Recent questions in Model Papers

Three numbers are selected at random (with out replacement ) from first six positive integers. If X denotes the smallest of the three numbers obtained , find the probability distribution of X.Also find the mean and variance of the distribution .

asked May 30, 2016 by meena.p

1 answer

A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods $F_1 \: and F_2$ are available . Food $F_1$ costs Rs. 4 perunit and $F_2$ costs Rs. 6 per unit. One unit of food $F_1$ contains 3 units of vitamin A and 4 units of minerals. One unit of food $F_2$ contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem and find graphically the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

asked May 30, 2016 by meena.p

1 answer

Find the equation of the plane containg two parallel lines $\large\frac{x-1}{2} = \frac{y+1}{-1} = \frac{z}{3}$ and $\large\frac{x}{4} = \frac{y-2}{-2} =\frac{z+1}{6}$ . Also find the plane thus obtained contains the line $\large\frac{x-2}{3} =\frac{y-1}{1} =\frac{z-2}{5}$ or not .

asked May 30, 2016 by meena.p

1 answer

Using integration find the area of the region $f(x,y): y^2 \leq 6ax$ and $x^2+y^2 \leq 16a^2$

asked May 30, 2016 by meena.p

1 answer

Find the maximum and minimum values of $f(x)=\sec x + \log \cos ^2x, 0 < x < 2 \pi$

asked May 30, 2016 by meena.p

0 answers

Determine the intervals in which the function $f(x)=x^4 -8x^3+22x^2-24 x +21$ is strictly increasing or strictly decreasing.

asked May 30, 2016 by meena.p

1 answer

Using of elementary row operations, find the inverse of the following matrix : $\begin{bmatrix} 2 & -1 & 3\\ -5 & 3 & 1\\-3 & 2 & 3\end{bmatrix}$

asked May 30, 2016 by meena.p

1 answer

Using properties of determinant prove that : $\begin{bmatrix}(b+c)^2 & a^2 & bc \\ (c+a)^2 & b^2 & ca \\ (a+b)^2 & c^2 & ab \end{bmatrix}$ $=(a-b)(b-c)(c-a) (a+b+c)(a^2+b^2+c^2)$

asked May 30, 2016 by meena.p

1 answer

Find the coordinates of the point where the line $\overrightarrow {r} =(-\hat {i} - 2 \hat {j} - 3 \hat {k} )+ \lambda ( 3\hat i + 4 \hat j +3 \hat k )$ meets the plane which is perpendicular to the vector $\overrightarrow n= \hat i + \hat j + 3 \hat k$ and at a distance of $\large\frac{4}{\sqrt {11}}$ from origin .

asked May 30, 2016 by meena.p

1 answer

Find the equation of plane passing through the point $A(3,2,1,) B(4,2,-1)$ and $C(6,5,-1)$ and $D(\lambda,5,5)$ are co planar

asked May 30, 2016 by meena.p

1 answer

Given that vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ from a triangle such that $\overrightarrow{a} = \overrightarrow{b}+ \overrightarrow{c}$ . Find p,q,r,s such that area of triangle is $5 \sqrt 6$ where $\overrightarrow{a} = p \hat i +q \hat j +r \hat k$ , $\overrightarrow{b} = s \hat i +3 \hat j +4 \hat k$ and $\overrightarrow{c} = 3 \hat i + \hat j -2 \hat k$

asked May 30, 2016 by meena.p

1 answer

There are two bags A and B . Bag A contains 3 white and 4 red balls whereas bag B contains 4 white and 3 red balls . Three balls are drawn at random ( with out replacement ) from one of the bags and are found to be two white and one red. Find the probability that these were drqwn from bag B.

asked May 30, 2016 by meena.p

1 answer

Solve the equation for $x: \cos ( \tan ^{-1} x ) = \sin \bigg( \cot ^{-1} \large\frac{3}{4}\bigg)$

asked May 27, 2016 by meena.p

0 answers

Prove that $2\sin ^{-1} \bigg( \large\frac{3}{5} \bigg) - \tan ^{-1} \bigg(\large\frac{17}{31} \bigg) = \large\frac{\pi}{4}$

asked May 27, 2016 by meena.p

1 answer

Ishan wants to donate a rectangular plot of land for a land for a school in his village . When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same. but if length is decreased by 10 m and breadth is decreased by 20 m. then its area will decrease by $5300\;m^2$ . Using matrices , find the dimension of the plot. Also give reasons why he wants to denote the plot for a school.

asked May 27, 2016 by meena.p

1 answer

Solve the differential equation : $2ye^{x/y} dx+ (y -2x e^{x/y})dy=0$

asked May 27, 2016 by meena.p

1 answer

Solve the differential equation : $(x+1)\large\frac{dy}{dx}$ $-y =e^{3x}(x+1)^3$

asked May 27, 2016 by meena.p

1 answer

Evaluate : $\int \limits_0^1 \cot ^{-1} (1-x+x^2)dx$

asked May 27, 2016 by meena.p

1 answer

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

asked May 27, 2016 by meena.p

1 answer

Find $\{\int (\log (\log x)+\large\frac{1}{(\log x)^2}\}$ $dx$

asked May 27, 2016 by meena.p

1 answer

Find $\int \large\frac{1- \sin x}{\sin x (1+\sin x)}$ $dx$

asked May 27, 2016 by meena.p

1 answer

Find the equation of normal to the curve $ay^2 = x^3$ at the point whose x coordinate is $am^2$

asked May 27, 2016 by meena.p

1 answer

Find k, if $f(x) = \left\{ \begin{array} {1 1} k \sin \frac{\pi}{2}(x+1), & \quad x \leq 0 \\ \frac{\tan x - \sin x}{x^3} ,& \quad x >0 \end{array} \right.$ is a continuous at x=0

asked May 27, 2016 by meena.p

1 answer

Differentiate $\tan ^{-1} \bigg( \large\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\bigg)$ with respect to $\cos ^{-1}x^2$

asked May 27, 2016 by meena.p

1 answer

Differentiate $(\sin 2x)^x+ \sin ^{-1} \sqrt {3x}$ with respected to x

asked May 27, 2016 by meena.p

1 answer

If $A = \begin{bmatrix} 0 & 3 \\2 & -5 \end{bmatrix}$ and $KA = \begin{bmatrix} 0 & 4a \\-8 & 5b \end{bmatrix}$ find the values of K and a

asked May 27, 2016 by meena.p

1 answer

If $A= \begin{bmatrix}1 & 2 \\ 3 & -1\end{bmatrix}$ and $B=\begin{bmatrix}1 & -4 \\ 3 & -2\end{bmatrix}$ find $|AB|$

asked May 27, 2016 by meena.p

1 answer

If A is a square matrix such that $|A|=5$ write the value of $|AA^T|$

asked May 27, 2016 by meena.p

1 answer

Find the distance between the planes $\overrightarrow {r}.(2 \hat i - 3 \hat j +6 \hat k)-4=0$ and $\overrightarrow {r} . (6 \hat i - 9 \hat j +18 k )+30=0$

asked May 27, 2016 by meena.p

1 answer

If $\overrightarrow {a}$ and $\overrightarrow {b}$ are unit vectors , then what is the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$ for $\overrightarrow {a} - \sqrt 2 \overrightarrow {b}$ to be a unit vector ?

asked May 27, 2016 by meena.p

1 answer

If vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ are such that $|\overrightarrow {a}| = \large\frac{1}{2}$ , $|\overrightarrow {b}| = \large\frac{4}{\sqrt 3}$ and $|\overrightarrow {a} \times \overrightarrow {b}| = \large\frac{1}{\sqrt 3}$ then find $|\overrightarrow {a}. \overrightarrow {b}|$

asked May 27, 2016 by meena.p

1 answer

$V-I$ graph for a metallic wire at two different temperatures $T_1$ and $T_2$ are shown in the figure. Which of the two temperature is higher and why ?

asked Jun 29, 2015 by meena.p

1 answer

What are the dimensions of electrical conductivity ?

asked Jun 29, 2015 by meena.p

1 answer

a)Three resistor $2 \Omega,4 \Omega$ and $5\;\Omega$ are combined in parallel. What is the total resistance of the combination ? b) If the combination is connected to a battery emf $20\;V$ and negligible internal resistance determine the current through each resistor, and the total current drawn from the battery

asked Jun 29, 2015 by meena.p

1 answer

What conclusion can you draw from the following observation on a resistor made of allong magnanin ?Choose the correct alternative?

asked Jun 29, 2015 by meena.p

1 answer

Given the resistance of $1 \Omega, 2 \Omega,3 \Omega$ how will you combine thus to get , an equivalent resistance of $(i) \large\frac{11}{3}$ $\Omega \qquad (ii) \large\frac{6}{11}$ $\Omega \qquad (iii) \large\frac{11}{5}$ $\Omega \qquad (iv) 6 \Omega?$

asked Jun 29, 2015 by meena.p

1 answer

A steady current flows in a metallic conductor of non- uniform cross section. Which of these quantities is constant along the conductor ?

asked Jun 29, 2015 by meena.p

1 answer

An arbitrary surface enclosed a dipole . what is the electric flux through this surface ?

asked Apr 29, 2015 by meena.p

0 answers

A hollow charged conductor has a tiny hole cut into its surface . show that the electric field in the hole is $\bigg( \large\frac{\sigma}{2 \in_0}\bigg)$ $\hat n$ , where $\hat n$ is the unit vector in the outward normal direction and $\sigma$ is the surface change density near the hole.

asked Apr 28, 2015 by meena.p

1 answer

A conductor A with a cavity as shown in the fig(a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor .

asked Apr 28, 2015 by meena.p

1 answer

As oil drop of 12 excess electron is held stationary under a constant electric field of $2.55 \times 10^4 \;N/C$ in Millikan's oil drop experiment . The density of the oil is $1.26\;g/cm^3$ Estimate the radius of the drop . $(g = 9.8 \;m/s^2; e = 1.60 \times 10^{-91}\;C)$

asked Apr 28, 2015 by meena.p

1 answer

Two point charges $+9e$ and $e$ are seperated by 412\;cm4 in air. determine the position of the point at which the resultant electric is zero.

asked Apr 28, 2015 by meena.p

1 answer

A conductor with a cavity in it is given a charge Q. What will be the total charge on the surface of this conductor if another carrying charge q is placed in the cavity without touching the cavity ?

asked Apr 28, 2015 by meena.p

1 answer

The electric field component in the following figure are $Ex = \alpha x^{1/2}, E_y =0, E_z=0$ in which $\alpha =800 NCm6{-1/2}$ Calculate the charge within the cube. Assume $a= 0.1\;m$

asked Apr 28, 2015 by meena.p

1 answer

The electric field component in the following figure are $Ex = \alpha x^{1/2}, E_y =0, E_z=0$ in which $\alpha =800 NCm6{-1/2}$ Calculate the flux $\phi _2$ through the cube

asked Apr 28, 2015 by meena.p

1 answer

Two points charges $q_1$ anb $q_2$ are located at points $(a,0,0)$ and $(0,b,0)$ respectively . Find the electric field bue to these charges at the point $(0,0,0)$

asked Apr 28, 2015 by meena.p

1 answer

Two large thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and magnitude $17.0 \times 10^{-22}C/m^2$ what is E? between the plates ?

asked Apr 28, 2015 by meena.p

1 answer

Two large thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and magnitude $17.0 \times 10^{-22}C/m^2$ what is E? In the outer region of the second plate ?

asked Apr 28, 2015 by meena.p

1 answer

Two large thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and magnitude $17.0 \times 10^{-22}C/m^2$ what is E? In the outer region of the first plate ?

asked Apr 28, 2015 by meena.p

1 answer

An infinite line charge produces a field of $9 \times 10^4 \;N/c$ at a distance of $2 \;cm$ . calculate the linear density .

asked Apr 28, 2015 by meena.p

1 answer

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