Mathematics Moc...

The solution of differential equation  \(\rm du = \left ( 16 + u^{2} \right )dx\) is 

If sin^-1 x + sin^-1 y = \(\frac{{2\pi }}{3},\) then cos^-1 x + cos^-1 y =

Find a vector in the direction of vector \(\rm \vec{a}= 3\hat i -4\hat j\) that has magnitude 10 units ?

The value of the integral \(\mathop \smallint \limits_{ - \frac{{\rm{\pi }}}{2}}^{\frac{{\rm{\pi }}}{2}} \left( {{\rm{x}}\cos {\rm{x}}} \right){\rm{dx}}\) is

The order and degree of the differential equation \(\dfrac {d^3y}{dx^3} + 4\times \sqrt {\left( \dfrac{dy}{dx}\right)^3 +y^2}\) = 0 are respectively:

What are the direction ratios of normal to the plane 2x - y + 2z + 1 = 0?

Let two events A, B be two mutually exclusive events. Let P(.) denote the probability. Which of the following statements is true?

What is the solution of the differential equation \(\ln \left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right) - {\rm{a}} = 0?\)

The equation of a plane passing through the point with position vector ‘a’ and perpendicular to ‘b’ is

The order of [x y z] \(\left[ {\begin{array}{*{20}{c}} {\rm{a}}&{\rm{h}}&{\rm{g}}\\ {\rm{h}}&{\rm{b}}&{\rm{f}}\\ {\rm{g}}&{\rm{f}}&{\rm{c}} \end{array}} \right]\,\left[ {\begin{array}{*{20}{c}} {\rm{x}}\\ {\rm{y}}\\ {\rm{z}} \end{array}} \right]\) is

\(\left| \begin{array}{l} {\begin{array}{*{20}{c}} {a + b}&{b + c}&{c + a}\\ {b + c}&{c + a}&{a + b}\\ {c + a}&{a + b}&{b + c} \end{array}} \end{array} \right|\) = K \(\left| \begin{array}{l} {\begin{array}{*{20}{c}} a&b&c\\ b&c&a\\ c&a&b \end{array}} \end{array} \right|\), then K =

The value of \(I = \mathop \smallint \limits_{ - 1}^1 {e^{\left| x \right|}}dx\) is equal to

If \(\,f\left( x \right)\, = \,\frac{1}{{1 - x}}\), then the derivative of the composite function f [f{f(x)}] is equal to

Fisher index number is the _______

Let y = t¹⁰ +1 and x = t⁸ + 1, \(then\,\frac{{{d^2}y}}{{d{x^2}}} is\)

The sum of two numbers is fixed. Then its multiplication is maximum, when

At which point the line \(\frac{x}{a} + \frac{y}{b} = 1\), touches the curve y = be^-x/a

A bond is said to be selling at a discount when

The function f(x) = cos x - 2px is monotonically decreasing for

The value of c in (0, 2) satisfying the mean value theorem for the function f(x) = x (x - 1)2, x ϵ [0, 2] is equal to

If \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {Kx^2}&{if}&{x \le 2}\\ 3&{if}&{x > 2} \end{array}} \right.\) is continuous at x = 2, then the value of K is

The solution set of the equation sin^-1 x = 2tan^-1 x is

Value of a 3 × 3 determinant is 3, value of determinant formed by its co - factor is

The component of \(\vec P= 2 \hat a_x - \hat a _z \ \rm{along} \ \vec Q = 2 \hat a_x - \hat a_y + 2 \hat a_z \) is

If A = \(\left[ {\begin{array}{*{20}{c}} 0&2\\ 3&{ - 4} \end{array}} \right]\) and kA = \(\left[ {\begin{array}{*{20}{c}} {\rm{0}}&{{\rm{3a}}}\\ {{\rm{2b}}}&{{\rm{24}}} \end{array}} \right]\), then the value of k, a, b are respectively

Find the area of the parallelogram whose adjacent sides are given by the vectors (3,1, 4) and (1, -1, 1)?

The solution of linear inequalities x + y ≥ 5 and x – y ≤ 3 lies

The system of equations

αx + y + z = α - 1

x + αy + z = α -1

x + y + αz = α -1

If the curve y = a√x + bx, passes through the point (1, 2) and the area bounded by the curve, line x = 4 and x-axis is 8 sq. unit, then :

Evaluate \(\rm \smallint \frac {\sec^2 ({ln{(x)}})}{x} dx\)

If A = \(\left[ {\begin{array}{*{20}{c}} 1&{ - 2}\\ 4&5 \end{array}} \right]\) and f(t) = t² - 3t + 7, then f(A) + \(\left[ {\begin{array}{*{20}{c}} 3&6\\ { - 12}&{ - 9} \end{array}} \right]\) is equal to

The differential form of the equation 

y = ae^-2x + be^2x 

Which of the following is the point of intersection of line \(\frac{{x - 4}}{2} = \frac{{y - 5}}{2} = \frac{{z - 3}}{1}\) and the plane, x + y + z = 2?

If A = \(\left[ {\begin{array}{*{20}{c}} {\rm{0}}&{\rm{1}}\\ {\rm{1}}&{\rm{0}} \end{array}} \right]\) and B = \(\left[ {\begin{array}{*{20}{c}} {\rm{0}}&{\rm{-i}}\\ {\rm{i}}&{\rm{0}} \end{array}} \right]\), then (A + B) (A + B) is equal to

If the points (2,-3, 4), (-1,2, 1) and (k, 1/3, 2) are collinear, then find the value of k.

There are two linear inequations represented by x + 2y ≥ 3 and x - y ≥ -3. The lines are being drawn in the figure below and some of the regions are being shaded with different colors. 

Which region based on color contains the solutions of these two inequations?

The per-unit profit of a product is given by 600 - 5x, where x is the number of units of the product being sold. What is the expression of marginal revenue?

Two events A and B are independent and equally likely.

Also \(P\left( {A \cup B} \right) = \frac{3}{4}\)

P(A) = ?

The probability density function for a continuous random variable x is given by

\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {3x,}&{0 \le x < 2}\\ {6,}&{2 \le x < 4}\\ { - 3x + 18,}&{4 \le x < 6} \end{array}} \right.\)

In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is

The value of C for which P (x = K) = CK² can serve as the probability function of a random variable x that takes 0, 1, 2, 3, 4 is

If A = {1, - 1, i, - i} and * is a operation on A such that a * b = ab ∀ a, b ∈ A then find the identity element of A with respect to * ?

The index number for the price of diesel in 2015 was 125 and in 2016, it was 140, on a base year of 2011. What is the percent increase in price of diesel from 2015 to 2016?

 In a race of 200 m, A beats B by 45m or 9 seconds. Find time taken by A to complete the race.

Joe Biden and Jeff Bezos are two partnership in a business. Joe is an active partner while Joff is a sleeping one. Joe invest $ 5000 and Jeff invest $ 6000. Joe receives 25/2 percent of the profit for managing the business and the rest is divided in proportion to their investment. What does each get out of a profit of $ 880?

A can row 15 km/h in still water, it takes him twice long as time to row up as to row as down the River. Find the rate downstream?

300 gm of sugar solution has 40% of sugar in the solution in it. How much sugar should be added to make it 50% in the solution?

When 67 is divided by a number, say x, a remainder of 3 is obtained. If x < 50, then largest value of x is,

If X = {a, b, c} and R is a relation on X such that R = {(a, a), (b, b), (c, c)}. Then R is a/an ?

Which of the following is an empty set?