Recent questions tagged medium

If $a_1,a_2,a_3.....a_n$ are in G.P then the determinant $\Delta=\begin{vmatrix}\log a_n&\log a_{n+1}& \log a_{n+2}\\\log a_{n+3}&\log a_{n+4}&\log a_{n+5}\\\log a_{n+6}&\log a_{n+7}&\log a_{n+8}\end{vmatrix}$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If $a^2+b^2+c^2=-2$ and $f(x)=\small\begin{vmatrix}1+a^2x&(1+b^2)x&(1+c^2)x\\(1+a^2)x&1+b^2x&(1+c^2)x\\(1+a^2)x&(1+b^2)x&1+c^2x\end{vmatrix}$ then $f(x)$ is a polynomial of degree

asked Nov 22, 2013 by sreemathi.v

1 answer

The system of equations $\alpha x+y+z=\alpha-1$, $x+\alpha y+z=\alpha-1$, $x+y+\alpha z=\alpha-1$ has infinite solutions if $\alpha$ is

asked Nov 22, 2013 by sreemathi.v

1 answer

$A=\begin{bmatrix}1&0&0\\0&1&1\\0&-2&4\end{bmatrix}$ and $I=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$ and $A^{-1}=[\large\frac{1}{6}$$(A^2+cA+dI)]$ then the value of $c$ and $d$ are

asked Nov 22, 2013 by sreemathi.v

1 answer

The parameter on which the value of the determinant $\begin{vmatrix}1&x&x+1\\\cos(p-d)x&\cos px&\cos(p+d)x\\\sin(p-d)x&\sin px&\sin(P+d)x\end{vmatrix}$ does not defined upon is

asked Nov 22, 2013 by sreemathi.v

1 answer

The momentum of a moving particle is vectorially given as $\overrightarrow{p}=p_0(\cos t \hat {i}+\sin t \hat {j}).$ Where t stands for time.

asked Nov 22, 2013 by meena.p

1 answer

Two blocks of masses $6\; kg$ and $4\;kg$ are attached to the two ends of a massless string passing over a smooth fixed pulley. If the system is released, the acceleration of the centre of mass of the system will be ;

asked Nov 22, 2013 by meena.p

1 answer

A cracker is thrown into air with a velocity of $10 m/s$ at an angle of $45^{\circ}$ with the vertical. When it is at a height of $0.5 \;m$ from the ground it explodes into a number of pieces which follow different parabolic paths. What is the velocity of the centre of mass when it is at a height of $1 \;m$ from the ground. $(g=10\;m/s^2)$

asked Nov 22, 2013 by meena.p

1 answer

A particle of mass 4 m which is at rest explodes into three fragments. Two of the fragments each of mass m are found to move with speed V each in mutually perpendicular directions. The minimum energy released in the process of explosion is

asked Nov 22, 2013 by meena.p

1 answer

If $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c$ and $\overrightarrow a\times\overrightarrow b=\overrightarrow a\times\overrightarrow c$ and if $\overrightarrow a\neq 0$, then

asked Nov 21, 2013 by rvidyagovindarajan_1

1 answer

Two particles having mass ratio $n:1$ are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of centre of mass of the system is

asked Nov 21, 2013 by meena.p

1 answer

Two particles of equal mass have velocities $\overrightarrow{V_1}=4 \hat {i}$ and $V_2= 4 \hat {j} m/s$. First particle has an accleration $\overrightarrow{a_1}=(5 \hat i+5 \hat{j})m/s^2$ While the acceleration of the other particle is zero. The center of mass of the two particles moves in a path of

asked Nov 21, 2013 by meena.p

1 answer

For positive numbers $x,y$ and $z$ the numerical value of the determinant $\begin{vmatrix}1 &\log_xy&\log_xz\\\log_yx&1&\log_yz\\\log_zx&\log_zy&1\end{vmatrix}$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $a,b,c$ be the real numbers. Then the following system of equations in $x,y$ and $z$: $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$, $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$, $\large\frac{-x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ has

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $p\lambda^4+q\lambda^3+r\lambda^2+s\lambda+t$ = $\begin{vmatrix}\lambda^3+3\lambda&\lambda-1&\lambda+3\\\lambda+1&-2\lambda&\lambda-4\\\lambda-3&\lambda+4&3\lambda\end{vmatrix}$ be an identity in $\lambda$ where $p,q,r,s$ and $t$ are constant. Then the value of $t$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

A uniform circular sheet has a radius r. A square sheet whose diagonal length is equal to the radius of the plate is removed. The maximum distance of the centre of mass of the square sheet from the center of original sheet is :

asked Nov 21, 2013 by meena.p

1 answer

A uniform metal rod is bent units L-shaped with the bent arms at 90 to each other. The distance of the center of mass of the remaining portion from the center of the original sheet is

asked Nov 21, 2013 by meena.p

1 answer

A uniform square sheet has a side of length $2R$. A circular sheet of maximum possible area is removed from one of the quadrants of the square sheet. The distance of the center of mass of the remaining portion from the center of the original sheet is

asked Nov 21, 2013 by meena.p

1 answer

From a sphere of radius 1m, a sphere of radius 0.5 m is removed from the edge. The shift in the CM is

asked Nov 21, 2013 by meena.p

1 answer

Half of the uniform rectangular plate of length 'L' is made of material of density $d_1$and the other half of density $d_2$. The horizontal distance of center of mass from AB is

asked Nov 21, 2013 by meena.p

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two non zero non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j,\:\:\overrightarrow b=2\hat j-\hat k$ and $\overrightarrow r\times \overrightarrow a=\overrightarrow b\times\overrightarrow a,\:\:\overrightarrow r\times\overrightarrow b=\overrightarrow a\times\overrightarrow b$ then a unit vector in the direction of $\overrightarrow r$ is ?

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

A uniform disc of radius R is put over another uniform disc of radius 2R of same thickness and density . The peripheries of the two dises touch each other. The position of their COM is

asked Nov 20, 2013 by meena.p

1 answer

Two uniform rods A and B of Lengths 5 m and 3 m are placed end to end. If their linear densities are $3\;kg/m$ and $2\;kg/m$, the position of their centre of mass from their interface is

asked Nov 20, 2013 by meena.p

1 answer

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j.$ and $\overrightarrow c$ is a vector such that $\overrightarrow a.\overrightarrow c=|\overrightarrow c|,\:\:|\overrightarrow c-\overrightarrow a|=2\sqrt 2 $ and angle between $\overrightarrow a\times\overrightarrow b\:\:and\:\:\overrightarrow c$ is $\large\frac{\pi}{6}$, then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

A uniform wire of length L is bent in the form of a circle. The shift in its centre of mass is

asked Nov 20, 2013 by meena.p

1 answer

If the magnitude of the vector $a\hat i+b\hat j+c\hat k$ is $|a|+|b|+|c|$, then $a,b,c$ should be ?

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

Given that the fourth and eighth term of a GP are 5 and 80, find the 12th term.

asked Nov 19, 2013 by harini.tutor

1 answer

The sum of an AP is 1815. If the first and last terms are -12 and 133 respectively, find the number of terms in the AP

asked Nov 19, 2013 by harini.tutor

1 answer

The system of equations $\lambda x+y+z=0$, $-x+\lambda y+z=0$, $-x-y+\lambda z=0$ will have a non-zero solutions if real values of $\lambda$ are given by

asked Nov 19, 2013 by sreemathi.v

1 answer

If $\begin{bmatrix}1 &-\tan\theta\\\tan\theta&1\end{bmatrix}\begin{bmatrix}1 &\tan\theta\\-\tan\theta&1\end{bmatrix}^{-1}$ = $\begin{bmatrix}a &-b\\b&a\end{bmatrix}$ then find $a,b$

asked Nov 19, 2013 by sreemathi.v

1 answer

Find the sum of even numbers between 50 and 100

asked Nov 19, 2013 by harini.tutor

1 answer

What is the sum of all odd natural numbers till 200 ?

asked Nov 19, 2013 by harini.tutor

1 answer

If $|\overrightarrow a|=5, \:|\overrightarrow b|=3\:|\overrightarrow c|=4$ and $\overrightarrow a$ is $\perp$ to $\overrightarrow b\:\:and\:\:\overrightarrow c$ then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=?$

asked Nov 18, 2013 by rvidyagovindarajan_1

1 answer