Email

Chat with tutors

Login

Ask Questions, Get Answers

Menu X

home ask tuition questions practice papers mobile tutors pricing

X

Recent questions tagged misc

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

asked Feb 5, 2013 by thanvigandhi_1

1 answer

sketch the graph of y=|x+3| and evaluate $\int_{-6}^0|x+3| dx.$

asked Jan 21, 2013 by sreemathi.v

1 answer

Using properties of determinants, prove the following : $ \begin{bmatrix} 3a & -a+b & -a+c \\ a-b & 3b & c-b \\ a-c & b-c & 3c \end{bmatrix} = 3(a + b + c)(ab+bc+ca) $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Sketch the graph of y=| x+3 | and evaluate$\Large \int\limits_{-6}^0\normalsize| x+3 |dx$

asked Dec 17, 2012 by sreemathi.v

1 answer

Find the equation of the plane passing through the line of intersection of the planes \(\overrightarrow r. (\hat i + \hat j + \hat k)=1\) and \( \overrightarrow r. (2\hat i + 3\hat j - \hat k) + 4 = 0\) and parallel to \(x\) - axis.

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the value of: $\cos^{-1} (\cos \large\frac{13\pi}{6} ) $

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Find the value of the following:<br> $ tan^{-1} \bigg(tan \frac{7\pi}{6}\bigg)$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

What does $ 2\sin^{-1} \frac{3}{5}$ reduce to

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write down a unit vector in XY plane, making an angle of 30 degress with the positive direction of $x$ axis.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the scalar components and magnitude of the vector joining the points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a = \overrightarrow b + \overrightarrow c$, then is it true that $| \overrightarrow a | = | \overrightarrow b | + | \overrightarrow c |$? Justify your answer.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the value of $x$ for which $x(\hat i + \hat j +\hat k)$ is a unit vector.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find a vector of magnitude $5$ units, and parallel to the resultant of the vectors $\overrightarrow a = 2\hat i + 3 \hat j - \hat k$ and $\overrightarrow b = \hat i - 2\hat j + \hat k$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - \hat j + 3\hat k$ and $\overrightarrow c = \hat i - 2\hat j + \hat k$, find a unit vector parallel to the vector $2\overrightarrow a - \overrightarrow b + 3\overrightarrow c$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are \((2\overrightarrow a + \overrightarrow b)\) and \((\overrightarrow a - 3\overrightarrow b)\) externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ

asked Dec 5, 2012 by thanvigandhi_1

1 answer

The two adjacent sides of a parallelogram are \(2\hat i - 4\hat j + 5\hat k\) and \( \hat i - 2\hat j - 3\hat k\) . Find the unit vector parallel to its diagonal. Also, find its area.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $ \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3} $

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Let \(\overrightarrow a = \hat i + 4 \hat j + 2\hat k, \overrightarrow b = 3\hat i − 2 \hat j + 7\hat k \: and \: \overrightarrow c = 2\hat i − \hat j + 4\hat k \) . Find a vector \( \overrightarrow d\) which is perpendicular to both \(\overrightarrow a\) and \(\overrightarrow b\) , and \( \overrightarrow c ⋅ \overrightarrow d =15\)

asked Dec 5, 2012 by thanvigandhi_1

1 answer

The scalar product of the vector \(\hat i + \hat j + \hat k\) with a unit vector along the sum of vectors \(2\hat i + 4 \hat j − 5\hat k\) and \(λ\hat i + 2 \hat j + 3\hat k\) is equal to one. Find the value of \( λ.\)

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If \( \overrightarrow a, \overrightarrow b, \overrightarrow c, \) are mutually perpendicular vectors of equal magnitudes, show that the vector \( \overrightarrow a + \overrightarrow b + \overrightarrow c\) is equally inclined to \( \overrightarrow a, \overrightarrow b and \overrightarrow c\).

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Prove that \( (\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a + \overrightarrow b) =| \overrightarrow a |^2 + |\overrightarrow b |^2\), if and only if \(\overrightarrow a,\: \overrightarrow b\) are perpendicular, given \(\overrightarrow a ≠ 0, \overrightarrow b ≠ 0\).

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Choose the correct answer if θ is the angle between two vectors $\overrightarrow a$ and $ \overrightarrow b$, then $ \overrightarrow a \: . \: \overrightarrow b\ \: \geq 0$ only when

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the following : let \( \overrightarrow a\) and \( \overrightarrow b\) be two unit vectors and θ is the angle between them. Then \( \overrightarrow a\ + \overrightarrow b\) is a unit vector if

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Choose the correct answer if the value of $ \hat i.( \hat j\times \hat k)+ \hat j . (\hat i \times \hat k) +\hat k. (\hat i \times \hat j)$ is

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Choose the correct answer if θ is the angle between any two vectors $\overrightarrow a$ and $\overrightarrow b$, then $| \overrightarrow a ⋅\overrightarrow b | \: = \: | \overrightarrow a \times\overrightarrow b |$ when θ is equal to

asked Dec 5, 2012 by thanvigandhi_1

1 answer

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

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If \(y = \begin{vmatrix} f(x) & g(x) & h(x) \\l & m &n \\ a & b & c \end{vmatrix}\), prove that \(\large\frac{dy}{dx}\normalsize = \begin{vmatrix} f'(x) & g'(x) & h'(x) \\l & m &n \\ a & b & c \end{vmatrix}\)

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Using the fact that \(\sin (A + B) = \sin A \cos B + \cos A \sin B\) and the differentiation, obtain the sum formula for cosines.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Using mathematical induction prove that \( \large\frac{d}{dx}\normalsize (x^{\large n}) = nx^{\large{n-1}} \) for all positive integers \(n\).

asked Dec 4, 2012 by thanvigandhi_1

1 answer

If \(f (x) = |\; x\; |^3\), show that \(f ″(x)\) exists for all real \(x\) and find it.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

If \(x = a (\cos t + t\sin t)\) and \(y = a (\sin t - t \cos\: t)\), find \( \large\frac{d^2y}{dx^2}\)

asked Dec 4, 2012 by thanvigandhi_1

1 answer

If \(cos\: y = x \cos (a + y)\), with $\cos$ \(a \neq \pm 1\), prove that \( \large\frac{dy}{dx}=\frac{\cos^2(a + y)}{\sin \: a}\)

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area under the given curves and given lines: $ (i) \: y = x^2, x = 1, x = 2 \: and\: x - axis$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area between the curves \(y = x\) and \(y = x^2.\)

asked Dec 4, 2012 by thanvigandhi_1

2 answers

Find the area of the region lying in the first quadrant and bounded by $y = 4x^2, x = 0, y = 1$ and $y = 4$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area bounded by the curve $(y = \sin\; x) $ between $ (x = 0) $ and $(x = 2π).$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area enclosed between the parabola \(y^2 = 4ax\) and the line \(y = mx.\)

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area enclosed by the parabola \(4y = 3x^2\) and the line \(2y = 3x + 12.\)

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the smaller region bounded by the ellipse \( \frac{\large x^2}{\large 9} + \frac{\large y^2}{\large 4} =1\) and the line \( \frac{\large x}{\large 3}+ \frac{\large y}{\large 2}= 1\)

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the smaller region bounded by the ellipse \(\Large { \frac{ x^2}{ a^2}}+\Large { \frac{ y^2}{ b^2}} =\normalsize 1\) and the line \(\Large { \frac{ x}{ a}}+\Large { \frac{y}{ b}} =\normalsize1\)

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the region enclosed by the parabola \(x^2 = y\), the line \(y = x + 2\) and the \(x\) - axis.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Using the method of integration find the area bounded by the curve I x I + I y I =1 . [Hint: The required region is bounded by lines \(x + y = 1, x - y = 1, -x + y = 1\) and \( -x -y = 1\)].

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area bounded by curves {(x, y)$ : y\: \geq\: x^2\: and \: y = |\; x\; |$}.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B(4, 5) and C(6, 3).

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Using the method of integration find the area of the region bounded by lines: \(2x + y = 4, 3x - 2y = 6\) and \(x - 3y + 5 = 0\)

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the region ${(x, y) : y^2\: \leq \: 4x, 4x^2 + 4y^2\: \leq\: 9}$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the area bounded by the curve $ y = x^3$, the $x$ - axis and the ordinates $x = -2$ and $x = 1$ is

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Page:

« prev
1
2
3
4
5
6
7
8
...
10
next »

Feedback Terms Facebook Twitter About Us

Your payment for is successful.

...