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How many terms of G.P. $3,3^2,3^3,$ ............ are needed to give the sum 120 ?

Let $f:R\to R$ be defined as
$f\left(x\right)=\{\begin{array}{cc}-55x,& \text{if}x<-5\\ 2x^3-3x^2-120x,& \text{if}-5\le x\le 4\\ 2x^3-3x^2-36x-336,& \text{if}x>4\end{array}$

Let $A=\{x\in R:f$ is increasing$\}.$ Then $A$ is equal to

If the $n^{\text{th}}$ term and the sum of $n$ terms of the series $2,12,36,80,150,252,.....$ is $T_n$ and $S_n$ repectively then

Let $0<x<\frac{\pi }{4}$, then the value of $(\sec 2x-\tan 2x)$ is

Number of solutions of the equation
$|x^2-2|x||=2^x$ is

Which of the fol

There are 18 stations between Hyderabad and Bangalore. How many second class ticket have to be printed, so that passenger can travel from one station to any other station?

If the distances from the origin of the centre of the three circles $C_i:x^2+y^2-2a_{i}x=b^2(i=1,2,3a_i\in N)$ are in G.P. Let the length of the tengents drawn to $C_1,C_2\&C_3$ from any point on the curve $x+\sqrt{b^2-y^2}=0$ are $l_1,l_2\&l_3$ respectively, then

Find the equation of the tangents to the curve $y=x^3+2x-4$, which are perpendicular to the line x + 14y + 3 = 0.

Find the value of $\underset{x\to 0}{lim}\frac{e^{2x}+e^{-2x}-2}{e^x-x^{-x}}$

Integrate the function.
$\int \sqrt{1+\frac{x^2}{9}}dx$

If $A^{\prime }=\left[\begin{array}{cc}3& 4\\ -1& 2\\ 0& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-1& 2& 1\\ 1& 2& 3\end{array}\right]$, then verify that
(ii)(A-B)'=A'-B'

If | vector A -vec B| = |vec A| = | vecB| , the angle between vector A and vector B is

There are 2000 students in a school out of these 1000 play cricket, 600 play basketball, and 550 play football, 120 play cricket and basketball, 80 play baketball and football and 150 play cricket and football and 45 play all the three games. How many students play none of the games?

The parametric equation $x=2+2cos\theta$ and $y=-2+2sin\theta$ represents

What are the closing entries? Give four examples of closing entries.

What do you mean by ordered pair and ordered triplet? Give example.

The real part of $(1-cos\theta +2isin\theta {)}^{-1}$ is

Solution of the diffferential equation $xdy=(y+x{y}^3(1+{\log }_{e}x\left)\right)dx$ is

If two vectors are perpendicular to each other give an equation to find the magnitude of resultant vector

In differentiation we go for finding the slope,but there we are not dividing but is just finding the derivatives. But slope is actually finded out by dividing both the variable. What's the difference between the two because in both the process we will get different answers

If log (m+n)=log m+ log n ,show that n=m/(m-1).

If$\left|\begin{array}{c}z-\frac{2}{z}\end{array}\right|=1$ then Range of$\left|Z\right|$ is

In how many ways can two 10-paise coins, two 20-paise coins, three 25-paise coins and one 50-paise coin be distributed among 8 children so that each child gets only one coin?

Let $z$ is a complex number and $\overline{z}$ is conjugate of $z$. If $(1+i)z=(1-i)\overline{z},$ then the value of $z+i\overline{z}$ is

The acute angle between the curves $y^2=x\mathrm{and}{x}^2=y$ at (1, 1) is .

Find the rational numbers having the following decimal expansions :

(i) $0.\overline{3}$

(ii) $0.\overline{231}$

(iii) $3.\overline{52}$

(iv) $0.6\overline{8}$

If $\frac{1}{a+b},\frac{1}{2b},\frac{1}{b+c}$ are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.

Prove that the function f is given by f(x) = |x-1|, x $ϵ$R is not differentiable at x = 1.

From a lot of 30 bulbs which include 6 defective, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

In a certain test, there are $n$ questions. In this test $2^{n-i}$ students gave wrong answers to at least $i$ questions, where $i=1,\mathrm{2.....},n$. If the total number of wrong answers given is $2047$, then $n$ is equal to ,

For each binary operation $\ast$ defined below, determine whether $\ast$ is binary, commutative or associative.
(iv) On $Z^{+}$, define $a\ast b=2^{ab}$

The range of values of $a$ such that the angle $\theta$ between the pair of tangents drawn from $(a,0)$ to the circle $x^2+y^2=1$ satisfies $\frac{\pi }{2}<\theta <\pi$, lies in

If a, b, c are odd integers and $a{x}^2+bx+c=0$ , has real roots then:

$\int \frac{1}{2+sin2x+cos2x}dx$ equal to

$\frac{2^{n+4}-{2.2}^n}{{2.2}^{n+3}}+2^{-3}$ is equal to

Show that the points (3, 2, 2), (-1, 4, 2), (0, 5, 6), (2, 1, 2) lie on a sphere whose centre is (1, 3, 4). Find also its radius.

Verify MVT (i.e., Mean Value Theorem) if $f\left(x\right)=x^2-4x-3$ in the interval [a, b], where a = 1 and b = 4.

Express the following matrix as the sum of a symmetric and a skew-symmetric matrices;

$\left[\begin{array}{ccc}6& -2& 2\\ -2& 3& -1\\ 2& -1& 3\end{array}\right]$