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Recent questions tagged easy

Find principal value of the expression \( cos^{-1}(cos(-680^{\circ})).\)

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If \( \begin{bmatrix} xy & 4 \\ z+6 & x+y \end{bmatrix} = \begin{bmatrix} 8 & w \\ 0 & 6 \end{bmatrix} \), then find values of x,y,z and w.

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the value of x if $ \begin{bmatrix} x & 2 \\ 18 & x \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 18 & 6 \end{bmatrix}$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

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

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Evaluate : $\int_{-\Large\frac{\pi}{2}}^{\Large\frac{\pi}{2}} \sin^7x\: dx$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

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

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If a line makes angles \( 90^{\circ}, 135^{\circ}, 45^{\circ}\) with the x, y and z axes respectively, find its direction cosines.

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Compute the magnitude of the following vector $\large\frac{1}{\sqrt 3}\hat i + \frac{1}{\sqrt 3}\hat j - \frac{1}{\sqrt 3}\hat k. $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If $ f(x)=\sqrt x (x \geq 0)\: and \: g(x) = x^2-1$ are two real functions, find \( fog\: and \: gof.\: Is\: fog = gof. \)

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Show that the function = 2x - | x | is continuous at x = 0.

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Differentiate the following function w.r.t. \( x.\) $ (sin\: x)^{\large cos^{-1}x} $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{dx}{\sqrt{8+2x-x^2}} $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If \( \overrightarrow a = \hat i + \hat j + \hat k \: and \: \overrightarrow b = \hat j - \hat k\), then find a vector \( \overrightarrow c\) such that \( \overrightarrow a \) x \( \overrightarrow c = \overrightarrow b\: and \: \overrightarrow a.\overrightarrow c = 3 \)

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the vector equation of the line passing through (1,2,3) and perpendicular to the plane \( \overrightarrow r.(\hat i + 2\hat j - 5\hat k)+9=0\)

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Solve for x : $ \begin{bmatrix} 1 - x & 1 \end{bmatrix} \begin{bmatrix} 2 & -1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 3 \end{bmatrix} = 0 $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Write the principal value of \( cot^{-1} \{ cot \bigg( -\frac{\pi}{4} \bigg) \} \)

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \begin{vmatrix} x^2-x+1 & x-1 \\ x+1 & x+1 \end{vmatrix} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Differentiate \( cos(sin\: x)\) with respect to x.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the value of x if $ \begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Determine the order and degree of following differential equation $ \bigg(\large \frac{ds}{dt} \bigg)^4 +$$ 3s\bigg(\large \frac{d^2s}{dt^2} \bigg) $$= 0 $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the projection of \( \overrightarrow a = 2\hat i - \hat j + \hat k\: on \: \overrightarrow b = \hat i - 2\hat j + \hat k. \)

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Write the perpendicular distance of the plane \( \overrightarrow r.(2\hat i - \hat j + 2\hat k)=12\) from the origin.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

If \( | \overrightarrow a | = 2, | \overrightarrow b | = 7 \: and \: \overrightarrow a \) x \( \overrightarrow b=3\hat i + 2\hat j + 6\hat k\), find the angle between \( \overrightarrow a \: and \: \overrightarrow b.\)

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the area of the parallelogram whose diagnols are represented by the vectors $ \overrightarrow d_1 = 3\hat i +\hat j -2\hat k\: and \: \overrightarrow d_2 = \hat i -3\hat j +4\hat k.$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Let * be a binary operation on N given by \( ab=H.C.F.(a,b), a,b \in N.\) Write value of 224.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

What is the principal value of \( \cos^{-1} \bigg( -\large\frac{\sqrt 3}{2} \bigg). \)

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Construct a 2 x 2 matrix \( A = [ a_{ij} ]\), whose elements are given by \( a_{ij} \) is \( \large\frac{( \hat i + \hat j )^2}{2} \)

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the value of x from the following : $\begin{bmatrix} 2x-y & 5 \\ 3 & y \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 3 & -2 \end{bmatrix} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix} $ then show that | 2A | = 4| A |

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{1+cot x}{x+\log \sin x}$$ dx $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int_1^2 \bigg( \large\frac{1}{x} - \frac{1}{x^2} \bigg) $$e^x \: dx$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

For two non zero vectors $ \overrightarrow a \: and \: \overrightarrow b$ write when $ |\overrightarrow a+\overrightarrow b | = | \overrightarrow a | + | \overrightarrow b | $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

The cartesian equation of a line is $ \large\frac{x+3}{2} = \large\frac{y-5}{4}=\large\frac{z+6}{2} $ Find vector equation of line.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Write $( fog, \: if \: f : R \rightarrow R)$ are given by $( f(x) = 8x^3)$ and $( g(x)=x^{\large\frac{1}{3}} )$

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\large\frac{\cos \sqrt x}{\sqrt x}$$dx $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Write \( fog,\) if \( f : R \rightarrow R \) and \( g: R \rightarrow R\) are given by $ f(x) = | x| \: and \: g(x) = | 5x-2 | $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\large \frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}$$dx$

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Bag I contains 3 red and 4 black balls and bag II contains 4 red and 5 black balls. One ball is transferred from bag I to bag II and then a ball is drawn from bag II at random. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

asked Feb 6, 2013 by thanvigandhi_1

1 answer

If \( f : R \rightarrow R\) is defined by \( f(x)=3x+2\), define \( f[f(x)]. \)

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Write the values of \( x-y+z\) from the following equation : $ \begin{bmatrix} x+y+z \\ x+z \\ y+z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Write the order of the product matrix : $ \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \begin{bmatrix} 2 & 3 & 4 \end{bmatrix} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

If $\begin{vmatrix} x & x \\ 1 & x \end{vmatrix} = \begin{vmatrix} 3 & 4 \\ 1 & 2 \end{vmatrix} $write the positive value of x.

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\limits_1^{\sqrt 3} \large\frac{dx}{1+x^2} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Write the position vector of the mid-point of the vector joining the points P(2,3,4) and Q(4,1,-2).

asked Feb 6, 2013 by thanvigandhi_1

1 answer

If \( \overrightarrow a.\overrightarrow a=0\: and \: \overrightarrow a.\overrightarrow b = 0\), then what can be concluded about the vector \( \overrightarrow b\)?

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Write the angle between two vectors \( \overrightarrow a \: and \: \overrightarrow b\) with magnitudes \( \sqrt 3 \) and 2 respectively having \( \overrightarrow a.\overrightarrow b=\sqrt 6 \).

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Write the unit vector in the direction of the vector \( \overrightarrow a = 2\hat i + \hat j + 2\hat k \).

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Prove the following : $ 2tan^{-1} \bigg(\large \frac{1}{2} \bigg)$$ +\tan^{-1} \bigg( \large\frac{1}{7} \bigg)$$ = \tan^{-1} \bigg( \large\frac{31}{17} \bigg) $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Using properties of determinants, solve the following for x : $ \begin{vmatrix} a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x \end{vmatrix} = 0 $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix} $ write \( A^{-1} \) in terms of A.

asked Feb 5, 2013 by thanvigandhi_1

1 answer

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