Mathematics Moc...

A straight line with direction cosines {0, 0, 1} is

The order and degree of the differential equation:

\(\rm x\left(d^2y\over dx^2\right)^{2\over3} = y^2\left({dy\over dx}\right)^{3\over2}\)

Derivative of x² w.r.t. x³ is:

If at point on the curve y = f(x) the slope of the line tangent to the curve is equal to 2xy. Then the function f is

\(\int\limits_0^{\frac{\pi }{2}} {\log (\tan x)dx}\) is equal to

The co-factor of the element '4' in the determinant

If f(x) is an increasing function and g(x) is a decreasing function then which of the following is correct for the real value of x as p and q. Given that for these values of x, both functions are defined?

The function f(x) = x² - 4x, x ∈ [0, 4] attains minimum value at

Let f and g be differentiable functions on R such that fog is the identify function. If for some a, b∈ R, g'(a) = 5 and g(a) = b, then f'(b) is equal to 

\(\mathop \smallint \limits_{1/\pi }^{2/\pi } \frac{{\cos \left( {1/x} \right)}}{{{x^2}}}dx\; = \;\_\_\_\_\_\_\_\)

If the tangent to the curve y = x + sin y at a point (a, b) is parallel to the line joining \(\left( {0,\frac{3}{2}} \right)\)and \(\left( {\frac{1}{2},2} \right)\), then 

What is the probability of getting a numbered card when the card drawn from the 52 card packs?

Given P (H) = 0.3

P(R) = 0.4

P(H/R) = 0.2

Let \(f(x)=cx^2\) for \(x=1,2,3\). The value of constant c such that f satisfies the conditions of being a probability mass function is -

Let S = {(x, y): x² + y² = 1,  - 1 ≤ x ∈ R ≤ 1 and - 1 ≤ y ∈ R ≤ 1} Which one of the following is correct?

A fair die is tossed thrice. If the probabilities of zero, one two, and three successes are 8/27, 4/9, 2/9, and 1/27 respectively. Find the mean of the number of successes ______

Let A = {a, b, c, d} and B = {1, 2, 3, 4, 5, 6}. Then the number of one-to-one functions from A to B is:

If A = {1, 2, 3, 4, 5} and let * is an operation on A such that a * b = min {a, b}

1. * is a binary operation on A

2. * is commutative on A

Durgesh is working in a restaurant in which he prepares two types of dishes A and B. Dish A takes 20 minutes to be prepared and Dish B takes 30 minutes for the same. He earns Rs 50 to make one packet of dish A, while Rs 70 for one packet of dish B. He works for 12 hours a day. He needs 1 hour in those 12 hours for his personal activities. What will be the constraints, if this example is formulated as a linear programming problem? Assume x and y be the packets of dishes A and B respectively.

The number of solutions in a linear programming model to maximize the objective function 5x + 4y subject to the constraints, 

x - 2y ≥ 2,

2x - 4y ≤ - 3,

x, y ≥ 0 will be,

The maximum value of the object function Z = 4x + 3y subject to the constraints 4x + 2y ≤ 12, 2x + 4y ≥ 6, x ≥ 0, y ≥ 0 is

If O(A) = 2 × 3, O(B) = 3 × 2 and O(C) = 3 × 3, which one of the following is not defined

In the following table, x is the discrete random variable and p(x) is the probability density function. The standard deviation of x is

If a ≠ 6, b, c satisfy \(\left| {\begin{array}{*{20}{c}} a&{2b}&{2c}\\ 3&b&c\\ 4&a&b \end{array}} \right| = 0,\) then abc =

Let the function f : [-7, 0] → R be continuous [-7, 0] and differentiable on (-7, 0). If f(-7) = -3 and f'(x) ≤ 2, for all x ∈ (-7, 0), then for all such functions f, f(-1) + f(0) lies in the interval 

The normal to the curve y(x - 2)(x - 3) = x + 6 at the point where the curve intersects the y-axis passes through the point

Set of equations a + b - 2c = 0, 2a - 3b + c = 0 and a -5b + 4c = α is consistent for what value of α if the cofactors of the matrix formed by coefficient of a, b and c is having the cofactors as C11 = 7, C12 = -7, C13 = 7, C21 = 6, C22 = - 6, C23 = 6, C31 = 5, C32 = -5, C33 = 5. Where, Cij is the cofactor of element in ith row and jth column.

If 2A + 3B = \(\left[ {\begin{array}{*{20}{c}} 2&{ - 1}&4\\ 3&2&5 \end{array}} \right]\) and A + 2B = \(\left[ {\begin{array}{*{20}{c}} 5&0&3\\ 1&6&2 \end{array}} \right]\), then B =

Find the area bounded by the curves y ≥ x² and y = |x|

The activities or limitations competing with one another to share the the amount of a resources in linear programming are called

What is the perpendicular distance from the point (2, 3, 4) to the line \(\rm \frac{x-0}{1}=\frac{y-0}{0}=\frac{z-0}{0} \ ?\)

If for a matrix A, A2 + I = 0, where I is the identity matrix of order 2, then A =

Let A = \(\left[ {\begin{array}{*{20}{c}} 1&2\\ { - 5}&1 \end{array}} \right]\) and A-1 = xA + yI, then value of x and y are

\(\smallint \frac{{{x^2}}}{{{x^2}\; + \;4}}\) dx =

Find the shortest distance between the lines \(\frac{x}{-1}=\frac{y-2}{0}=\frac{z}{1}\) and \(\frac{x+2}{1}=\frac{y}{1}=\frac{z}{0}\)

Find the area between the curve y = sin x and lines  \(\rm x = -\frac {\pi} {3} \) to \(\rm x = \frac {\pi} {3} \).

The value of \(\mathop \smallint \limits_0^1 \left| {5x - 3} \right|dx\) is

In throwing a six faced die, let A be the event that an even number occurs, B be the event that an odd number occurs and C be the event that a number greater than 3 occurs. Which one of the following is correct?

The area under the curve y = x⁴ and the lines x = 1, x = 5 and x-axis is:

The curve satisfying the differential equation ydx + (x - y)dy = 0 and passing through the point (1, 1) is

The integrating factor of the differential equation \(\frac{dy}{dx}(xlogx)+y=2log x\) is given by

What is the area bound by the curve xy = m², x-axis and ordinates. Given x = p, x = q, and p > q > 0.

The function  \(f(x)=x^3-3 \log x\) has - 

If  f(x) = a tan ^-1x + 2b log (1 + x) + x + 1 has  critical points at  x = 0 and x = 2 , then the values of the constants a and b respectively are -

Suppose \(\rm \mathop v\limits^ \to = 2\hat i + \hat j - \hat k\)  and \(\rm \mathop w\limits^ \to = \hat i + 3\hat k\). If \(\rm \mathop u\limits^ \to \) is unit vector, then the maximum value of scalar triple product \(\rm \left[ {\mathop u\limits^ \to \mathop v\limits^ \to \mathop w\limits^ \to } \right]\) is -

Find the projection of the vector \(\vec a = 2\hat i + 3\hat j + 2\hat k\) on the vector \(\vec b = \vec i + 2\vec j + \hat k\) ?

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is:

Find the image of point (-2, 1, 1) in the plane x + y + z = 0

If cos^-1 x + cos^-1 y + cos^-1z + cos^-1 t = 4π, then the value of x² + y² + z² + t² is  

The value of cos(2 tan ^-1(-7)) is