Mathematics Moc...

If A is a singular matrix, then adj A is 

What is the degree of the following differential equation?

\(\rm x=\sqrt{1+\frac{d^2y}{dx^2}}\)

The variance σ² of a random variable X is given by

What is the interval over which the function f(x) = 6x - x², x > 0 is increasing? 

A coin is tossed 5 times. The probability of head is \(\frac{1}{2}\). The probability of exactly 2 heads is

Which of the following is correct regarding the analysis of four components of time series analysis?

If \(4\hat i + \hat j - 3\hat k\) and \(p\hat i + q\hat j - 2\hat k\) are collinear vectors, then what are the possible values of p and q respectively?

If aN = {ax : x∈N} then 2N ∩ 5N is

What is the general solution of (1 + e^x) ydy = e^x dx ?

where c is a constant of integration.

If I₃ is the identify matrix of order 3, then \(I_3^{ - 1}\) is

Max z = 4x₁ + 3x₂ subject to constraints

2x₁ + x₂ ≤ 1000

x₁ + x₂ ≤ 800

x₁ ≤ 400

x₂ ≤ 700

x₁, x₂ ≥ 0

Let f(x) = x + x^-1. Then which of the following is correct?

Rate of growth of bacteria is proportional to the number of bacteria present at time. If x is the number of bacteria present at any instant t, then which one of the following is correct? (Let the proportional constant equal to 2)

Find the condition on k, so that the system of equations: x + 3y = 5 and 2x + ky = 8 has a unique solution.

If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?

The value of

\(\rm [\vec{a} + 2\vec{b} - \vec{c}, \vec{a} - \vec{b}, \vec{a}-\vec{b}- \vec{c}]=\)   is ?

If f(x) = |x + 1| + |x + 10|, then find the minimum value of f(x).

The length of the perpendicular drawn from the origin to the plane 2x - 3y + 6z - 42 = 0 is

If a line has direction ratios < a + b, b + c, c + a >, then what is the sum of the squares of its direction cosines?

If x^e = e^{\(\rm {x^2+y^2}\)}, then find \(\rm dy\over dx\)

Consider the Linear Programming problem:

Maximize: 7X₁ + 6X₂ + 4X₃

subject to:

X₁ + X₂ + X₃ ≤ 5;

2X₁ + X₂ + 3X₃ ≤ 10,

X₁, X₂, X₃ ≥ 0 (Solve by algebraic method).

The number of basic solutions is:

A manufacturing firm has its variable cost given by C(x) = x(12 - x³) where 'x' is the number of quantities produced. The price per unit is p(x) = 6x - 2 where 'x' is the number of units in demand. The ratio of marginal cost and marginal revenue when 3 units were both produced and in demand - 

A solution of 100L contains 75 percent water and rest liquid sugar. How much liquid sugar must be added to make 50 percent sugar solution?

A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either Ace or a King?

The mean of the probability distribution function given by the following table will be:

Maximize, z = 5x₁ + 3x₂ subjected to the following constraint

x₁ + x₂ ≥ 3

x₁ - x₂ ≤ 2

If f and g are differentiable functions in (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ϵ (0, 1)

Given that x is a random variable in the range [0, ∞] with a probability density function \(\frac{e^-{\frac{x}{2}}} {K}\) the value of the constant K is___________.

A cricket bat manufacturing firm assesses its variable cost to be ‘2x’ times ‘x - 40’, where ‘x’ is the number of bats produced, and also the cost incurred on storage is Rs. 1200. Then how many bats should be manufactured for the minimum total cost?

The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has non-trivial solution is

Consider the data given in the table -

Taking the base year 1985, the index number calculated by the simple aggregate method comes out to be 125, then the value of (4β - 5α) will be -

Let k be the order of a mod n then a^b ≡ 1(mod n) if and only if 

Which of the following statement is true regarding sinking fund and  saving account?

If |3x - 5| ≤ 2 then

A continuous random variable, X is distributed in interval 0 to 10.

The probability, P(X = 2) is ______.

\(\mathop \smallint \limits_{\frac{1}{2}}^2 \frac{1}{x}sin\left( {x - \frac{1}{x}} \right)dx = \)

Let, R = {(a, b): a, b ϵ N and a² = b}, then what is the relation R

\(\rm \int \frac{1}{e^x+e^{-x}}dx=\)

Find the area under the curve y = cos x in the interval \(\rm 0

Consider the following statements

I. The derivative, where the function attains maxima or minima be zero.

II. If a function is differentiable at a point, then it must be continuous at that point.

Which of the above statement(s) is/are correct?

If \({a_{ij}} = \frac{1}{2}\left( {3i - 2j} \right)and\,A = {\left[ {{a_{ij}}} \right]_{2 \times 2}}\), then A is equal to 

Find the area of the region (in sq. units) bounded by the curve y = x, y = x² + 2 for x ∈ (‑1, 1)

Let \(A = \left[ {\begin{array}{*{20}{c}} 4&6&{ - 1}\\ 3&0&2\\ 1&{ - 2}&5 \end{array}} \right]\),\(B = \left[ {\begin{array}{*{20}{c}} 2\\ 0\\ { - 1} \end{array}\begin{array}{*{20}{c}} 4\\ 1\\ 2 \end{array}} \right]\)and C = [3 1 2]. The expression which is not defined is 

The area bounded by the curve x² = ky, k > 0, and the line y = 3 is 12 unit². Then k is?

Find the value of f(x) when \(\rm f(x)=\int_{0}^{x} \frac{dt}{t^{2}+9}\)

If tan^-1(2), tan-1(3) are two angles of a triangle, then what is the third angle ? 

What is the domain of the function f(x) = cos sin-1 (x + 1) ?

If the area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 square units, then what is the value of k?

If y = cos (sin² x), then find the value of \(\rm\frac{dy}{dx}\) at x = \(\rm\frac{\pi}{2}\).