Recent questions tagged eamcet

If $p$ and $q$ are the perpendicular distance from the origin to the straight lines $x\; \sec \theta-y \;cosec \theta=a$ and $x \cos \theta+ y \sin \theta= a \cos 2 \theta,$ then

asked Sep 16, 2013 by meena.p

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The origin is translated to (1,2). The point $(7,5)$ in the old system undergoes the following transformations successively. (i) Moves to the new point under the given translation of origin. (ii) Translated through 2 units along the negative direction of the new X-axis. (iii) Rotated through an angle $\large\frac{\pi}{4}$ about the origin of new system in the clockwise direction. The final position of the point (7,5) is

asked Sep 16, 2013 by meena.p

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If $X$ is a Poisson variate and $P(X=1)=2P(X=2)$ then $P(X=3)=$

asked Sep 16, 2013 by meena.p

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The random variable takes the value $1,2,3,..........,m$. If $P(X=n)=\large\frac{1}{m}$ to each n, then the variance of $X$ is

asked Sep 16, 2013 by meena.p

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A bag contains $2n+1$ coins. It is known that $n$ of these coins have a head on both sides. Whereas the remaining $n+1$ coins are fair. A coins is picked up at random from the bag and tossed. If the probability that the toss results in a head is $\large\frac{31}{42}.$ then $n$=

asked Sep 16, 2013 by meena.p

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Two fair dice are rolled. The probability of the sum of digits on their faces to be greater that or equal to 10 is

asked Sep 16, 2013 by meena.p

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Two numbers are chosen at random from $\{1,2,3,4,5,6,7,8\}$ at a time. The probability that smaller of the two numbers is less than 4 is:

asked Sep 16, 2013 by meena.p

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If $\overrightarrow {a}$ and $\overrightarrow {b}$ are two non-zero perpendicular vectors, then a vector $\overrightarrow {y}$ satisfying equations $\overrightarrow {a}.\overrightarrow {y}=c$ (c scalar) and $\overrightarrow {a} \times \overrightarrow {y} = \overrightarrow {b}$ is

asked Sep 16, 2013 by meena.p

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A unit vector co planar with $ \overrightarrow {i}+\overrightarrow {j}+ 3\overrightarrow {k}$ and $ \overrightarrow {i} +3 \overrightarrow {j}+ \overrightarrow {k}$ and perpendicular to $\overrightarrow {i}+ \overrightarrow {j}+ \overrightarrow {k}$ is

asked Sep 16, 2013 by meena.p

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The shortest distance between the lines $ \overrightarrow {r}=3\overrightarrow {i}+5 \overrightarrow {j}+ 7 \overrightarrow {k}+ \lambda (\overrightarrow {i}+2 \overrightarrow {j}+\overrightarrow {k})$ and $\overrightarrow {r}=- \overrightarrow {i} -\overrightarrow {j} -\overrightarrow {k}+ \mu (7\overrightarrow {i}-6 \overrightarrow {j}+\overrightarrow {k}) $ is

asked Sep 16, 2013 by meena.p

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$\overrightarrow {a} \neq \overrightarrow {0},\;\overrightarrow {b} \neq \overrightarrow {0},\;\overrightarrow {c} \neq \overrightarrow {0},\;\overrightarrow {a} \times \overrightarrow {b} = \overrightarrow {0},\;\overrightarrow {b} \times \overrightarrow {c}=0\;=>\; \overrightarrow {a} \times \overrightarrow {c}=$

asked Sep 16, 2013 by meena.p

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$P,Q,R$ and $S$ are four points with the position vectors $3 \overrightarrow {i}- 4 \overrightarrow {j}+5 \overrightarrow {k}, 4 \overrightarrow {k},-4 \overrightarrow {i}+ 5\overrightarrow {j}+\overrightarrow {k}$ and $-3\overrightarrow {i}+ 4\overrightarrow {j}+3 \overrightarrow {k}$ respectively. Then the line $PQ$ meets the line RS at the point.

asked Sep 16, 2013 by meena.p

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The points whose position vectors are $2 \overrightarrow {i}+3 \overrightarrow {j}+4 \overrightarrow {k},\; 3 \overrightarrow {i}+4\overrightarrow {j}+2 \overrightarrow {k}$ and $4 \overrightarrow {i}+2 \overrightarrow {j}+3 \overrightarrow {k}$ are the verticies of

asked Sep 16, 2013 by meena.p

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A person observes the top of a tower from a point A on the ground. The elevation of the tower from this point is $60^{\circ}$. He moves $60\;m$ in the direction perpendicular to the line joining A and base of the tower. The angle of elevation of the tower from this point is $45^{\circ}.$ Then the height of the tower (in meters) is

asked Sep 16, 2013 by meena.p

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If, in $\Delta\; ABC,\large\frac{1}{a+c}+\frac{1}{b+c}=\frac{3}{a+b+c}$ then the angle $C=$

asked Sep 16, 2013 by meena.p

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In any triangle $ABC, r_1r_2+r_2r_3+r_3r_1=$

asked Sep 14, 2013 by meena.p

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$\tan\; h^{-1} \bigg(\large\frac{1}{2}\bigg)$$+\cot h^{-1}(2)=$

asked Sep 14, 2013 by meena.p

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$\cos ^{-1} \bigg(\large\frac{5}{13}\bigg)$$+\cos ^{-1} \bigg(\large\frac{3}{5}\bigg)$$=\cos ^{-1} x=>x=$

asked Sep 14, 2013 by meena.p

1 answer

The set of solution of the system of equations: $x+y=\large\frac{2 \pi}{3}$ and $\cos x +\cos y=\large\frac{3}{2},$ where $x,y$ are real, is

asked Sep 14, 2013 by meena.p

1 answer

If $\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$ then a value of $ \cos \bigg( \theta-\large\frac{\pi}{4}\bigg)$ among the following is :

asked Sep 14, 2013 by meena.p

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$\sin \theta+\cos \theta=p, \sin ^3 \theta+\cos ^3 \theta=q=>p(p^2-3)=$

asked Sep 14, 2013 by meena.p

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The period of $f(x)=\cos \bigg(\large\frac{x}{3}\bigg)$$+\sin \bigg(\large\frac{x}{2}\bigg)$ is

asked Sep 14, 2013 by meena.p

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$\large\frac{(1+i)x-i}{2+i}+\frac{(1+2i)y+i}{2-i}$$=1=>(x,y)=$

asked Sep 14, 2013 by meena.p

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If a complex number z satisfies $|z^2-1|=|z|^2+1,$ then z lies on :

asked Sep 14, 2013 by meena.p

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$\bigg(\large\frac{1+i}{1-i}\bigg)^4+\bigg(\frac{1-i}{1+i}\bigg)^4=$

asked Sep 14, 2013 by meena.p

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The number of real values of $t$ such that the system of homogeneous equations:\[tx+(t+1)y+(t-1)z=0\]\[(t+1)x+ty+(t+2)z=0\] \[(t-1)x+(t+2)y+tz=0\] has non-trivial solutions, is

asked Sep 14, 2013 by meena.p

1 answer

The system of equations $3x+2y+z=6, 3x+4y+3z=14, 6x+10 y +8z=a,$ has infinite number of solutions, if $a=$

asked Sep 14, 2013 by meena.p

1 answer

$\begin{vmatrix} x+2 & x+3 & x+5 \\ x+4 & x+6 & x+9 \\ x+8 & x+11 & x+15 \end{vmatrix}=$

asked Sep 14, 2013 by meena.p

1 answer

If $A=\begin{bmatrix} -8 & 5 \\ 2 & 4 \end{bmatrix}$ satisfies the equation $x^2+4x-p=0,$ then $p=$

asked Sep 14, 2013 by meena.p

1 answer

If $\alpha$ and $\beta$ are the roots of the equation $x^2-2x+4=0,$ then $\alpha^9+\beta ^9=$

asked Sep 14, 2013 by meena.p

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If the roots of $x^3-42 x^2+336 x -512=0,$ are in increasing geometric progression, then its common ratio is

asked Sep 14, 2013 by meena.p

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The set of solutions satisfying both $x^2+5x+6 \geq 0$ and $x^2+3x-4 < 0$ is:

asked Sep 14, 2013 by meena.p

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If the harmonic mean between the roots of $(5+ \sqrt 2)x^2-bx+(8+ 2\sqrt 5)=0$ is $4$, then the value of b

asked Sep 13, 2013 by meena.p

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$\large\frac{1}{2.3}+\frac{1}{4.5}+\frac{1}{6.7}+\frac{1}{8.9}+............$

asked Sep 13, 2013 by meena.p

1 answer

If $\large\frac{1}{x^4+x^2+1}=\frac{Ax+B}{x^2+x+1}+\frac{Cx+D}{x^2-x+1}$, then $C+D=$

asked Sep 13, 2013 by meena.p

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If $x$ is small so that $x^2$ and higher powers can be neglected, then the approximate value for $\large\frac{(1-2x)^{-1}(1-3x)^{-2}}{(1-4x)^{-3}}$ is :

asked Sep 13, 2013 by meena.p

1 answer

The term independent of $x\;(x>0,x \neq 1)$ in the expansion of $\bigg[\large\frac{(x+1)}{ x^{2/3}-x^{1/3}+1)}-\frac{(x-1)}{(x -\sqrt x)}\bigg]^{10}$ is

asked Sep 13, 2013 by meena.p

1 answer

If $t_n$ denotes the number of triangles formed with n points in a plane no three of which are collinear and if $t_{n+1}-t_n=36,$ then $n=$

asked Sep 13, 2013 by meena.p

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10 men and 6 women are to be seated in a row so that no two women sit together. The number of ways they can be seated is :

asked Sep 13, 2013 by meena.p

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$^nC_{r-1}=330,\;^n C_r =462,\;^n C_{r+1}=462 =>r\;$=

asked Sep 13, 2013 by meena.p

1 answer

If I is the identify matrix of order 2 and $A= \begin {bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then for $ n \geq 1$, mathematical induction gives

asked Sep 13, 2013 by meena.p

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$\bigg\{x \in R \bigg | \log \bigg[(1.6)^{1-x^2}-(0.625)^{6(1+x)}\bigg] \in R\bigg\}$=

asked Sep 13, 2013 by meena.p

1 answer

If $f(x)=(p-x^n)^{\Large\frac{1}{n}}$$, p\; >\; 0$ and n is a positive integer, then $f(f(x))$=

asked Sep 13, 2013 by meena.p

1 answer

$\int \large\frac{3 \cos x +2 \sin x}{4 \sin x+ 5 \cos x}$$dx$=.............. .

asked Sep 13, 2013 by meena.p

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Given $x$ is positive, the values of $f(x)=-3 \cos \sqrt {3+x+x^2}$ lie in the interval .............. .

asked Sep 13, 2013 by meena.p

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If $u=\log \tan \bigg(\large\frac{\pi}{4}+\frac{\theta}{2}\bigg), $ then $cos\; u$=............... .

asked Sep 13, 2013 by meena.p

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Two die thrown simultaneously. The probability of getting even numbers on both the die is ...............

asked Sep 13, 2013 by meena.p

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The greatest negative integer satisfying $x^2-4x-77=0$ and $x^2 >4$ is ................... .

asked Sep 13, 2013 by meena.p

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The condition for $ax^2+2cxy+by^2+2bx+2ay+c$ is resolvable into two linear factors, is ................

asked Sep 13, 2013 by meena.p

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$\lim \limits _{x \to 0} \large\frac{x-\sin x}{x+ \cos ^2 x}$=............... .

asked Sep 13, 2013 by meena.p

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