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Recent questions tagged maths

For what values of $x$ and $y$ are the following matrices equal ? $A = \begin{bmatrix} 2x+1 & 3y \\ 0 & y^2-5y \end{bmatrix} , B = \begin{bmatrix} x+3 & y^2+2 \\ 0 &-6 \end{bmatrix}$

asked Dec 8, 2016 by priyanka.c

1 answer

Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1, x = 4$ and the $x- axis.$

asked Dec 8, 2016 by priyanka.c

1 answer

Find the point on the curve $y = x^3 - 11 x + 5$ at which the target is $y = x -11.$

asked Dec 8, 2016 by priyanka.c

1 answer

The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?

asked Dec 8, 2016 by priyanka.c

1 answer

If $f : R \to R$ be given by $f(x) = (3-x^3)^{\frac{1}{3}}$, then evaluate $f o f(x)$

asked Dec 7, 2016 by priyanka.c

1 answer

The radius of a circle is increasing uniformly at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10cm long ?

asked Dec 7, 2016 by priyanka.c

1 answer

The total revenue in Rupees received from the sales of $x$ units of a product is given by $Rx = 3x^2 + 36x +5$ . Find the marginal revenue , when $x=15$, where by marginal.

asked Dec 6, 2016 by priyanka.c

1 answer

If A and B are symmetric matrices, prove that AB - BA is a skew symmetric matrix

asked Dec 6, 2016 by priyanka.c

1 answer

Using cofactors of elements of second row, evaluate $\triangle = \begin{vmatrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{vmatrix}$

asked Dec 5, 2016 by priyanka.c

1 answer

Evaluate : $\tan^{-1} (1) + cos^{-1} ( \frac{-1}{2} )+ \sin^{-1} (\frac{-1}{2})$

asked Dec 5, 2016 by priyanka.c

2 answers

If $A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix} $ , Evaluate $A^TA^{-1}$

asked Dec 1, 2016 by priyanka.c

1 answer

Find the value of $\tan^{-1} (\frac{x}{y}) - \tan^{-1}(\frac{x-y}{x+y})$

asked Nov 30, 2016 by priyanka.c

1 answer

Define a binary operation $\ast$ on the set {0, 1, 2, 3, 4, 5} as \[a*b=\left \{ \begin{array} {1 1} a+b, & \quad \text{ if a+b<6} \\ a+b-6, & \quad { if a+b \geq 6} \end{array} \right.\] show that the zero is the identity for this operation and each element $a \neq 0$ of the set is invertible with $6-a$ being the inverse of $a$.

asked Nov 30, 2016 by priyanka.c

1 answer

A coin is tossed 6 times. What Is the probability that tail appears an odd no of times ?

asked Nov 30, 2016 by priyanka.c

1 answer

If $\theta$ be the angle between two unit vectors. Evaluate $\sin \frac{\theta}{2}$

asked Nov 25, 2016 by priyanka.c

1 answer

Form the differential equation for the family of curves $y = a \sin(x+b)$ where $a \;and \; b$ are parameters

asked Nov 25, 2016 by priyanka.c

1 answer

Evaluate : $\begin{align}\int\limits_{-1}^1 log (\frac{2+x}{2-x}) dx \end{align}$

asked Nov 25, 2016 by priyanka.c

1 answer

Find the approximate value of $f'(3.02)$ where $f(x) = 3x^2+5x+3$

asked Nov 25, 2016 by priyanka.c

1 answer

The total cost C(x) in rupees associated with the production of x units of an item is given by $ C(x) = 0.007 x^3 - 0.003 x^2 + 15x + 4000$. Find the marginal cost when 10 units are produced.

asked Nov 23, 2016 by priyanka.c

1 answer

If $y = \sin (m \sin^{-1} x),$ evaluate $(1-x) \frac{d^2y}{dx^2} - x \frac{dy}{dx} + m^2y = 0$

asked Nov 23, 2016 by priyanka.c

1 answer

Find the value of x if $\begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2& 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} = 0$

asked Nov 23, 2016 by priyanka.c

1 answer

Let A = {1, 2}. Find the number of possible binary operations defined on A.

asked Nov 23, 2016 by priyanka.c

1 answer

A balloon which always remain spherical has a variable diameter$ \frac{3}{2} (2x+ 3)$ : Determine the rate of change of volume w.r.t x

asked Nov 23, 2016 by priyanka.c

1 answer

Evalute : $\begin{vmatrix}152 & 24 & 40 \\ 3 & 7 & 1 \\ 19 & 3 & 5 \end{vmatrix}$

asked Nov 23, 2016 by priyanka.c

1 answer

Evaluate :$\sec^2 (\tan^{-1}(2)) + cosec^2(\cot^{-1}(3))$

asked Nov 23, 2016 by priyanka.c

1 answer

Event A and B are such that $P(A) = \frac{1}{2}, P(B) = \frac{7}{12} $, P (not A or not B) =$ \frac{1}{4}$. State whether A and B are independent.

asked Nov 23, 2016 by priyanka.c

1 answer

If A, B, C are position vectors (2, 0, 0), (0, 1, 0) and (0, 0, 2) show that $\triangle ABC$ is isosceles .

asked Nov 23, 2016 by priyanka.c

1 answer

Find the value of $\lambda$, so that the lines $\frac{1-x}{3} = \frac{7y - 14}{2 \lambda} = \frac{z-3}{2} \;and\; \frac{7-7 \lambda}{3 \lambda} = \frac{y-5}{1} = \frac{6-z}{5} $ are at right angle

asked Nov 22, 2016 by priyanka.c

1 answer

Find the value of 'a ' so that the function f(x) is defined by $f(x) = \begin{cases} \frac{\sin ^2 a x}{x^2} & x \neq 0 \\ 1 , & x =0 \end{cases}$ may be continuous at x = 0

asked Nov 22, 2016 by priyanka.c

1 answer

Use matrix method to examine if the following system of equation for consistency or inconsistency $4x - 2y = 3, \; \; 6x - 3y = 5$

asked Nov 22, 2016 by priyanka.c

1 answer

If $|\overrightarrow{a}| = 11, |\overrightarrow {b} | = 23 and |\overrightarrow {a} - \overrightarrow {b} |= 30 $

asked Nov 22, 2016 by priyanka.c

1 answer

Solve the differential equation $\frac{dy}{dx} = log (x+1)$

asked Nov 22, 2016 by priyanka.c

1 answer

$\begin{align}\int_0^\frac{\pi}{2} \frac{\sin x}{1 + \cos^2 x } dx \end{align}$

asked Nov 22, 2016 by priyanka.c

1 answer

Without expanding evaluate: $\begin{vmatrix} \frac{1}{a} & a^2 & bc \\ \frac{1}{b} & b^2 & ca \\ \frac{1}{c} & c^2 & ab \end{vmatrix}$

asked Nov 22, 2016 by priyanka.c

1 answer

Evaluate : $\tan \frac{1}{2} (\cos^{-1} \frac{\sqrt 5}{3})$

asked Nov 22, 2016 by priyanka.c

1 answer

Verify Rolle's theorem for $f(x) = x^2 + 2$ in the interval [-2,2]

asked Nov 21, 2016 by priyanka.c

1 answer

differentiate $y = (\sin x)^x + \sin^{-1} \sqrt x$

asked Nov 21, 2016 by priyanka.c

1 answer

Using elementary row transformation, find the inverse of $A = \begin{bmatrix} 2 & -6 \\ 1 & -2\end{bmatrix}$

asked Nov 21, 2016 by priyanka.c

1 answer

If $P(A) = 0.25, P(B) = 0.4 \; and \; P (A \cup B) = 0.5 \; find \; P (A \cap B) \;and \; P (A \cap \bar{B})$

asked Nov 21, 2016 by priyanka.c

1 answer

Are the vectors $(\hat {i} + \hat{j} + \hat{k}), (2\hat{i} +3\hat{j} -\hat{k})$ and $(-\hat{i} -2\hat{j} +2 \hat{k})$ are linearly dependent ?

asked Nov 21, 2016 by priyanka.c

1 answer

A car stands from a point P at time t = 0 sec and stops at point Q. The distance x, in metres, covered by it, in t seconds in given by $x = t^2 (2 - \frac{t}{3})$. Find the time taken by it to reach Q and also find the distance between P and Q.

asked Nov 21, 2016 by priyanka.c

1 answer

Find the point at which the target to the curve $y = \sqrt{4x-3} - 1$ has its slope $\frac{2}{3}$

asked Nov 21, 2016 by priyanka.c

1 answer

Solve the system of equation $2x + 5y = 1 \; \ \; \; and \; \; \; \; 3x + 2y = 7$

asked Nov 20, 2016 by priyanka.c

1 answer

Find X and Y, if $X + Y= \begin{bmatrix} 5 & 2 \\ 0 & 9 \end{bmatrix}$ and $X - Y = \begin{bmatrix} 3 & 6 \\ 0 & -1 \end{bmatrix}$

asked Nov 20, 2016 by priyanka.c

1 answer

Evaluate $tan^{-1} (\frac{\cos x}{1-\sin x}), \;\; \; -\frac{\pi}{2} < x < \frac{\pi}{2}$

asked Nov 20, 2016 by priyanka.c

1 answer

On Q the set of all rational numbers, a binary operation $\ast$ is defined by $a \ast b=\frac{ab}{5}$ for all $a, b \in Q $. Find the identity element $\ast$ in Q. Also prove that every non-zero element of Q is invertible.

asked Nov 20, 2016 by priyanka.c

1 answer

Find the shortest distance between the line $l_ 1$ and $l_2$ given by: $\overrightarrow {r} = \hat{i} +2\hat{j} -4\hat{k} + \lambda (2 \hat{i} + 3 \hat {j} + 6 \hat {k}) and \overrightarrow {r }= 3\hat{i} + 3\hat{j} -5\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}) $

asked Nov 20, 2016 by priyanka.c

1 answer

Evaluate : $\begin{align}\int_4^9 \frac{\sqrt x}{(30 - x^{\frac{3}{2}})^2} dx \end{align}$

asked Nov 20, 2016 by priyanka.c

1 answer

Find the value of k if f(x) is continuous at $x = \frac{\pi}{2}$, when $f(x) =\begin{cases}\frac{k \cos x}{\pi - 2x }\;;\; x \neq \frac{\pi}{2} \\ 3 ,\; \; \; \; \; \; \; \; \; x = \frac{\pi}{2} \end{cases}$

asked Nov 20, 2016 by priyanka.c

1 answer

If $ A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$, then find the value of $\theta$ satisfying the equation $A^T + A = I_2$

asked Nov 20, 2016 by priyanka.c

1 answer

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