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Recent questions tagged 2011

Write the number of all one-one functions from the set A = { a, b, c} to itself.

asked Dec 29, 2012 by thanvigandhi_1

1 answer

Find \( x \: if \;\tan^{-1} 4 + \cot^{-1} x =\large \frac{\pi}{2} \)

asked Dec 29, 2012 by thanvigandhi_1

0 answers

What is the value of \( | 3\: I_3 | \) where \( I_3 \) is the identity matrix of order 3?

asked Dec 29, 2012 by thanvigandhi_1

0 answers

For what value of \( k \) , the matrix \( \begin{bmatrix} 2-k & 3 \\ -5 & 1 \end{bmatrix} \) is not invertible?

asked Dec 29, 2012 by thanvigandhi_1

0 answers

If A is a matrix of order 2 x 3 and B is a matrix of order 3 x 5, what is the order of matrix (AB)' or T?

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Write a value of $ \int \: \large\frac{dx}{\sqrt {4-x^2}} $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find f(x) satisfying the following : $ \int \: e^x ( sec^2 x + tan \: x ) dx = e^x\: f (x) +C $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

In a triangle ABC, the sides AB and BC are represented by vectors \( 2\hat i - \hat j + 2\hat k, \hat i + 3\hat j + 5\hat k\) respectively. Find the vector representing CA.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find the value of \( \lambda \) for which the vector \( \overrightarrow a = 3\hat i + \hat j - 2\hat k \) and \( \overrightarrow b = \hat i + \lambda\hat j - 3\hat k \) are perpendicular to each other.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find the value of \( \lambda \) such that the line \(\large \frac{x-2}{9} = \large\frac{y-1}{\lambda} = \large\frac{z+3}{-6} \) is perpendicular to the plane \( 3x - y - 2z = 7 \).

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Show that the function f : R \( \rightarrow \) R be defined by \( f(x) = 2x^3 - 7\), for \( x \: \in \: R\), is bijective.

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Prove that \( tan^{-1}\: 1 + tan^{-1} \: 2 + tan^{-1} \: 3 = \pi \)

asked Dec 28, 2012 by thanvigandhi_1

0 answers

If \( A = \begin{bmatrix} 3 & -5 \\ -4 & 2 \end{bmatrix} \) show that \( A^2 - 5A - |4| = 0\). Hence find \( A^{-1} \)

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Show that \( f(x) = |x-3|, \large\frac{1}{4} \normalsize \forall \: x\: \in\: R, \) is continuous but not differentiable at $x = 3.$

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Verify Roll's theorem for the function f, given by \( f(x) = e^x (\sin x - \cos x ) \: on \: \begin{bmatrix} \large\frac{\pi}{4}, & \large\frac{5\pi}{4} \end{bmatrix} \)

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Using differentials, find the approximate value of \( \sqrt {25.2} \)

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int_{-1}^{\Large\frac{1}{2}} \mid x\cos ( \pi\: x ) \mid dx $

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Solve the following differential equation : $ ye^{\large\frac{x}{y}}$$dx = (xe^{\large\frac{x}{y}} $$+ y ) dy $

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Solve the following differential equation : \( ( 1 + y + x^2y ) dx + ( x + x^3 ) dy = 0, \: where \: y = 0 \: when \: x = 1 \)

asked Dec 28, 2012 by thanvigandhi_1

0 answers

If \( \overrightarrow a, \overrightarrow b \) and \( \overrightarrow c \) are three unit vectors such that \( \overrightarrow a.\overrightarrow b = \overrightarrow a. \overrightarrow c = 0\) and angle between \( \overrightarrow b \: and \: \overrightarrow c \) is \( \large\frac{\pi}{6}, \) prove that \( \overrightarrow a = \pm\: 2 ( \overrightarrow b\) x \( \overrightarrow c ) \).

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Show that the four points ( 0, -1, -1 ), ( 4, 5, 1 ) and (-4, 4, 4 ) are coplanar. Also find the equation of the plane containing them.

asked Dec 28, 2012 by thanvigandhi_1

1 answer

A coin is based so that the head is 3 times as likely to occur as tail. If the coin is tossed three times, find the probabilty distribution of number of tails.

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Using properties of determinants, show that $ \Delta = \begin{bmatrix} (a+b)^2 & ab & ca \\ ab & (a+b)^2 & bc \\ ac & bc & (a+b)^2 \end{bmatrix} = 2abc\: (a + b + c )^3 $

asked Dec 28, 2012 by thanvigandhi_1

0 answers

The sum of the perimeter of a circle and a square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Evaluate : $\int \large\frac{1}{\sin x (5-4\cos x )}$$ dx$

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Using integration, find the area of the region $ \{ (x,y) : | x - 1 | \leq y \leq \sqrt {5-x^2} \} $

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Show that the lines $ \large\frac{x+3}{-3} = \frac{y-1}{1} = \frac{z-5}{5} $ and $\large \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z-5}{5} $ are coplanar. Also find the equation of the plane.

asked Dec 26, 2012 by thanvigandhi_1

1 answer

From a pack of 52 cards, a card is lost. Fro the remaining 51 cards, two cards are drawn at random ( without replacement ) and are found to be both diamonds. What is the probability that the lost card was a card of heart?

asked Dec 26, 2012 by thanvigandhi_1

0 answers

A diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1400 calories. Two foods X and Y are available at a cost of Rs.4 and Rs.3 per unit respectively. One unit of food X contains 200 units of vitamins, 1 unit of minerals and 40 calories, whereas 1 unit of food Y contains 100 units of vitamins, 2 units of minerals and 40 calories. Find what combination of foods X and Y should be used to have atleast cost, satisfying the requirements. Make it an LPPand solve it graphically.

asked Dec 26, 2012 by thanvigandhi_1

0 answers

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