Recent questions in Model Papers

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

0 answers

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

1 answer

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

asked Jan 23, 2015 by meena.p

0 answers

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

0 answers

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

asked Jan 23, 2015 by meena.p

1 answer

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

1 answer

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

asked Jan 23, 2015 by meena.p

1 answer

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

asked Jan 23, 2015 by meena.p

1 answer

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

Find the area enclosed by the curve $y=1x$ and $y= -|x-1|+1$

asked Jan 21, 2015 by meena.p

1 answer

find the area bounded by the lines $y= 4x+5,y=5-x$ and $4y= x+5$

asked Jan 21, 2015 by meena.p

1 answer

Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm

asked Jan 21, 2015 by meena.p

1 answer

Evaluate $\int\limits_0^{\pi/2} \large\frac{\cos x}{1+ \cos x+ \sin x}$$dx$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate $\int\limits_0^{\pi} \large\frac{x}{1- \cos \alpha \sin x}$$dx$

asked Jan 21, 2015 by meena.p

1 answer

The cost of $4kg$ Onion,$3kg$ wheat and $2kg$ rice is $\$60$. The cost of $2\;kg$ onion,$4\;kg$ wheat and $6\;kg$ rice is $\$90$. The cost of $6\;kg$ onion, $2\;kg$ wheat and $3\;kg$ rice is $\$70$. Find the cost of each item per kg by matrix method.

asked Jan 21, 2015 by meena.p

1 answer

If $x \sqrt {1+y} +y\sqrt {1+x}=0$. Then prove that $(1+x)^2 \large\frac{dy}{dx}$$+1=0$

asked Jan 21, 2015 by meena.p

0 answers

A coin is biased , so that head is 3 times as to occur as tail. If the coin is tossed twice. Find the probability distribution of number of tails.

asked Jan 21, 2015 by meena.p

1 answer

In a die game , a player pays a stake of $\$1$ for each throw of a die. She receives $\$5$, if the die shows a 3, $\$2$ if the die shows 1 or 6 and nothing otherwise. What is the player expected profit per throw over a long series of throws?

asked Jan 21, 2015 by meena.p

1 answer

The volume of a cube is increasing at a rate of $9\;cm^2/s$ . How fast is the surface area increasing . When the length of the edge is $10\;cm$

asked Jan 21, 2015 by meena.p

1 answer

Find the value of $\tan \bigg[\sin^{-1}\bigg(\large\frac{2x}{1+x^2}\bigg)+$$\cos^{-1} \bigg( \large\frac{1-y^2}{1+y^2}\bigg)\bigg]$

asked Jan 21, 2015 by meena.p

1 answer

Find the value of $\sin (2 \tan ^{-1} \large\frac{1}{3})$$+ \cos(\tan^{-1} 2 \sqrt 2)$

asked Jan 21, 2015 by meena.p

0 answers

Find the inverse of $A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}$ by elementary transformation and hence solve the following system of linear equation : $2x+y=3; 4x+2y=6$

asked Jan 21, 2015 by meena.p

1 answer

If $f(x) = \left\{ \begin{array} {1 1} 1 & \quad, \text{ if $ x \leq$ 3 }\\ ax+b & \quad, \text{if $3 < x < 5$ } \\ 7 & \quad, \text{ if $ 5 \leq x $ } \end{array} \right.$ Determine the values if a and b so that $f(x)$ is continuous?

asked Jan 21, 2015 by meena.p

1 answer

$\begin{align} \int \limits_{\large\frac{\pi}{3}}^{\large\frac{\pi}{2}}\frac{\sqrt {1+\cos x}}{(1- \cos x)^{5/2}}dx \end{align}$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate : $ \int \large\frac{dx}{(x-1)\sqrt {2x+3}}$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate = $\int \large\frac{x^2}{(x \sin x +\cos x)^2}$

asked Jan 21, 2015 by meena.p

1 answer

Solve the differential equation : $(x+2y^2) \large\frac{dy}{dx}$$=y$, given that when $x=2$ and $y=1$. If x devotes the percentage of who are intelligent and y denotes the percentage of people who are work holic, find x when $y=2 \%$ workoholics are always preferable. Do you agree ?

asked Jan 21, 2015 by meena.p

1 answer

Find the equation of the plane containing the line intersection of the plane $x+y+z-6=0$ and $2x+3y+4z+5=0$ and Passing through the pay $(1,1,1)$

asked Jan 21, 2015 by meena.p

1 answer

Find the shortest distance between the lines whose vector equations are : $\overrightarrow{r}= (\hat i+2 \hat j+3 \hat k)+ \lambda (2 \hat i+ 3 \hat j +4 \hat k)$ and $\overrightarrow{r}= (2 \hat i+4 \hat j+5 \hat k)+ (4 \hat i+ 6 \hat j +8 \hat k)$

asked Jan 21, 2015 by meena.p

1 answer

Using the properties of determines evaluate : $\begin{vmatrix} 1 & a & a^2-bc \\1 & b & b^2-ca \\1 & c & c^2-ab\end{vmatrix}$

asked Jan 21, 2015 by meena.p

1 answer

Let $f : N \to R$ be a function defined as $f(x)=4x^2+12x+15$. Show that $f: N \to R$ is invertible. Find the inverse of f

asked Jan 21, 2015 by meena.p

0 answers

Differentiate $\sqrt {\tan \sqrt {x}}$ with respect to x

asked Jan 21, 2015 by meena.p

1 answer

The side of a square is increasing at rate of $0.2\;cm/s$ Find the rate of increase of x perimeter of the square.

asked Jan 21, 2015 by meena.p

1 answer

Find the order and degree of the following differential equation : $\bigg( \large\frac{d^2y}{dx^2}\bigg)^3+\bigg(\large\frac{dy}{dx}\bigg)^2$$+\sin \bigg( \large\frac{dy}{dx}\bigg)$$+1=0$

asked Jan 21, 2015 by meena.p

1 answer

Find the area of the parallelogram whose adjacent sides are $\overrightarrow{a}= \hat i+ 2 \hat j +3 \hat k$ and $\overrightarrow{b}= 3 \hat i - 2 \hat j + \hat k$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate : $\begin{vmatrix}x+2 & x+3 & x+2a\\x+3 & x+4 & x+2b\\x+4 & x+5 & x+2c\end{vmatrix}$ if $a,b,c$ are in A.P

asked Jan 21, 2015 by meena.p

1 answer