Recent questions tagged 2011

Let $A$ and $B$ be events in a sample spaces $S$ such that $P(A)=0.5, P(B)=0.4$ and $P(A \cup B)=0.6$. observe the following lists:

asked Sep 23, 2013 by meena.p

1 answer

Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is

asked Sep 23, 2013 by meena.p

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A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The probability that three are two boys and one girl is

asked Sep 23, 2013 by meena.p

1 answer

Let $\bar {v}=2 \bar{i}+\bar {j}-\bar {k}$ and $\bar {w}=\bar {i}+3 \bar{k}$. If $ \bar u$ is any unit vector then the maximum value of the scalar triple product $(\bar {u} \; \bar {v}\; \bar {w})$ is

asked Sep 23, 2013 by meena.p

1 answer

If $|\bar {a}|=1$,$ |\bar {b}|=2$ and the angle between $\bar {a} $ and $\bar {b}$ is $120^{\circ},$ then $\{(\bar {a}+ 3 \bar {b}) \times (3 \bar {a}-\bar {b})\}^2=$

asked Sep 23, 2013 by meena.p

1 answer

For any vector $\bar r,\bar {i} \times (\bar {r} \times \bar {i}) \div \bar {j} \times (\bar {r} \times \bar {j})+ \bar k \times (\bar {r} \times {\bar k})=$

asked Sep 23, 2013 by meena.p

1 answer

If the vector $\bar {i}-2x \bar {j}-3 y \bar{k}$ and $\bar {i}+3 x \bar{ j}+2 y \bar {k}$ are orthogonal to each other, then the locus of the point $(x,y)$ is

asked Sep 23, 2013 by meena.p

1 answer

The magnitude of the projection of the vector $\bar {a}=4 \bar {i}-3 \bar {j}+2 \bar k $ on the line which makes equal angles with the coordinate axes is

asked Sep 23, 2013 by meena.p

1 answer

The angle of elevation of a stationary cloud from a point 2500 m above a lake is $15^{\circ}$ and from the same point the angle of depressed its reflection in the lake is $45^{\circ}$. The height (in meters) of the cloud above the lake , given that $\cot 15^{\circ}=2+\sqrt {3}$, is

asked Sep 23, 2013 by meena.p

0 answers

In a triangle $ABC$ if $\large\frac{\cos A}{a}=\frac {\cos B}{b} =\frac{\cos C}{c}$, then $\Delta ABC$ is

asked Sep 20, 2013 by meena.p

1 answer

In triangle ABC if $a \cos ^2 \large\frac{C}{2}$$+c \cos ^2 \large\frac{A}{2}=\frac{3b}{2}$, then the sides of the triangle are in

asked Sep 20, 2013 by meena.p

1 answer

For $0 < x \leq \pi, \sin h^{-1} (\cot x)=$

asked Sep 20, 2013 by meena.p

1 answer

$(\tan ^{-1}x)^2+(\cot ^{-1}x)^2=\large\frac{5 \pi^2}{8}$$=>x=$

asked Sep 20, 2013 by meena.p

1 answer

The most general value of $\theta$ which satisfies both the equations $\tan \theta=-1$ and $\cos \theta=\large\frac{1}{\sqrt 2}$ is :

asked Sep 20, 2013 by meena.p

1 answer

If $f(x)=\sin ^6 x+ \cos ^6x$ for $x \in IR,$ then $f(x)$ lies in the interval

asked Sep 20, 2013 by meena.p

1 answer

$\cos A =\large\frac{3}{4}$$=>32 \sin \bigg(\large\frac{A}{2}\bigg)$$ \sin \bigg(\large\frac{5A}{2}\bigg)=$

asked Sep 20, 2013 by meena.p

1 answer

If $f:IR \to IR$ is defined by $f(x)=7+ \cos (5x+3)$ for $ x \in IR,$ then the period of f is :

asked Sep 20, 2013 by meena.p

1 answer

$\large\frac{(1+i)^{2011}}{(1-i)^{2009}}=$

asked Sep 20, 2013 by meena.p

1 answer

The locus of the complex number z such that $arg \bigg (\large\frac{z-2}{z+2}\bigg)=\frac{\pi}{3}$ is :

asked Sep 20, 2013 by meena.p

1 answer

Let $z=a-\large\frac{i}{2};$$ \alpha \; \in IR.$ Then $|i+z|^2-|i-z|^2=$

asked Sep 20, 2013 by meena.p

1 answer

$\begin{vmatrix} 24 & 25 & 26\\ 25 & 26 & 27 \\ 26 & 27 & 27\end{vmatrix}=$

asked Sep 20, 2013 by meena.p

1 answer

$A=\begin{bmatrix} 1 & 0 & 1\\ 0 & 1 & 1 \\ 0 & 1 & 0\end{bmatrix} \;=>\;A^2-2A=$

asked Sep 20, 2013 by meena.p

1 answer

If A is a matrix such that $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} A\begin{bmatrix} 1 & 1 \end{bmatrix} =\begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}$ then A=

asked Sep 20, 2013 by meena.p

1 answer

$A(\alpha, \beta)=\begin {bmatrix} \cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^{\beta} \end{bmatrix} => [A(\alpha, \beta)]^{-1}=$

asked Sep 20, 2013 by meena.p

1 answer

If $x$ is real, the value of $\large\frac{x^2-3x+4}{x^2+3x+4}$ lies in the interval

asked Sep 20, 2013 by meena.p

1 answer

The value of $'\alpha'$ for which the equation $x^3+ax+1=0$ and $x^4+ax^2+1=0$ have a common root is

asked Sep 20, 2013 by meena.p

1 answer

If $\tan A $ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0,$ then $\sin^2 (A+B)$=

asked Sep 20, 2013 by meena.p

1 answer

If $a \;>\;0$ and $b^2-4ac=0,$ then the curve $y=ax^2+bx+c$

asked Sep 20, 2013 by meena.p

1 answer

$ \sum \limits ^{\infty}_{n=1} \large\frac{2n}{(2n+1)\ !} =$

asked Sep 20, 2013 by meena.p

1 answer

$\large\frac{x^2+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}$ then find $A+C=$

asked Sep 20, 2013 by meena.p

1 answer

If the coefficient of $r$th and $(r+1)$th terms in the expansion of $(3+7x)^{29}$ are equal , then $r=$

asked Sep 20, 2013 by meena.p

1 answer

If $^{(n-1)} C_3+^{n-1} C_4 \;>\;^n C_3$, then the minimum value of $n$ is

asked Sep 20, 2013 by meena.p

1 answer

$^{15}P_{8}=A+8.^{14}P_7 =>A=$

asked Sep 20, 2013 by meena.p

1 answer

The number of five digit numbers divisible by 5 that can be formed using the numbers $0,1,2,3,4,5$ without repetition is

asked Sep 20, 2013 by meena.p

1 answer

A bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively, until the bag is empty. If the number of ways in which each pair consists of one white and one black balls is $14,400.$ then $n=$

asked Sep 20, 2013 by meena.p

1 answer

If $a,b$ and $n$ are natural numbers then $a^{n-1}+b^{n-1}$ is divisible by:

asked Sep 20, 2013 by meena.p

1 answer

If $f :IR \to IR$ is defined by $f(x) =\bigg[\large\frac{x}{5}\bigg]$ for $ x \in IR,$ Where $[y]$ denotes the greatest integer not exceeding y, then $ (f(x):|x| < 71)=$

asked Sep 20, 2013 by meena.p

1 answer

If $f:[2, \infty) \to B$ defined by $f(x)=x^2-4x+5$ is a bijection, then B=

asked Sep 20, 2013 by meena.p

1 answer

If $y=y(x)$ is the solution of the differential equation $\bigg(\large\frac{2+ \sin x}{y+1}\bigg) \frac{dy}{dx} $$+ cos x=0$ with $y(0)=1,$ then $y\bigg(\large\frac{\pi}{2}\bigg)=$

asked Sep 20, 2013 by meena.p

1 answer

The solution of the differential equation $\large\frac{dy}{dx}=\frac{y}{x}+\frac{\phi (y/x)}{\phi ' (y/x)}$ is

asked Sep 20, 2013 by meena.p

1 answer

Let $f(0)=1,f(0.5)=\large\frac{5}{4}$$, f(1)=2,f(1.5)=\large\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule, $\int \limits_0^{2} f(x) dx=$

asked Sep 20, 2013 by meena.p

1 answer

If $I_n=\int \limits _0^{\pi/4} \tan ^n \theta d \theta$ for $n=1,2,3........$ then $I_{n-1}+I_{n+1}=.............$

asked Sep 20, 2013 by meena.p

1 answer

The area (in square units) of the region bounded by the curves $x=y^2$ and $x=3-2y^2$ is

asked Sep 20, 2013 by meena.p

1 answer

$\int \large\frac{1+\cos 4x}{\cot x -\tan x}$$dx$=

asked Sep 20, 2013 by meena.p

1 answer

If $\int \large\frac{\sin ^8 x -\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x}$$dx=A \sin 2x+B,$ then $A=$

asked Sep 20, 2013 by meena.p

1 answer

$\large\int \bigg(\sqrt {\large\frac{a+x}{a-x}}+\sqrt {\large\frac{a-x}{a+x}}\bigg)$$dx= $

asked Sep 20, 2013 by meena.p

1 answer

$u=u(x,y)=\sin (y+ax)-(y+ax)^2=>$

asked Sep 20, 2013 by meena.p

1 answer

The length of the sub tangent at any point $(x_1,y_1)$ on the curve$y=5^x$

asked Sep 20, 2013 by meena.p

1 answer

If the distance travelled by a particle in time $t$ is given by $s=t^2-2t+5$ then its acceleration is

asked Sep 20, 2013 by meena.p

1 answer

If $1^{\circ}=\alpha$ radians then the approximate value of $\cos(60^{\circ}1')$ is

asked Sep 20, 2013 by meena.p

0 answers

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