Recent questions in Mathematics

In a $\Delta ABC, a (\cos ^2 B+\cos^2 C)+ \cos A(c \cos C+b \cos B)$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

$2 \tan h^{-1} \large\frac{1}{2}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

$\sin^{-1} \large\frac{4}{5}$ $+2 \tan ^{-1} \large\frac{1}{3}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

If $\cos 2x =(\sqrt 2 +1) \bigg(\cos x - \large\frac{1}{\sqrt 2}\bigg), \cos x \neq \large\frac{1}{2}$ then $x \in :$

asked Nov 12, 2013 by meena.p

1 answer

$A+B=C=> \cos ^2 A +\cos ^2 B+\cos ^2 C- 2 \cos A \cos B \cos C$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

If $A+C=2B$ then $\large\frac{\cos C- \cos A}{\sin A- \sin C}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

If $\large\frac{\tan 3A}{\tan A}$ $=a$ then $\large\frac{\sin 3A}{\sin A}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

The extreme values of $4 \cos (x^2) \cos \bigg( \large\frac{\pi}{3}$ $+x^2\bigg) - \cos \bigg(\large\frac{\pi}{3}$ $-x^2\bigg)$ over R, are :

asked Nov 12, 2013 by meena.p

1 answer

If $\cos \theta-4 \sin \theta=1$ then $\sin \theta+4 \cos \theta$ is equal to :

asked Nov 11, 2013 by meena.p

0 answers

If $\alpha$ is a non-real root of $x^6=1$ , then $\large\frac{\alpha ^5+ \alpha ^3+ \alpha +1}{\alpha ^2+1}$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $\alpha_1, \alpha_2, \alpha_3$ respectively denote the moduli of the complex number $-i, \large\frac{1}{3}$ $(1+i)$ and $-1+i$ , then their increasing order is :

asked Nov 11, 2013 by meena.p

1 answer

If $A= \begin {bmatrix} -1 & 0 \\ 0 & 2 \end {bmatrix}$ then $A^3-A^2$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

adj $\begin {bmatrix} 1 & 0 & 2 \\ -1 & 1 &-2 \\ 0 & 2 & 1 \end {bmatrix}=\begin {bmatrix} 5 & a & -2 \\ 1 & 1 &0 \\ -2 & -2 & b \end {bmatrix}$ then $[a \quad b]$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $m [-3 \quad 4]+n [ 4 \quad -3]=[10 \quad -11]$ then $3m+7n$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $\alpha, \beta, \gamma$ are the roots of $x^3+2x^2-3x-1=0$ , then $\alpha^{-2}+\beta^{-2}+\gamma^{-2}=$

asked Nov 11, 2013 by meena.p

1 answer

The roots of the equation $x^3-3x-2=0$ are :

asked Nov 11, 2013 by meena.p

1 answer

$E_1: a+b+c=0$ , if 1 is a root of $ax^2+bx+c=0$ . $E_2:b^2-a^2=2ac,$ if $\sin \theta, \cos \theta$ are the roots of $ax^2+bx+c=0$ Which of the following is true?

asked Nov 11, 2013 by meena.p

1 answer

If x is real, then the minimum value of $\large\frac{x^2-x+1}{x^2+x+1}$ , is :

asked Nov 11, 2013 by meena.p

1 answer

If $|a| < 1,b= \sum \limits_{k=1} ^{ \infty} \; \large\frac{a^k}{k}$ then a is equal to :

asked Nov 11, 2013 by meena.p

1 answer

$\sum \limits _{n=1}^{\infty} \large\frac{2n^2+n+1}{n !}$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $\large\frac{x^3}{(2x-1)(x+2)(x-3)}$ $=A+\large\frac{B}{2x-1}+\frac{C}{x+2}+\frac{D}{x-3}$ then A is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $|x| < \large\frac{1}{2}$ , then the coefficient of 'x' in the expansion of $\large\frac{1+2x}{(1-2x)^2}$ is :

asked Nov 11, 2013 by meena.p

1 answer

The coefficient of $x^3y^4z^5$ in the expansion of $(xy+yz+xz)^6$ is :

asked Nov 11, 2013 by meena.p

1 answer

If $(1+x)^{15}=a_0 +a_1 x +.....+ a_{15} x^{15},$ then $\sum \limits_{r=1}^{15} r \large\frac{a_r}{a_{r_1}}$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

A three digit number n is such that the last two digits of it are equal and differ from the first. Then number of such n's is :

asked Nov 11, 2013 by meena.p

1 answer

$\{ n(n+1)(2n+1): n \in Z \} \in$

asked Nov 11, 2013 by meena.p

1 answer

If $a,bc \neq 0$ and belong to the set $\{0,1,2,3.......,9\},$ then $\log _{10} \bigg(\large \frac{a+10 b +10^2 c}{10^{-4} a +10^{-3}b +10^{-2} c}\bigg)$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

$x=\large\frac{1}{2}$ $\bigg(\sqrt 3+\large\frac{1}{\sqrt 3} \bigg)$ then $\large\frac{\sqrt {x^2-1}}{x-\sqrt {x^2-1}}$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If N denotes the set of all positive integers and if $f: N \to N$ is defined by $f(n) =$ the sum of positive divisors of n then, $f(2^k.3),$ where k is a positive integers, is :

asked Nov 11, 2013 by meena.p

1 answer

The function $f: C \to C$ defined by $f(x) =\large\frac{ax+b}{cx+d}$ for $x \in C$ where $bd \neq 0$ reduces to a constant function , if :

asked Nov 11, 2013 by meena.p

1 answer

If $( x \in R: [x -|x|\;]=5)$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

The solution of $\large\frac{dx}{dy}+\frac{x}{y}$ $=x^2$ is :

asked Nov 7, 2013 by meena.p

1 answer

The solution of $(1+x^2) \large\frac{dy}{dx}$ $+2xy-4x^2=0$ is :

asked Nov 7, 2013 by meena.p

1 answer

The solution of $(x^2+y^2)dx =2xy \;dy$ is :

asked Nov 7, 2013 by meena.p

1 answer

$\int _{-1} ^ 1 \large\frac{\cos h x }{1+e^{2x}}$ $dx$ is equal to :

asked Nov 7, 2013 by meena.p

1 answer

$\int \limits_0^{\pi/2} \large\frac{dx}{1+ \tan^3 x}$ is equal to :

asked Nov 7, 2013 by meena.p

1 answer

Dividing the interval [0,6] into 6 equal parts and by using trapezoidal rule the value of $\int \limits_0^6 x^3 dx$ is approximately:

asked Nov 7, 2013 by meena.p

1 answer

Observe the following statements : $A : \int \bigg(\large\frac { x^2-1}{x^2} \bigg)e. ^{\large\frac{x^2-1}{x}}\; dx= e^{\large\frac{x^2-1}{x}}+c.$ $\qquad R:\int f'(x)e^{f(x)}dx=f(x)+c.$ Then which of the following is true ?

asked Nov 7, 2013 by meena.p

1 answer

If $\int \large\frac{dx}{x^2+2x+2}$ $=f(x) +c,$ then f(x) is equal

asked Nov 7, 2013 by meena.p

1 answer

If $\int \sqrt {\large\frac{x}{a^3-x^3}}dx=g(x)+c,$ then $g(x)$ is equal to :

asked Nov 7, 2013 by meena.p

1 answer

If $f(x,y )= \large\frac{\cos (x-4y)}{\cos (x+4y)}$ , then $\large\frac{\partial f}{\partial x} \bigg|_{y-\large\frac{x}{2}}$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $u= \sin ^{-1} \bigg( \large\frac{x^2+y^2}{x+y}\bigg)$ then $x \large\frac{\partial u}{\partial x}$ $+ y \large\frac{\partial u}{\partial y}$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

The perimeter of a sector is a constant. If its area is to be maximum, the sectorial angle is :

asked Nov 6, 2013 by meena.p

1 answer

In the interval $(-3,3)$ the function $f(x) =\large\frac{x}{3}+\frac{3}{x}$ $x \neq 0$ is :

asked Nov 6, 2013 by meena.p

1 answer

If 0 is the angle between the curves $xy=2$ and $x^2+4y=0$ and $x^2+4y=0$ , then $\tan \theta$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $f(x)= \left\{ \begin{array}{1 1} \frac{1- \sqrt 2 \sin x}{\pi-4x} & \quad if\;x \neq \frac{\pi}{4} \\ \alpha & \quad if\;x= \frac{\pi}{4} \end{array}. \right.$ is continuous at $\large\frac{\pi}{4},$ then $\alpha$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $l_1=\lim \limits _{x \to 2^{+}} (x+[x]). l_2 \lim \limits_{x \to 2^{-}} (2x-[x])$ and $l_3=\lim \limits_{x \to x/2} \large\frac{\cos x}{(x-\pi/2)}$ then :

asked Nov 6, 2013 by meena.p

1 answer

If $\lim \limits_{x \to 0} \bigg(\large\frac{\cos 4x+a \cos 2x+b}{x^4}\bigg)$ is finite, then the values of a,b are respectively :

asked Nov 6, 2013 by meena.p

1 answer

$\lim \limits_{x \to \infty} [ \sqrt {x^2+2x-1}-x]$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $0 < p < q,$ then $\lim \limits _{n \to x}( q^n+p^n)^{1/n}$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

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