Mathematics Moc...

The projection of a vector on another vector is 

The solution of ∫logx/x²dx is

The degree of the given equation is

\(\rm {dy\over dx}-x=(y-x{dy\over dx})^{-6}\)

The function y = f(x) has relative minima where:

What is the principal value of \(cosec ^{-1}(-\sqrt2)?\)

The line with direction ratios 1, 0, -1 is inclined with z - axis at an angle

If \(\rm \begin{bmatrix}1&x&1\end{bmatrix}\) \(\begin{bmatrix}1&2&3\\\ 4&5&6\\\ 3&2&5\end{bmatrix} \) \(\rm \begin{bmatrix}1\\\ -2\\\ 3\end{bmatrix} \) = 0 then the value of x is

Let \(\rm f(x)=\left\{\begin{matrix}3x-4,&0\le x\le2\\\ 2x+l, &2

If f is continuous at x = 2, then what is the value of l?

The number that exceeds its square by the greatest amount is 

If c is a point at which Rolle's theorem holds for the function \(f\left( x \right) = {\log _e}\left( {\frac{{{x^2} + α }}{{7x}}} \right)\) in the interval [3, 4], where α ∈ R, then the value of c is equal to 

If the curve y = ax² + bx + c, x ∈ R, passes through the point (1, 2) and the tangent line to this curve at origin is y = x, then the possible values of a, b, c are 

The mean of the numbers obtained on throwing a die having written 5 on four faces, 4 on three faces, 3 on two faces and 2 on one face is?

A continuous random variable X has a probability density function f (x) = e^-x, 0 < x < ∞, Then P{X > 1} is

A discrete random variable X has the probability functions as:

A continuous random variable X has uncountable many values in the interval [a, b]. If C is a values in the interval [a, b], then P{ X = C }

Let R be a relation on the set of natural numbers defined by ‘xRy ⟺ x ≤ y’. Which one of the following is correct?

if a function defined as  f : N → N f(x) = (x - 1)/2 Then which of the following is true regarding this function?

For the following Linear Programming Problem, the constraints are Graphically expressed as shown. What will be the optimal maximized value of objective function z?

Where,
Z = 2x + 4y

x ≥ 0 and y ≥ 0

M is a square matrix of order ‘n’ and its determinant value is 5. If all the elements of M are multiplied by 2, its determinant value becomes 40. The value of ‘n’ is

Evaluate:

tan^-1(1) + cos^-1(-1/2) + sin^-1(-1/2) = ?

The differential coefficient of f [log(x)] when f (x) = log x is 

The system of equations

x + 2y + z = 0, x – z = k, x + y = 0

has infinite many solution then the possible value of k?

Given: \(Adj A = {\begin{bmatrix}\ 1&\ 1& \ -2 \\\ \ -1&\ -1&\ 2\\\ 1&\ 1&\ -2\end{bmatrix}}\)

 The points (5, -2), (8, -3) and (a, -12) are collinear if the value of a is 

In the figure, \(\vec{a}\ =\ \vec{2i},\ \vec{b} = \ \hat{i}\ +\ \hat{j\ +\ \hat{k}},\ \vec{c}\ =\ \hat{2k}\)  and vector x satisfies the equation x - w = v. Then x is

The two lines \(\frac{{x + 3}}{{ - 4}} = \frac{{y - 6}}{3} = \frac{z}{2}\:and\:\frac{{x + 2}}{{ - 4}} = \frac{y}{1} = \frac{{z - 7}}{1}\)  are?

Take \( {(\vec B_1×\vec B_2)} = (1, -4, 8)\) where \(\vec B_1 \ and \ \vec B_2 \) are representing the directions of the first and second lines respectively.

Find \(\displaystyle\lim_{n \rightarrow \infty} \left(\frac{1}{n} + \frac{1}{n+1} + \frac{1}{n+2}+ ... + \frac{1}{3n}\right)\)

If a matrix  A is such that 3A³ + 2A² + 5A + I = O, then what is A^-1 equal to?

Let A and B be two events such that \(P(\overline{A \cup B}) = \dfrac{1}{6}\), P(A ∩ B) = \(\dfrac{1}{4}\)and P(A̅) = \(\dfrac{1}{4}\), where A̅ stands for complement of event A. Then, events A and B are:

Maximize Z = 2X₁ + 3X₂

Subject to

2X₁ + X₂ ≤ 6

X₁ – X₂ ≥ 3

X₁, X₂ ≥ 0

Assuming that the sums and products given below are defined, which of the following is not true for matrices?

What is the area bounded by the curves |y| = 1 – x²?

If \(I_1 =\int\frac{e^x dx}{e^x + e^{-x}}\) and \(I_2 =\int\frac{dx}{e^{2x} + 1},\)then what is I₁ + I₂ equal to?

If \(f(x)=2\ln(\sqrt{e^x})\), what is the area bounded by f(x) for the interval [0, 2] on the x-axis?

Find the area of the parabola y² = 4ax bounded by it's latus rectum.

Ram is a fruit seller who can purchase apples at the rate of Rs 80/kg and mango at the rate of Rs 120/kg. Both can be sold at a profit of Rs 10/kg and Rs 12/kg. The total kgs of fruit that can be bought for one time is limited to 20 kg. Ram has a budget of Rs 2000 to bring the fruits. Ram wants to minimize the purchase cost of the fruits. Let x be the number of kilograms of apples being bought and y be the number of kilograms of mangoes being bought. The objective function Z of such a problem will be:

The function y = e^-4x is a solution to the differential equation

The value of \(\displaystyle \int_{-1}^3\left[tan^{-1}\left(\frac{x}{x^2+1}\right)+tan^{-1}\left(\frac{x^2+1}{x}\right)\right]dx \) is

Solved \(\frac{dy}{dx}=e^{x-y}(e^x-e^y)\)

The function f(x) = 8 loge x - x2 + 3 attains its global minimum over the interval [1, e] at x = ________.

(Here loge x is the natural logarithm of x and  e2 = 7.39)

For a point of inflection of y = f(x), which one of the following is correct?

The identity element for the binary operation * defined on Q - {0} (Where Q is a set of rational numbers) as: a * b = \(\rm \frac{ab}{2}\), is:

What is the cosine of angle between the planes x + y + z + 1 = 0 and 2x - 2y + 2z + 1 = 0?

If the position vector of a point P with respect to origin O is î + 3ĵ - 2k̂ and that of a point Q is 3î + ĵ - 2k̂, then what is the position vector of the bisector of the angle POQ? 

If x is a real number, then the given single valued function f(x) = x³ + x² + x + 1 has

Find the absolute minimum value of the function \(\rm y=3x^{2}-4\) in the interval \(\left [ -1,5 \right ]\)

Find the solution set of y if the system of inequalities is:

10x + 8y ≤ 80

X < 4

If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B?

What is the area under the curve f(x) = xe^x above the x-axis and between the lines x = 0 and x = 1?

Fine the value of \(\rm sin \ ({\pi\over3} \ - \ sin^{-1}(-{1\over2})) \)

A pair of fair dice is thrown, what is the probability of getting a six on both, given atleast one die gets six?