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Answers posted by pady_1
Questions
4370
answers
1
best answer
0
votes
The locus of a point such that the sum of its distance from the points $(0,2)$ and $(0,-2)$ is $6,$ is
answered
Nov 7, 2013
$(c)\;9x^2+5y^2=45$
0
votes
If the vectors $\bar {AB}=-3 \bar {i}+ 4 \bar {k}$ and $\bar {AC}=5 \bar {i}-2 \bar j+4 \bar {k} $ are the sides of a triangle ABC, then the length of the medium through A is
answered
Nov 7, 2013
$(b)\; \sqrt {18}$
0
votes
The probability distribution of a random variable $X$ is given below :X=x 0 1 2 3 P(X=x) $\frac{1}{10}$ $\frac{2}{10}$ $\frac{3}{10}$ $\frac{4}{10}$ Then the variance of $X$ is
answered
Nov 7, 2013
(a) 1
0
votes
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:
answered
Nov 7, 2013
(d)
0
votes
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
answered
Nov 7, 2013
$ (a)\;\frac{35}{76}$
0
votes
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
answered
Nov 7, 2013
$ (c)\;\sqrt {59}$
0
votes
If $|\bar {a}|=1$,$ |\bar {b}|=2$ and the angle between $\bar {a} $ and $\bar {b}$ is $120^{\circ},$ then $\{(\bar {a}+ 3 \bar {b}) \times (3 \bar {a}-\bar {b})\}^2=$
answered
Nov 7, 2013
(d) 300
0
votes
For any vector $\bar r,\bar {i} \times (\bar {r} \times \bar {i}) \div \bar {j} \times (\bar {r} \times \bar {j})+ \bar k \times (\bar {r} \times {\bar k})=$
answered
Nov 7, 2013
$(b)\;2 \bar {r}$
0
votes
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
answered
Nov 7, 2013
$(b)\;\sqrt 3$
0
votes
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
answered
Nov 7, 2013
(a) circle
0
votes
In a triangle $ABC$ if $\large\frac{\cos A}{a}=\frac {\cos B}{b} =\frac{\cos C}{c}$, then $\Delta ABC$ is
answered
Nov 7, 2013
(c) Equilateral
0
votes
In triangle ABC if $a \cos ^2 \large\frac{C}{2}$$+c \cos ^2 \large\frac{A}{2}=\frac{3b}{2}$, then the sides of the triangle are in
answered
Nov 7, 2013
(a) an arithmetic progression
0
votes
For $0 < x \leq \pi, \sin h^{-1} (\cot x)=$
answered
Nov 7, 2013
$ (a)\;\log (\cot \frac{x}{2})$
0
votes
$(\tan ^{-1}x)^2+(\cot ^{-1}x)^2=\large\frac{5 \pi^2}{8}$$=>x=$
answered
Nov 7, 2013
$ (a)\;-1$
0
votes
If $f(x)=\sin ^6 x+ \cos ^6x$ for $x \in IR,$ then $f(x)$ lies in the interval
answered
Nov 7, 2013
$ (c)\;\bigg[\frac{1}{4},1\bigg]$
0
votes
The most general value of $\theta$ which satisfies both the equations $\tan \theta=-1$ and $\cos \theta=\large\frac{1}{\sqrt 2}$ is :
answered
Nov 7, 2013
$(b)\;2n\pi+\frac{7\pi}{4} $
0
votes
$\cos A =\large\frac{3}{4}$$=>32 \sin \bigg(\large\frac{A}{2}\bigg)$$ \sin \bigg(\large\frac{5A}{2}\bigg)=$
answered
Nov 7, 2013
(d) 11
0
votes
If $f:IR \to IR$ is defined by $f(x)=7+ \cos (5x+3)$ for $ x \in IR,$ then the period of f is :
answered
Nov 7, 2013
(d) $\frac{2\pi}{5}$
0
votes
$\large\frac{(1+i)^{2011}}{(1-i)^{2009}}=$
answered
Nov 7, 2013
(d) -2
0
votes
The locus of the complex number z such that $arg \bigg (\large\frac{z-2}{z+2}\bigg)=\frac{\pi}{3}$ is :
answered
Nov 7, 2013
(a) a circle
0
votes
Let $z=a-\large\frac{i}{2};$$ \alpha \; \in IR.$ Then $|i+z|^2-|i-z|^2=$
answered
Nov 7, 2013
(b) -2
0
votes
$\begin{vmatrix} 24 & 25 & 26\\ 25 & 26 & 27 \\ 26 & 27 & 27\end{vmatrix}=$
answered
Nov 7, 2013
(c) 1
0
votes
$A=\begin{bmatrix} 1 & 0 & 1\\ 0 & 1 & 1 \\ 0 & 1 & 0\end{bmatrix} \;=>\;A^2-2A=$
answered
Nov 7, 2013
(b) $-A^{-1}$
0
votes
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=
answered
Nov 7, 2013
$(d)\;\begin{bmatrix} 2 \\ 3 \end{bmatrix} $
0
votes
$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}=$
answered
Nov 7, 2013
$(b)\;A(- \alpha, -\beta)$
0
votes
If $x$ is real, the value of $\large\frac{x^2-3x+4}{x^2+3x+4}$ lies in the interval
answered
Nov 7, 2013
$(d)\;\bigg[\frac{1}{7},7\bigg] $
0
votes
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
answered
Nov 7, 2013
(a) -2
0
votes
If $\tan A $ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0,$ then $\sin^2 (A+B)$=
answered
Nov 7, 2013
$(d)\;\frac{p^2}{p^2+(1-q)^2} $
0
votes
If $a \;>\;0$ and $b^2-4ac=0,$ then the curve $y=ax^2+bx+c$
answered
Nov 7, 2013
(d) touches the x-axis and lies above it
0
votes
$ \sum \limits ^{\infty}_{n=1} \large\frac{2n}{(2n+1)\ !} =$
answered
Nov 7, 2013
$ (a)\;\frac{1}{e}$
0
votes
$\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=$
answered
Nov 7, 2013
<div class="clay6-step-odd"><div class="clay6-basic" id="pr10"...
0
votes
If the coefficient of $r$th and $(r+1)$th terms in the expansion of $(3+7x)^{29}$ are equal , then $r=$
answered
Nov 7, 2013
(d) 21
0
votes
If $^{(n-1)} C_3+^{n-1} C_4 \;>\;^n C_3$, then the minimum value of $n$ is
answered
Nov 7, 2013
(d) 8
0
votes
$^{15}P_{8}=A+8.^{14}P_7 =>A=$
answered
Nov 7, 2013
$(b)\;^{14}P_8$
0
votes
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
answered
Nov 7, 2013
(b) 216
0
votes
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=$
answered
Nov 7, 2013
(b) 5
0
votes
If $a,b$ and $n$ are natural numbers then $a^{n-1}+b^{n-1}$ is divisible by:
answered
Nov 7, 2013
$(a)\;a+b$
0
votes
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)=$
answered
Nov 7, 2013
$ (d)\;\{-15,-14,......,0,.......,13,14\} $
0
votes
If $f:[2, \infty) \to B$ defined by $f(x)=x^2-4x+5$ is a bijection, then B=
answered
Nov 7, 2013
(b) $[1, \infty)$
0
votes
The solution of the differential equation $\large\frac{dy}{dx}=\frac{y}{x}+\frac{\phi (y/x)}{\phi ' (y/x)}$ is
answered
Nov 7, 2013
$(b)\;\phi \bigg(\frac{y}{x}\bigg)=kx$
0
votes
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 $y\bigg(\large\frac{\pi}{2}\bigg)=$
answered
Nov 7, 2013
$(a)\;\frac{1}{3}$
0
votes
Let $f(0)=1,f(0.5)=\large\frac{5}{4}$$, f(1)=2,f(1.5)=\large\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule, $\int \limits_0^{2} f(x) dx=$
answered
Nov 7, 2013
$ (a)\;\frac{14}{3}$
0
votes
If $I_n=\int \limits _0^{\pi/4} \tan ^n \theta d \theta$ for $n=1,2,3........$ then $I_{n-1}+I_{n+1}=.............$
answered
Nov 7, 2013
$(c)\;\frac{1}{n}$
0
votes
The area (in square units) of the region bounded by the curves $x=y^2$ and $x=3-2y^2$ is
answered
Nov 7, 2013
$ (d)\;4 $
0
votes
$\int \large\frac{1+\cos 4x}{\cot x -\tan x}$$dx$=
answered
Nov 7, 2013
$(d)\;-\frac{1}{8} \cos 4x+c $
0
votes
If $\int \large\frac{\sin ^8 x -\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x}$$dx=A \sin 2x+B,$ then $A=$
answered
Nov 7, 2013
$ (a)\;-\frac{1}{2}$
0
votes
$\large\int \bigg(\sqrt {\large\frac{a+x}{a-x}}+\sqrt {\large\frac{a-x}{a+x}}\bigg)$$dx= $
answered
Nov 7, 2013
$(b)\; 2a \sin ^{-1} \bigg(\frac{x}{a}\bigg)+c$
0
votes
$u=u(x,y)=\sin (y+ax)-(y+ax)^2=>$
answered
Nov 7, 2013
$(a)\;u_{xx}=a^2.u_{yy}$
0
votes
The length of the sub tangent at any point $(x_1,y_1)$ on the curve$y=5^x$
answered
Nov 7, 2013
$(d)\;\frac{1}{\log_e5}$
0
votes
If the distance travelled by a particle in time $t$ is given by $s=t^2-2t+5$ then its acceleration is
answered
Nov 7, 2013
(c) 2
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