Recent questions tagged 2013

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

1 answer

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

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

1 answer

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

1 answer

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

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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

1 answer

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

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

1 answer

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

1 answer

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

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

Where can I find the NEET 2013 UG results? Thanks!

asked Jun 5, 2013 by balaji

1 answer

Find the particular solution of the differential equation $\large\frac{dx}{dy}$$+x\cot y=2y+y^2\cot y,(y\neq 0)$,given that $x=0$ when $y=\large \frac{\pi}{2}$.

asked Mar 22, 2013 by sreemathi.v

1 answer

Find the area of the region $\{(x,4):y^2\leq 4x,4x^2+4y^2\leq9\}$ using method of integration.

asked Mar 22, 2013 by sreemathi.v

1 answer

Using properties of determinants,prove the following $\begin{vmatrix}3x& -x+y & -x+z\\x-y & 3y & z-y\\x-z & y-z & 3z\end{vmatrix}=3(x+y+z)(xy+yz+zx)$

asked Mar 22, 2013 by sreemathi.v

1 answer

If $x\sin (a+y)+\sin a \cos(a+y)=0$,Prove that $\large\frac{dy}{dx}=\large\frac{\sin^2(a+y)}{\sin a}$

asked Mar 22, 2013 by sreemathi.v

1 answer

Evaluate :$\int \large \frac{dx}{x(x^3+1)}$

asked Mar 22, 2013 by sreemathi.v

1 answer

Using vectors,find the area of triangle ABC,whose vertices are $A(1,2,3),B(2,-1,4),C(4,5,-1).$

asked Mar 22, 2013 by sreemathi.v

1 answer

L and M are two points with position vectors $2\overrightarrow{a}-\overrightarrow{b}$ and $\overrightarrow{a}+2\overrightarrow{b}$ respectively.Write the position vector of a point N which divides the line segment LM in the ratio 2 : 1 externally.

asked Mar 22, 2013 by sreemathi.v

1 answer

If Matrix A = $\begin{bmatrix} 3 &-3 \\ -3 & 3 \end{bmatrix}$, and $A^2=\lambda A$, then write the value of $\lambda$.

asked Mar 22, 2013 by sreemathi.v

1 answer

Using the property of determinants, evalute: $\begin{vmatrix}x& x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}$

asked Mar 22, 2013 by balaji.thirumalai

1 answer

What is the value of $tan\bigg(\frac{1}{2}sin^{-1}\frac{3}{4}\bigg)$

asked Mar 22, 2013 by balaji.thirumalai

1 answer

Show that the differential equation $[xsin^2\big(\frac{y}{x}\big)-y]dx+xdy=0.$ is homogeneous.Find the particular solution of this differential equation ,given that $y=\frac{\pi}{4}$ when x=1.

asked Mar 22, 2013 by sreemathi.v

1 answer

Find the area of the region $\{(x,y):y^2\leq 6ax$ and $x^2+y^2\leq 16a^2\}$ using method of integration.

asked Mar 22, 2013 by sreemathi.v

1 answer

If $\overrightarrow{p}=5\hat{i}+\lambda\hat{j}-37\hat{k}$ and $\overrightarrow{q}=\hat{i}+3\hat{j}-5\hat{k}$,then find the value of $\lambda$,so that $\overrightarrow{p}+\overrightarrow{q}$ and $\overrightarrow{p}-\overrightarrow{q}$ are perpendicular vectors.

asked Mar 22, 2013 by sreemathi.v

1 answer

Evaluate :$\int\limits_0^{\pi}\large\frac{xsin x}{1+cos^2x}dx.$

asked Mar 22, 2013 by sreemathi.v

1 answer

Evaluate :$\int \large \frac{dx}{x(x^3+8)}$

asked Mar 22, 2013 by sreemathi.v

1 answer

If $x^y=e^{x-y}$,prove that $\Large \frac{dy}{dx}=\frac{log x}{(1+log x)^2}$

asked Mar 22, 2013 by sreemathi.v

1 answer

A and B are two points with position vectors $2\overrightarrow{a}-3\overrightarrow{b}$ and $6\overrightarrow{b}-\overrightarrow{a}$ respectively.Write the position vector of a point P which divides the line segment AB internally in the ratio 1 : 2.

asked Mar 22, 2013 by sreemathi.v

1 answer

If Matrix A = $\begin{bmatrix} 2 &-2 \\ -2 & 2 \end{bmatrix}$, and $A^2=pA$, then write the value of $p$.

asked Mar 22, 2013 by sreemathi.v

1 answer

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