Recent questions in Math

Two eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.

asked Nov 19, 2016 by priyanka.c

1 answer

Find the vector and Cartesian equation of the line through the point (5, 2, -4) and which is parallel to the vector $3 \hat{i} +2 \hat{j} -8 \hat{k}$

asked Nov 19, 2016 by priyanka.c

1 answer

$\begin{align}\int_0^1 \frac{\tan^{-1} x}{1+x^2} dx \end{align}$

asked Nov 19, 2016 by priyanka.c

1 answer

Fine the maximum and minimum value of $f(x) = x + \sin 2x$ in the invervat $0, 2\pi$

asked Nov 19, 2016 by priyanka.c

1 answer

Differentiate $\tan^-1 \frac{[\sqrt{1+x^2} + 1}{x}], x \neq 0$

asked Nov 18, 2016 by priyanka.c

1 answer

Find the equation of the line joining (1,3) and B (0, 0) using determinants and find K if D (K,0) is a point such that area of $\triangle ABD$ is 3 sq. units

asked Nov 18, 2016 by priyanka.c

1 answer

Show that function $f : R \to R$ given by $f(x) = x^3 + x$ I a bijection.

asked Nov 18, 2016 by priyanka.c

1 answer

$\begin{align}\int \frac{dx}{\sqrt {x^2 - a^2}} \end{align}$

asked Nov 18, 2016 by priyanka.c

1 answer

Two cards are drawn without replacement from a well shuffled pack of 52 cards. Find the probability that one is spade and other is a queen of red colour.

asked Nov 18, 2016 by priyanka.c

1 answer

A line passes through (2, -1, 3) and is perpendicular to the line $\overrightarrow {r} = ( {\hat{i} + \hat {j} - \hat{k}}) + \lambda (2\hat{i} - 2\hat{j} +\hat{k})$ and $\overrightarrow {r} = (2\hat{i} - \hat{j} -3\hat {k}) +\mu (\hat{i} + 2 \hat{j} +2\hat{k})$ . Obtain its equation.

asked Nov 18, 2016 by priyanka.c

1 answer

If $\overrightarrow {a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\overrightarrow {b} = 2\hat{i} + 4\hat{j} - 5\hat{k}$ represents two adjacent sides of a parallelogram, find unit vectors parallel to the diagonals of the parallelogram.

asked Nov 18, 2016 by priyanka.c

1 answer

If $A=\begin{bmatrix} 9 & 1 \\ 7 & 8 \end{bmatrix}$ , $B =\begin{bmatrix} 1 & 5 \\ 7 & 12 \end{bmatrix}$ find matrix C such that 5A + 3B + 2C is a null matrix.

asked Nov 17, 2016 by priyanka.c

1 answer

If $\cos^{-1} x + cos^{-1} y + cos^{-1} z = \pi$ , Evaluate $x^2 + y^2 + z^2 + 2xyz$

asked Nov 17, 2016 by priyanka.c

1 answer

If the function $f: [1, \alpha) \ implies [ 1, \alpha)$ defined by $f(x) = 2^{x(x-1)}$ is invertible, find $f^{-1}(x)$

asked Nov 17, 2016 by priyanka.c

1 answer

A die which is marked with 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event 'number is even' and B be the event 'number is red' and Are A and B independent?

asked Nov 17, 2016 by priyanka.c

1 answer

$\begin{equation} \int\limits_0^1 \sin^{-1} x \; \mathrm{d} x \end{equation}$

asked Nov 17, 2016 by priyanka.c

1 answer

If the points $A(-1, 3, 2),\; B(-4, 2, -2)$ and $C (5, 5, \lambda)$ are collinear, find the value of $\lambda$

asked Nov 16, 2016 by priyanka.c

1 answer

Differentiate $a^x$ w.r.t x, where a is a constant

asked Nov 16, 2016 by priyanka.c

1 answer

$\tan ^{-1}x +\tan^{-1} \frac{2x}{1-x^2} = 3 \tan ^{-1}(x) \;, |x| < \frac{1}{\sqrt 3}$ . Is this true ? Justify.

asked Nov 16, 2016 by priyanka.c

1 answer

Let f : N $\to$ Y be a function defined as $f(x) = 4x + 3f(x)=4x+3$ where $Y = \{ y \in N ; y = 4x + 3Y=\{ y \in N; y= 4x+3$ for some $x \in N \}x \in N \}$ . If 'f' is invertible.

asked Nov 14, 2016 by priyanka.c

1 answer

Prove that $\cos^{-1}x = 2 \sin^{-1} \sqrt{\frac{1-x}{2}}$

asked Nov 9, 2016 by priyanka.c

0 answers

Find the differential equation whose general solution is $y= Ae^x+Be^2x+Ce^3x+De^4x+E$ where A,B,C,D,E are constant

asked Oct 17, 2016 by meena.p

1 answer

In the ground state of hydrogen atom, its Bohr radius is given as $5.3 \times 10^{-11}\;m$ . The atom is excited such that the radius becomes $21.2 \times 10^{-11}\;m$ . Find (i) the value of the principal quantum number and (ii) the total energy of the atom in this excited state.

asked May 30, 2016 by meena.p

1 answer

Three numbers are selected at random (with out replacement ) from first six positive integers. If X denotes the smallest of the three numbers obtained , find the probability distribution of X.Also find the mean and variance of the distribution .

asked May 30, 2016 by meena.p

1 answer

A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods $F_1 \: and F_2$ are available . Food $F_1$ costs Rs. 4 perunit and $F_2$ costs Rs. 6 per unit. One unit of food $F_1$ contains 3 units of vitamin A and 4 units of minerals. One unit of food $F_2$ contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem and find graphically the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

asked May 30, 2016 by meena.p

1 answer

Find the equation of the plane containg two parallel lines $\large\frac{x-1}{2} = \frac{y+1}{-1} = \frac{z}{3}$ and $\large\frac{x}{4} = \frac{y-2}{-2} =\frac{z+1}{6}$ . Also find the plane thus obtained contains the line $\large\frac{x-2}{3} =\frac{y-1}{1} =\frac{z-2}{5}$ or not .

asked May 30, 2016 by meena.p

1 answer

Using integration find the area of the region $f(x,y): y^2 \leq 6ax$ and $x^2+y^2 \leq 16a^2$

asked May 30, 2016 by meena.p

1 answer

Find the maximum and minimum values of $f(x)=\sec x + \log \cos ^2x, 0 < x < 2 \pi$

asked May 30, 2016 by meena.p

0 answers

Determine the intervals in which the function $f(x)=x^4 -8x^3+22x^2-24 x +21$ is strictly increasing or strictly decreasing.

asked May 30, 2016 by meena.p

1 answer

Using of elementary row operations, find the inverse of the following matrix : $\begin{bmatrix} 2 & -1 & 3\\ -5 & 3 & 1\\-3 & 2 & 3\end{bmatrix}$

asked May 30, 2016 by meena.p

1 answer

Using properties of determinant prove that : $\begin{bmatrix}(b+c)^2 & a^2 & bc \\ (c+a)^2 & b^2 & ca \\ (a+b)^2 & c^2 & ab \end{bmatrix}$ $=(a-b)(b-c)(c-a) (a+b+c)(a^2+b^2+c^2)$

asked May 30, 2016 by meena.p

1 answer

Find the coordinates of the point where the line $\overrightarrow {r} =(-\hat {i} - 2 \hat {j} - 3 \hat {k} )+ \lambda ( 3\hat i + 4 \hat j +3 \hat k )$ meets the plane which is perpendicular to the vector $\overrightarrow n= \hat i + \hat j + 3 \hat k$ and at a distance of $\large\frac{4}{\sqrt {11}}$ from origin .

asked May 30, 2016 by meena.p

1 answer

Find the equation of plane passing through the point $A(3,2,1,) B(4,2,-1)$ and $C(6,5,-1)$ and $D(\lambda,5,5)$ are co planar

asked May 30, 2016 by meena.p

1 answer

Given that vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ from a triangle such that $\overrightarrow{a} = \overrightarrow{b}+ \overrightarrow{c}$ . Find p,q,r,s such that area of triangle is $5 \sqrt 6$ where $\overrightarrow{a} = p \hat i +q \hat j +r \hat k$ , $\overrightarrow{b} = s \hat i +3 \hat j +4 \hat k$ and $\overrightarrow{c} = 3 \hat i + \hat j -2 \hat k$

asked May 30, 2016 by meena.p

1 answer

There are two bags A and B . Bag A contains 3 white and 4 red balls whereas bag B contains 4 white and 3 red balls . Three balls are drawn at random ( with out replacement ) from one of the bags and are found to be two white and one red. Find the probability that these were drqwn from bag B.

asked May 30, 2016 by meena.p

1 answer

Solve the equation for $x: \cos ( \tan ^{-1} x ) = \sin \bigg( \cot ^{-1} \large\frac{3}{4}\bigg)$

asked May 27, 2016 by meena.p

0 answers

Prove that $2\sin ^{-1} \bigg( \large\frac{3}{5} \bigg) - \tan ^{-1} \bigg(\large\frac{17}{31} \bigg) = \large\frac{\pi}{4}$

asked May 27, 2016 by meena.p

1 answer

Ishan wants to donate a rectangular plot of land for a land for a school in his village . When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same. but if length is decreased by 10 m and breadth is decreased by 20 m. then its area will decrease by $5300\;m^2$ . Using matrices , find the dimension of the plot. Also give reasons why he wants to denote the plot for a school.

asked May 27, 2016 by meena.p

1 answer

Solve the differential equation : $2ye^{x/y} dx+ (y -2x e^{x/y})dy=0$

asked May 27, 2016 by meena.p

1 answer

Solve the differential equation : $(x+1)\large\frac{dy}{dx}$ $-y =e^{3x}(x+1)^3$

asked May 27, 2016 by meena.p

1 answer

Evaluate : $\int \limits_0^1 \cot ^{-1} (1-x+x^2)dx$

asked May 27, 2016 by meena.p

1 answer

Evaluate: $\int \limits_0^{\large\frac{\pi}{2}} \large\frac{sin ^2 x}{\sin x + \cos x}$ $dx$

asked May 27, 2016 by meena.p

1 answer

Find $\{\int (\log (\log x)+\large\frac{1}{(\log x)^2}\}$ $dx$

asked May 27, 2016 by meena.p

1 answer

Find $\int \large\frac{1- \sin x}{\sin x (1+\sin x)}$ $dx$

asked May 27, 2016 by meena.p

1 answer

Find the equation of normal to the curve $ay^2 = x^3$ at the point whose x coordinate is $am^2$

asked May 27, 2016 by meena.p

1 answer

Find k, if $f(x) = \left\{ \begin{array} {1 1} k \sin \frac{\pi}{2}(x+1), & \quad x \leq 0 \\ \frac{\tan x - \sin x}{x^3} ,& \quad x >0 \end{array} \right.$ is a continuous at x=0

asked May 27, 2016 by meena.p

1 answer

Differentiate $\tan ^{-1} \bigg( \large\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\bigg)$ with respect to $\cos ^{-1}x^2$

asked May 27, 2016 by meena.p

1 answer

Differentiate $(\sin 2x)^x+ \sin ^{-1} \sqrt {3x}$ with respected to x

asked May 27, 2016 by meena.p

1 answer

If $A = \begin{bmatrix} 0 & 3 \\2 & -5 \end{bmatrix}$ and $KA = \begin{bmatrix} 0 & 4a \\-8 & 5b \end{bmatrix}$ find the values of K and a

asked May 27, 2016 by meena.p

1 answer

If $A= \begin{bmatrix}1 & 2 \\ 3 & -1\end{bmatrix}$ and $B=\begin{bmatrix}1 & -4 \\ 3 & -2\end{bmatrix}$ find $|AB|$

asked May 27, 2016 by meena.p

1 answer

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