sin 2$\theta$ is equal to

If $x^2+y^2+z^2=1$, then $yz+zx+xy$ lies in the interval

If point $(k,k^2)$ lies inside the region bounded by parabolas $y^2=64x$ and $-x^2+x-1+y=0$ then $k$ lies in the interval

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

The sum of infinite terms of a G.P. is x and on squaring the each term of it, the sum will be y, then the common ratio of this series is