Recent questions tagged mock-test-series-2015

The half life of $^{238}_{92} U$ against $\alpha$ decay is $1.5 \times 10^{17}\;s$ . What is the activity of a sample of $ ^{238}_{92}U$ having $25 \times 10^{20}$ atoms ?

asked Jan 28, 2015 by meena.p

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Show that the delay rate 'R' of a sample of a radio nuclei is related to the number of radio active nuclei 'N' at the same instant by the expression $R = \lambda N$

asked Jan 28, 2015 by meena.p

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A plane lamp placed $70\;cm$ from a screens one side produces the same illusion as a standard $60\; cd$ lamp placed $105\; cm$ away on other side of the screen. What is the deminous intensity of the first lamp ?

asked Jan 28, 2015 by meena.p

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For a single slit of width 'a', the first minutes of the inference pattern of a monochromatic light of wave length $\lambda$ occurs at an angle of $\large\frac{x}{a}$ . At the same angle of $\large\frac{\lambda}{a}$, we get a maximum for two narrow slits seperated by a distance 'a' Explain

asked Jan 28, 2015 by meena.p

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The half life of $^{90}_{30} sr$ is $28$ years. What is the disintegration rate of $15\;mg$ of their isotope ?

asked Jan 28, 2015 by meena.p

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For what kinetic energy of a neutron, will be associate by the de - Brogile wave length be $1.32\;kg$ given that mass of a $neutron = 1.675 \times 10^{-27}\;kg$

asked Jan 28, 2015 by meena.p

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Four hydrogen nuclei combine to form a helium nucleus, what amount of energy in mev will a released in this process?

asked Jan 28, 2015 by meena.p

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A cylindrical metallic wire is stretched to increase its length by $5\%$. Calculate the percentage change resistance.

asked Jan 28, 2015 by meena.p

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Find the difference of kinetic energies of photo electric emitted from a surface by light of wavelength $3000^{\circ} A$ and $1000^{\circ}A$

asked Jan 28, 2015 by meena.p

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What is the angle between the direction of electric field at any. (i) axial point and (ii) equatorial point due to an electrical dipole ?

asked Jan 28, 2015 by meena.p

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What is the angle between the direction of electric field at any. (i) axial point and (ii) equatorial point due to an electrical dipole ?

asked Jan 28, 2015 by meena.p

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State the relation between the frequency $\gamma$ of radiation emitted by LED and the band gap energy $E$ of the semiconductor used to fabricate it .

asked Jan 28, 2015 by meena.p

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What is the polarizing angle of medium of refractive index $1.732$?

asked Jan 28, 2015 by meena.p

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When we switch on an electric bulk, it almost lights up instantaneously through drift velocity of electron in copper wires is very small. give reason.

asked Jan 28, 2015 by meena.p

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Write the formula for magnetic moment of a current loop.

asked Jan 28, 2015 by meena.p

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Evaluate $I= \int \limits _0^{\large\frac{\pi}{2}} \large\frac{x}{\sin x +\cos x}$$dx$

asked Jan 23, 2015 by meena.p

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A wire of length $36\;cm$ is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.

asked Jan 23, 2015 by meena.p

1 answer

Make a rough sketch of the region given below and find its area using the method of integration $\{(x,y): 0 \leq y \leq x^2 +3, 0 \leq y \leq 2x+3,0 \leq x \leq 3 \}$

asked Jan 23, 2015 by meena.p

1 answer

Using integration find the area of the triangular region whose sides have the equation $y = 2x+1, y=3x+1,x=4$

asked Jan 23, 2015 by meena.p

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Show that the differential equation $(x-y) \large\frac{dy}{dx}$$ = x+2y$ is homogenous and solve it

asked Jan 23, 2015 by meena.p

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Determine the product of $\begin{bmatrix}-4 & 4 & 4\\ -7 & 1 & 3\\ 5 & -3 & -1\end{bmatrix}$ and $\begin{bmatrix}1 & -1 & 1 \\ 1 & -2 & -2\\ 2 & 1 & 3\end{bmatrix}$ Use this product to solve the system of equations $x-y+z=4, x-2y-2z=9$ and $2x+y+3z=1$

asked Jan 23, 2015 by meena.p

1 answer

Using matrix method , solve the following system of linear equations: $5x+y-z=7, 4x-2y-3z=5, 7x+2y+2z=7.$

asked Jan 23, 2015 by meena.p

1 answer

A company produces two types of goods $A$ and $B$ that require gold and silver. Each unit of type $A$ requires $1\; gm$ of silver and $2 \;gm$ of gold. Type $B$ requires(each unit) $2\; gm$ of silver and $1\;gm$ of gold. The company has only $80\; gm$ of gold. Each unit of type A brings profit of $Rs. 500$ and each unit of type $B$ brings profit of $Rs. 400.$ Find the no of units of each type the company should produce to maximize the profit.

asked Jan 23, 2015 by meena.p

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There are $80$ workers in a publication house. Out of which $20$ are hardworking and honest. Three workers are selected at random out of them. Write the probability distribution for the selected workers who are hardworking and honest. Also find the mean of the distribution. Write the importance of hardworking and honesty in one’s life.

asked Jan 23, 2015 by meena.p

1 answer

Differentiate w.r.t x $y= e^{\sin x } +(\tan x) ^x $

asked Jan 23, 2015 by meena.p

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Show that the lines $\overrightarrow{r} = (\overrightarrow{i} +\overrightarrow{j} - \overrightarrow{k} ) + \lambda (4 \overrightarrow{i} -\overrightarrow{k})+ \mu ( 2 \overrightarrow{i} +3 \overrightarrow{k}) $ intersect. Find their point of intersection.

asked Jan 23, 2015 by meena.p

1 answer

Prove that $tan^{-1} \large\frac{3}{4} $$ + tan^{-1}\large\frac{3}{5} $$+ tan^{-1} \large\frac{8}{19} = \frac{\pi}{4}$

asked Jan 23, 2015 by meena.p

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Use this to evaluate $\int \limits_0^2 x \sqrt {2-x} dx$

asked Jan 23, 2015 by meena.p

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Prove that $\int \limits_0^a f(x)dx =\int \limits_0^a f(a-x)dx$

asked Jan 23, 2015 by meena.p

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An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls. Two balls are drawn from the first urn and put into the second urn and then a ball is drawn from the second urn. Find the probability that it is a white ball.

asked Jan 23, 2015 by meena.p

1 answer

Find the equation of the two planes through the points $(4,2,1),(2,1,-1)$ and making angles of $\large\frac{\pi}{4}$ with the plane $x-4y+z-9=0$

asked Jan 23, 2015 by meena.p

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Find the coordinates of the point where the line passing through the points $(3,4,1)$ and $(5,1,6)$ crosses the xy plane

asked Jan 23, 2015 by meena.p

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Evaluate $\int \cos 2x \log \sin x dx $

asked Jan 23, 2015 by meena.p

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Evaluate $\int \large\frac{1+\tan x}{x+ lo \sec x}$

asked Jan 23, 2015 by meena.p

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Find the angle of intersection of the curves $x^2+4y^2=8$ and $x^2-2y^2=4$

asked Jan 23, 2015 by meena.p

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Find the equation of the normal to the point of the curve $x^2+2y^2-4x-6y+8=0$ at the point whose abscissa is $2$

asked Jan 23, 2015 by meena.p

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$f(x) = \left\{ \begin{array} {1 1} 5, & \quad\text{ if x_1 \leq x \leq \sqrt 2 } \\ ax+b ,& \quad \text{if $2x$ < 10 }\\ 21 ,& \quad \text{if $x$ \geq 10 } \end{array} \right. $ Find the values of a and b

asked Jan 23, 2015 by meena.p

1 answer

If $ y = \large\frac {\sqrt{1- \sin x}}{\sqrt{1+\sin x} }$ then show that $ \large\frac{dy}{dx} $$+ \sec^2 \bigg( \large\frac{\pi}{4} $$-x \bigg)=0$

asked Jan 23, 2015 by meena.p

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Using Rolle’s theorem, find the points on the curve $Y= x^2, x\in [-2,2]$ where the tangent is parallel to the x-axis.

asked Jan 23, 2015 by meena.p

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A binary operation is defined by $ab = 2^{ab}.$ Determine whether $$ is commutative or associative?

asked Jan 23, 2015 by meena.p

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Using the properties of determinants prove that $\begin{vmatrix} x+y & x & x \\ 5x+4y & 4x & 2x \\10x+8y & 8x & 3x \end{vmatrix}=x^3$

asked Jan 23, 2015 by meena.p

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Write the degree of the equation, $\sqrt{\large\frac{d^2y}{dx^2}}+y=\sin x$

asked Jan 23, 2015 by meena.p

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A line makes an angle of $\large\frac{\pi}{4}$ with each of $x$ - axis and $y$ - axis. Find the angle between the line and the $z$ -axis.

asked Jan 23, 2015 by meena.p

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If $f(x) =a ^x.x^2$, find $f'(x) $

asked Jan 23, 2015 by meena.p

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Find the domain of the function $f(x) = \sqrt{(9-x^2 )}$

asked Jan 23, 2015 by meena.p

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What is the value of $tan^{-1} \bigg(cos^{-1}\large\frac{8}{17}\bigg)$ ?

asked Jan 23, 2015 by meena.p

1 answer

For the determinant $\begin{vmatrix}3 & -2 & 1\\4 & 6 & 5\\0 & 1 & 1\end{vmatrix}$ , find the minor $M_{32}$ and cofactor $A_{12}$

asked Jan 23, 2015 by meena.p

1 answer

Find the length and foot of the perpendicular from the point $(1,1,2)$ to the plane $\overrightarrow{r}(\hat i - 2 \hat j + 4 \hat k) +5=0$

asked Jan 21, 2015 by meena.p

1 answer

A dealer wishes to purchase a number of fans and radio. He has only $\$5760$ to invest and has a space for atmost 20 items. A fan costs him $\$360$ and a radio $\$240$. His expectation is this he can sell a fan at a profit of $\$22$ and a radio at a profit of $\$18$ . Assuming that he can sell all the items that he buys, how should be invert his money for maximum profit? Translate the problem as LPP and solve it graphically . What is the importance of electricity in our life .

asked Jan 21, 2015 by meena.p

1 answer

By examining the chest X-ray , the probability that TB is detected when a person is actually suffering is $0.99$ . The probability of an healthy person diagnosed to have TB is $0.001$ . In a certain city, 1 in 1000 people suffer from TB. A person selected at random and is diagnosed to have TB. What is the probability that be action has TB?

asked Jan 21, 2015 by meena.p

1 answer

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