Recent questions in Model Papers

Evaluate the determinant : $\begin{bmatrix} log_ba & 1 \\ 1 & log_ab \end{bmatrix} .$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Find the values of x, y and z from the following equation: $\begin{bmatrix} x+y+z \\ x+z \\ y+z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} .$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

If $\begin{vmatrix} 3x & 7 \\ 2 & 4 \end{vmatrix}$ = 10, find x.

asked Jan 23, 2013 by thanvigandhi_1

1 answer

If $f(x) = 2^{\sin^2x},$ then find $\large \frac{dy}{dx}$ .

asked Jan 23, 2013 by thanvigandhi_1

0 answers

What is the degree of the following differential equation ? $4 \bigg( \frac{dy}{dx} \bigg)^2 - 7y - \bigg( \frac{dy}{dx} \bigg)^3 + \sin x = 0$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

The coordinates of P and Q are (2, -3) and (1, -2) respectively. Find the coordinates of the position vector, equivalent to $\overrightarrow {PQ}$ .

asked Jan 23, 2013 by thanvigandhi_1

0 answers

If angle between the two vectors $\overrightarrow a \: and \: \overrightarrow b$ of same magnitude is $60^{\circ}$ and $\overrightarrow a. \overrightarrow b = 32,$ then find $|\overrightarrow a | \: and \: | \overrightarrow b |.$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Find the vector equation of the line through the points $2\hat i - \hat j + \hat k$ and $\hat i + 2\hat j - 3\hat k$ .

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b): both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset{1, 3, 5, 7} are related to each other and all elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7}} is related to any element of the subset {2, 4, 6}.

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Solve for x : $tan^{-1} \bigg( \frac{2x}{1-x^2} \bigg) +cot^{-1} \bigg( \frac{1-x^2}{2x} \bigg) = \frac{\pi}{3}, x > 0$

asked Jan 23, 2013 by thanvigandhi_1

1 answer

If $\sin \bigg( \sin^{-1} \large\frac{1}{5}$ $+\cos^{-1}x \bigg) = 1,$ then find the value of x.

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Two firms X and Y decided to award prizes to their employees for three norms Obedience (O), Punctual (P), Quality of work (Q). Firm X decided to award Rs. 40000 for the three values to 2, 4, 7 employees respectively while Y decided to award Rs. 51000 to 4, 2, 8 employees respectively. If all the three prizes together amount to Rs. 8750, then (i) Represent the above situation by a matrix equation and form linear equation using matrix multiplication. (ii) Is it possible to solve the system of linear equations so obtained using matrices? (iii) Which value you prefer to be rewarded most and why?

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation : $e^x \sqrt{1-y^2}dx+\large\frac{y}{x}$ $dy=0$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

If $y = e^{a\: cos^{-1}x}, -1 \leq x \leq 1,$ show that : $(1-x^2)\large\frac{d^2y}{dx^2}$ $-x\large \frac{dy}{dx}$ $-a^2y=0$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Find the values of a and b, so that the function f given by $f(x) = \left\{ \begin{array}{l l} 1, & \quad if { x \leq 3}\\ ax+b, & \quad if { 3<x<5} \\ 7, & \quad if {x \geq 5} \end{array} \right.$ is continuous at x = 3 and x = 5.

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Differentiate $sin(x^x)$ w.r.t. $\tan^{-1} \sqrt{ \large\frac{1-x^2}{1+x^2}}$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int \large\frac{\cos x}{(1+\sin x)(2+\sin \: x)}$ $dx$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int \large\frac{\log x }{(1+\log\: x)^2}$ $dx$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int \large\frac{1-x^2}{x(1-2x)}$ $dx.$

asked Jan 23, 2013 by thanvigandhi_1

0 answers