Recent questions tagged 2012

Find the projection of $ \overrightarrow a \: on \: \overrightarrow b\: if \: \overrightarrow a.\overrightarrow b=8\: and \: \overrightarrow b = 2\hat i + 6\hat j + 3\hat k$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Find the direction cosines of the line passing through the points $(-2,4,-5)$ and $(1,2,3)$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If matrix A = (1,2,3), write AA' where A' is the transpose of matrix A.

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Write the value of the determinants \[ \begin{vmatrix} 2 & 3 & 4 \\ 5 & 6 & 8 \\ 6x & 9x & 12x \end{vmatrix} \]

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Using principal value, evaluate the following : \[ sin^{-1} \bigg( sin \frac{3\pi}{5} \bigg) \]

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{\sec^2x}{3+\tan\:x}$$dx $

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If $ \int_0^1 (3x^2+2x+k)dx=0,$ find the value of k

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If the binary operation * on the set of integers Z, is defined by $ab=( a+3b^2)$ then find the value of $24$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

if A is an invertible matrix of order 3 and |A|=5, then find |adj.A|.

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If $ \overrightarrow a \times \overrightarrow b=\overrightarrow c \times \overrightarrow d\: and \: \overrightarrow a \times \overrightarrow c=\overrightarrow b \times \overrightarrow d$ show that $ \overrightarrow a-\overrightarrow d$ is parallel to $ \overrightarrow b-\overrightarrow c$ where $ \overrightarrow a \neq \overrightarrow d\: and \overrightarrow b \neq\overrightarrow c$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Prove that : $ \sin^{-1} \bigg(\large \frac{4}{5} \bigg)$$+\sin^{-1} \bigg(\large \frac{5}{13} \bigg) $$+ \sin^{-1} \bigg( \large\frac{16}{65} \bigg) = \large\frac{\pi}{2} $

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Solve for x : $ \tan^{-1}3x+\tan^{-1}2x=\large\frac{\pi}{4} $

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Find the value of $ \lambda $ so that the line $\large \frac{1-x}{3}=\frac{7y-14}{2\lambda}=\frac{5z-10}{11} $$\: and \; \large\frac{7-7x}{3\lambda}=\frac{y-5}{1}=\frac{6-z}{5}$ are perpendicular to each other.

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Solve the following differential equation : $\large \frac{dy}{dx}$$+y=\cos\: x-\sin\: x$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Find the particular solution, satisfying the given condition, for the following differential equation : $\large \frac{dy}{dx}-\frac{y}{x}$$+cosec \bigg( \large\frac{y}{x} \bigg)$$=0; y=0\: when \: x = 1$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

By using properties of determinants, prove the following: \[ \begin{vmatrix} x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{vmatrix}=(5x+4)(4-x)^2 \]

asked Feb 17, 2013 by thanvigandhi_1

1 answer

A die is thrown again and again untill three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

asked Feb 17, 2013 by thanvigandhi_1

1 answer