Recent questions in Model Papers

Let * ba a binary operation on set Q of rational defined as $ ab=\large\frac{ab}{5}.$ Write the identity for , if any.

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Using the principal values, evaluate the following \[ tan^{-1}\frac{1}{\sqrt{3}}+sin^{-1} \bigg( -\frac{1}{2} \bigg) \]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If $\begin{bmatrix} 15 & x+y \\ 2 & y \end{bmatrix} = \begin{bmatrix} 15 & 8 \\ x-y & 3 \end{bmatrix} $find the value of x and y

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Evaluate : $ 2\begin{vmatrix} 7 & -2 \\ -10 & 5 \end{vmatrix} $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int_0^{\large\frac{\pi}{2}} \large\frac{\sin\: x-\cos\: x}{1+\sin\: x.\cos\:x}$$dx $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int (cosec^2x-\cot\: x)e^x\: dx $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find a unit vector in the direction of the vector $ \overrightarrow a = -2\hat i + \hat j + 2\hat k$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find $ \overrightarrow a.\overrightarrow b\: if \: \overrightarrow a = 3\hat i - \hat j + 2\hat k\: and \: \overrightarrow b = 2\hat i + 3\hat j + 3\hat k$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Write the direction cosines of a line parallel to the line $ \large\frac{3-x}{3} = \frac{y+2}{-2} = \frac{z+2}{6}.$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If the function $( f : R \rightarrow R )$ is given by $( f(x) =\large \frac{x+3}{2} )$ and $( g : R \rightarrow R)$ is given by $( g(x)=2x-3,)$ find (i) fog and (ii) gof. Is $( f^{-1}=g)$?

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Solve the following for x : \[ tan^{-1} \bigg( \frac{x-1}{x-2} \bigg) + tan^{-1} \bigg( \frac{x+1}{x+2} \bigg) = \frac{\pi}{4} \]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Using the properties of determinants, prove the following : \[ \begin{vmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{vmatrix} = 2 \begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix} \]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If the function defined by $ f(x) = \left\{ \begin{array}{l l}2x-1, & \quad if { x < 2 } \\ a, & \quad if { x = 2 } \\ x+1, & \quad if { x > 2 } \end{array} \right. $ is continuous at x = 2, find the value of a. Also discuss the continuity of f(x) at x = 3.

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If $ y=(\log\: x)^x+(x)^{\large \cos\:x},\: find\: \large\frac{dy}{dx} $.

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If $ x=a \bigg( \cos\: \theta +\log \tan\large \frac{\theta}{2} \bigg) $ and $ y = a\sin\: \theta,$ find the value of $ \large\frac{d^2y}{dx^2}$$\: at \: \theta = \large\frac{\pi}{4}.$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find the intervals in which the following function is (a) increasing (b) decreasing : $ f(x) = x^3-12x^2+36x+17 $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find the equation of the tangent to the curve $ x^2+3y=3$, which is parallel to the line $ y-4x+5=0$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{2x+5}{\sqrt{7-6x-x^2}}$$dx$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Using properties of definite integrals, evaluate the following : $ \int_0^{\pi}\large\frac{x\: sin\: x}{1+cos^2x}$$dx $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Form the differential equation representing the family of ellipses having foci on x - axis and center at the origin.

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Solve the following differential equation : $ x\: \log\: x\: \frac{dy}{dx}+y=\large\frac{2}{x}$$\log\:x $

asked Feb 9, 2013 by thanvigandhi_1

1 answer