Recent questions in Model Papers

If $ \begin{bmatrix} x+3y & y \\ 7-x & 4 \end{bmatrix}=\begin{bmatrix} 4 & -1 \\ 0 & 4 \end{bmatrix} $, find the values of x and y.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} 2x & 5 \\ 8 & x \end{bmatrix}=\begin{bmatrix} 6 & 5 \\ 8 & 3 \end{bmatrix} $, then find x.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Differentiate with respect to x. $( \sec(\tan(\sqrt x)))$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Find order and degree ( if defined ) of following differential equation : $ \bigg( \large\frac{d^2y}{dx^2} \bigg)^2$$+\cos \bigg( \large\frac{dy}{dx} \bigg)=0$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ |\overrightarrow a|=\sqrt 3, |\overrightarrow b|=2$ and the angle between $ \overrightarrow a \: and \: \overrightarrow b$ is $ 60^{\circ}$, find $ \overrightarrow a.\overrightarrow b$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Find a vector in the direction of vector $ \overrightarrow a = \hat i - 2\hat j$, whose magnitude is 7.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If the equation of the line AB is $ \large\frac{x-3}{1}=\frac{y-2}{-2}=\frac{z-5}{4}$, find the direction ratios of a line parallel to AB.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

if $ \begin{bmatrix} x+2 & 3 \\ x+5 & 4 \end{bmatrix}=3,$ find the value of x.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Let T be the set of all triangles in a plane with R as relation in T given by $ R = {(T_1,T_2): T_1 \cong T_2}$. Show that R is an equivalence relation.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Solve : \[ tan^{-1}(x+1)+tan^{-1}(x-1)=tan^{-1}\frac{8}{31}\]

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Prove the following : \[ tan^{-1} \bigg( \frac{x}{y} \bigg)- tan^{-1} \bigg( \frac{x-y}{x+y} \bigg)= \frac{\pi}{4},y \neq 0. \]

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Using the properties of determinants, prove the following : \[ \begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & c+a \\ a+b & b+c & c+a \end{vmatrix} = 2(a+b+c)(ab+bc+ca-a^2-b^2-c^2).\]

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Discuss the continuity of the following function at x = 0: $ f(x) = \left\{ \begin{array}{l l}\large\frac{x^4+2x^3+x^2}{\tan^{-1}x}, & \quad if { x \; \neq 2 } \\ 0, & \quad if { x\; = 0 } \end{array} \right. $

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Verify Lagrange's mean value theorem for the following function: $ f(x)=x^2-2x+3,\: for \: [4,6]$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ f(x)=\sqrt{\large\frac{\sec x-1}{\sec x+1}}$$\: find\: f'(x). $ Also find $( f' \bigg( \large\frac{\pi}{2}\bigg).)$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ x\sqrt{1+y}+y\sqrt{1+x}=0\:, find \: \large\frac{dy}{dx}$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Show that $ \int_0^{\large\frac{\pi}{2}} \sqrt{\tan\: x}+\sqrt{\cot x}=\sqrt {2\pi} $

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ y=e^{\large \tan\: x},$ prove that $ \cos^2x\large\frac{d^2y}{dx}$$-(1+\sin\: 2x)\large\frac{dy}{dx}$$=0$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ y=(x)^x+(\cos x)^{2x} \: find \: \large\frac{dy}{dx}$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Evaluate : $\begin{align} \int \limits_{0}^{2}(x^2+3)dx \end{align}$ as limit of sum.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{8\: dx}{(x+2)(x^2+4)}$

asked Feb 15, 2013 by thanvigandhi_1

1 answer