Recent questions tagged modelpaper

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy . How much power is generated by the turbine ? $( g = 10\: m/s^2)$

asked Dec 14, 2013 by thanvigandhi_1

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Three forces acting on a body are shown in the figure. To have the resultant force only along the $y$ - direction, the magnitude of the minimum additional force needed is :

asked Dec 14, 2013 by thanvigandhi_1

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Sand is being dropped on a conveyor belt at the rate of M / kg s. The force necessary to keep the belt moving with a constant velocity of $ v\: m/s$ will be :

asked Dec 14, 2013 by thanvigandhi_1

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A particle of mass $m$ is projected with velocity $v$ making an angel of $45^{\circ}$ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be :

asked Dec 14, 2013 by thanvigandhi_1

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A particle shows distance - time curve as given in the figure. The maximum instantaneous velocity of the particle is around the point :

asked Dec 14, 2013 by thanvigandhi_1

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A particle moves in a straight line with a constant acceleration. It changes its velocity from $ 10 \: ms^{-1} $ to $ 12 \: ms^{-1} $ while passing through a distance 135 m in $t$ second. The value of $t$ is :

asked Dec 14, 2013 by thanvigandhi_1

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The distance travelled by a particle starting from rest and moving with an acceleration $ \large\frac{4}{3}\: ms^{-2}$, in the third second is :

asked Dec 14, 2013 by thanvigandhi_1

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If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be :

asked Dec 14, 2013 by thanvigandhi_1

1 answer

Which two of the following five physical parameters have the same dimensions ?

asked Dec 14, 2013 by thanvigandhi_1

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Use the truth table to establish which of the following statements are tautologies and which are contradictions.

asked Sep 13, 2013 by sreemathi.v

1 answer

Use the truth table to establish which of the following statements are tautologies and which are contradictions.

asked Sep 13, 2013 by sreemathi.v

1 answer

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: $ f (x) = \sin x+\cos x, x \in [0,\pi] $

asked Aug 7, 2013 by sreemathi.v

1 answer

Show that of all the rectangles with a given perimeter,the square has the largest area.

asked Jul 25, 2013 by sreemathi.v

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Differentiate $( x \cos \: x )^x + ( x\sin\: x )^{\Large\frac{1}{x}}$ w.r.t. $ x $.

asked Jul 25, 2013 by sreemathi.v

1 answer

Find the value of x from the following : $\begin {vmatrix} x & 4 \\ 2 & 2x \end {vmatrix} = 0 $

asked Jul 19, 2013 by sreemathi.v

1 answer

Obtain the inverse of the following matrix using elementary operations :$A=\begin{bmatrix}3 & 0 & -1\\2 & 3 & 0\\0 & 4& 1\end{bmatrix}$

asked Jul 18, 2013 by sreemathi.v

1 answer

Solve the following differential equation :$x\large\frac{dy}{dx}$$-y=\sqrt{x^2+y^2}$.

asked Jul 16, 2013 by sreemathi.v

1 answer

Solve the following differential equation : $(1+x^2)\large\frac{dy}{dx}$$-2xy=(x^2+2)(x^2+1)$

asked Jul 16, 2013 by sreemathi.v

1 answer

Form the differential equation representing the family $y^2-2ay+x^2=a^2$ where $a$ is an arbitrary constant.

asked Jul 16, 2013 by sreemathi.v

1 answer

Evaluate :$\int\large\frac{\sqrt{16+(\log x)^2}}{x}$$dx$

asked Jul 16, 2013 by sreemathi.v

1 answer

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

asked Jul 16, 2013 by sreemathi.v

1 answer

A class consists of $10$ boys and $8$ girls.Three students are selected at random.Find the probability that the selected row has

asked Jul 16, 2013 by sreemathi.v

1 answer

Show that $\begin{vmatrix}x+1 &x+2 &x+a\\x+2 &x+3 &x+b\\x+3 &x+4 &x+c\end{vmatrix}=0$ where $a,b,c$ are in A.P.

asked Jul 16, 2013 by sreemathi.v

1 answer

If $A=\begin{vmatrix}2 & 3\\1 & 2\end{vmatrix}$ prove that $A^3-4A^2+A=0$

asked Jul 16, 2013 by sreemathi.v

1 answer

Find the equation of the plane passing through the points $(3,4,1)$ and $(0,1,0)$ and parallel to the line $\large\frac{x+3}{2}=\frac{y-3}{7}=\frac{z-2}{5}$

asked Jul 15, 2013 by sreemathi.v

1 answer

If $\tan\bigg(\large\frac{x^2-y^2}{x^2+y^2}\bigg)$$=a$,then prove that $\large\frac{dy}{dx}=\frac{y}{x}$.

asked Jul 14, 2013 by sreemathi.v

1 answer

Find the equation of the hyperbola if centre: $(0 , 0 )$ length of the semi-transverse axis is $6; e=3$ and the transverse axis is parallel to $y$-axis.

asked Jun 19, 2013 by sreemathi.v

1 answer

Find all the values of $\bigg(\large\frac{1}{2}$$-i\large\frac{\sqrt 3}{2}\bigg)^{\Large\frac{3}{4}}$ and hence prove that the product of the values is 1.

asked Jun 13, 2013 by sreemathi.v

1 answer

Solve : $x^4+4=0$

asked Jun 12, 2013 by sreemathi.v

1 answer

If $\cos \alpha +\cos \beta + \cos \gamma = 0 = \sin \alpha + \sin \beta + \sin \gamma$, prove that $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = 0$

asked Jun 11, 2013 by sreemathi.v

1 answer

$P$ represents the variable complex number $z$.Find the locus of $P$,if $\mid 2z-3\mid=2$

asked Jun 10, 2013 by sreemathi.v

1 answer

$P$ represents the variable complex number $z$.Find the locus of $P$,if $\mid z-5i\mid=\mid z+5i\mid$

asked Jun 10, 2013 by sreemathi.v

1 answer

Find the square root of $(-8-6i)$

asked Jun 7, 2013 by sreemathi.v

1 answer

The marks secured by $400$ students in a Mathematics test were normally distributed with mean $65$. If $120$ students got more marks above $85$, the number of students securing marks between $45$ nd $65$ is

asked Jun 3, 2013 by poojasapani_1

1 answer

The random variable $X$ follows normal distribution $f(x)=ce\large\frac{-1/2(x-100)^{2}}{25}$ Then the value of $c$ is

asked Jun 3, 2013 by poojasapani_1

1 answer

If $f(x)$ is a p.d.f of a normal distribution with mean $\mu$ then $\int\limits_{-\infty}^{\infty}f(x)dx$ is

asked Jun 3, 2013 by poojasapani_1

1 answer

For a poisson distribution with parameter $ \lambda=0.25$ the value of the $2^{nd}$ moment about the origin is

asked Jun 3, 2013 by poojasapani_1

1 answer

The distribution function $F(X)$ of a random variable $X$ is

asked Jun 3, 2013 by poojasapani_1

1 answer

What type of set is "The set of poor students of a class"?

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

If a random variable $X$ follows poisson distribution such that $E(X^{2})=30$ then the variance of the distribution is

asked May 30, 2013 by poojasapani_1

1 answer

If in a poisson distribution $P(X=0)=k$ then the variance is

asked May 30, 2013 by poojasapani_1

1 answer

In $16$ throws of a die getting an even number is considered a success. Then the variance of the successes is

asked May 28, 2013 by poojasapani_1

1 answer

In $5$ throws of a die, getting $1$ or $2$ is a success. The mean number of successes is

asked May 28, 2013 by poojasapani_1

1 answer

Var $(4X+3)$ is

asked May 28, 2013 by poojasapani_1

1 answer

$\mu_{2}=20, \mu'_{2}=276$ for a discrete random variable $X$. Then the mean of the random variable $X$ is

asked May 28, 2013 by poojasapani_1

1 answer

Variance of the random variable $X$ is$4$ .Its mean is $2.$ Then $E(X^{2})$ is

asked May 28, 2013 by poojasapani_1

1 answer

$X$ is a random variable taking the values $3, 4 $and $12$ with probabilities $\large\frac{1}{3},\frac{1}{4}$ and $\large\frac{4}{7}.$ Then $E(X)$ is

asked May 28, 2013 by poojasapani_1

1 answer

Given $E(X+c)=8$ and $E(X-c)=12$ then the value of $c$ is

asked May 28, 2013 by poojasapani_1

1 answer

$X$ is a discrete random variable which takes the values $0, 1, 2 $ and $P(X=0)=\large\frac{144}{169},$$ P(X=1)=\large\frac{1}{169}$ then the value of $P(X=2)$ is

asked May 28, 2013 by poojasapani_1

1 answer

If $f(x)=\large\frac{A}{\pi}\frac{1}{16+x^{2'}}$$-\infty<x<\infty$\[\]is a p.d.f of a continuous random variable $X,$ then the value of $A$ is

asked May 28, 2013 by poojasapani_1

1 answer

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