Recent questions tagged easy

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

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

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

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 $ \hat i+ \hat j+\hat k,\: 2\hat i+5\hat j,\: 3\hat i+2\hat j=3\hat k\: and \: \hat i-6\hat j-\hat k$ are the position vectorsof the points A,B,C and D, find the angle between $ \overrightarrow{AB}\: and \: \overrightarrow{CD}$. Deduce that $ \overrightarrow{AB}\: and \: \overrightarrow{CD}$ are collinear.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

A man is known to speak truth 3 out of 4 times. He throws a die and report that it is a 6. Find the probability that it is actually 6.

asked Feb 11, 2013 by thanvigandhi_1

1 answer

If $ f(x) = x+7\: and \: g(x) = x-7, x \in R, \: find \: (fog) \: (7) $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Compute $ \begin{bmatrix} a & b \\ -b & a \end{bmatrix} \begin{bmatrix} a & -b \\ b & a \end{bmatrix} $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\large\frac{x^2}{1+x^3}$$dx $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int_0^1\large\frac{dx}{1+x^2} $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find a unit vector in the direction of $ \overrightarrow a = 3\hat i - 2\hat j + 6\hat k $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find the angle between the vectors : $ \overrightarrow a = \hat i - \hat j + \hat k\: and \: \overrightarrow b = \hat i + \hat j -\hat k$

asked Feb 11, 2013 by thanvigandhi_1

1 answer

For what value of $ \lambda $ are the vectors $ \overrightarrow a = 2\hat i - \lambda \hat j + \hat k\: and \: \overrightarrow b = \hat i - 2\hat j + 3\hat k$ perpendicular to each other?

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Prove the following : \[ cos^{-1} \bigg( \frac{4}{5} \bigg)+ cos^{-1} \bigg( \frac{12}{13} \bigg)= cos^{-1} \bigg( \frac{33}{65} \bigg) \]

asked Feb 11, 2013 by thanvigandhi_1

1 answer

(i) Is the binary operation defined on set N, given by $ a*b = \large\frac{a+b}{2}$ for all a,b $ \in$ N. commutative? (ii) Is the above binary operation associative?

asked Feb 11, 2013 by thanvigandhi_1

1 answer

For what value of k is the following function continuous at x = 2?$ f(x) = \left\{ \begin{array}{l l}2x+1, & \quad if { x \: < \: 2 } \\ k, & \quad if { x = 2 } \\ 3x-1, & \quad if { x > 2 } \end{array} \right. $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

If $ y = 3\cos (\log\: x)+4\sin (\log\: x),$ show that $ x^2\large\frac{d^2y}{dx^2}$$+x\large\frac{dy}{dx}$$+y=0$

asked Feb 11, 2013 by thanvigandhi_1

1 answer