Mathematics Moc...

The order of a matrix is defined as

Solve the differential equation xdy - 2ydx = 0

If \(\frac{4}{x}<\frac{1}{3}\), what is the possible range of values for x?

The vector \(\rm \vec a \times (\vec b \times \vec a)\) is coplanar with:

The order and degree of the differential equation \(\rm {\left[ {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2} + \sin \left( {\frac{{dy}}{{dx}}} \right)} \right]^{3/4}} = \frac{{{d^2}y}}{{d{x^2}}}\)

For the given ordinary differential equation,

 \(\frac{{dx}}{{dy}} + \frac{x}{{co{s^2}y}} = {e^{ - \tan y}}\)

The integrating factor will be equal to-

If \(A = \left[ {\begin{array}{*{20}{c}} 2&0&0\\ 0&2&0\\ 0&0&2 \end{array}} \right]\), then A⁵ = 

What will be the weekday on 15^th of August if 15^th of July on the same year was Sunday?

A tap can fill a tank in 8 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

A LED TV costs ₹ 25000 is expected to have a life of 8 years and its final scrap value is ₹5000. The annual depreciation according to the linear method of depreciation is -

If the expected value of a random variable X is 2 and its variance is 1, then what will be the variance of 3X + 4?

The principal value of sin^-1 \(\left( {\frac{1}{{\sqrt {17} }}} \right) + {\cos ^{ - 1}}\frac{5}{{\sqrt {34} }}is\)

A manufacturing company has its variable cost given by C(x) = x(80 - x²) where 'x' is the number of quantities produced. The price per unit is p(x) = 5x where 'x' is the number of units in demand. The ratio of marginal cost and marginal revenue when 5 units were both produced and in demand - 

On the set of positive rational numbers, a binary operation * is defined by,

a * b = |a -b| 

If 5 * p  ≤ 5 then the maximum value of p is?

Let S denote all integers, define a relation R on S as aRb if ab ≥ 0 where a, b ∈ S’. Then R is :

The system of equations,

7x+ 9y =15,

14x +18y =30 

has-

Find the area of triangle with vertices at points A (1, 1) ,B ( 6, 0) and C ( 3, 2).

Mrs. Shivani takes a loan of 10,00,000 Rs with a 10% annual rate of interest for 5 years. The EMI under the flat rate system is -

Find the value of det(2²A) for the following matrix:

\({\rm{A}} = {\rm{\;}}\left[ {\begin{array}{*{20}{c}} 2&3&1\\ { - 1}&0&2\\ { - 3}&1&2 \end{array}} \right]\)

The index number calculated for the data given in below table by simple weighted aggregate method comes out to be 110.

Given 60p + 3q = 360, then the value of p will be 

A boat takes 2 hours to go 16 km downstream; while covering the same distance upstream, it takes 4 hours. What is the speed of the current?

If Rolle's theorem holds for the function f(x) = x³ - ax² + bx - 4, x ∈ [1, 2] with \(f'\left( {\frac{4}{3}} \right) = 0\), then ordered pair (a, b) is equal to 

If ∑p₀q₀ = 160, ∑p₀q₁ = 250, ∑p₁q₀ = 200 and ∑p₁q₁ = 288, then Fisher ideal index number is equal to:

If y = 4x - 5 is tangent to the curve y² = px³ + q at (2, 3), then 

The maximum slope of the curve \(\begin{array}{l} y = \frac{1}{2}{x^4} - 5{x^3} + 18{x^2} - 19x\\ \end{array}\) occurs at the point 

In a 500m race, the ratio of speed pf P and Q is 3:4. When the race starts, P is 140 m ahead. What is the distance between P and Q when P wins the race?

A piecewise-defined function is defined as,

 \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} { - 1}&{{\rm{if}}}&{{\rm{x}} \le 0}\\ {{\rm{ax}} + {\rm{b}}}&{{\rm{if}}}&{0 < {\rm{x}} < 1}\\ 1&{{\rm{if}}}&{{\rm{x}} \ge 1} \end{array}} \right.\);

Where a, and b are constants. The function is continuous everywhere. What is the value of a?

If x = 3 tan t and y = 3 sec t, then the value of \(\frac{{{d^2}y}}{{d{x^2}}}\) at \(t = \frac{\pi }{4}\), is

For the linear programming problem:

Maximum Z = 3X₁ + 2X₂

Subject to

-2X₁ + 3X₂ ≤ 9

X₁ – 5X₂ ≥ -20

X₁, X₂ ≥ 0

The above problem has

Lifetime value = ________ - (Fixed Cost + Variable Cost)

Let f : (0, +∞) → R and \(F\left( x \right) = \int\limits_0^x {f\left( t \right)dt}\)

If F(x²) = x²(1 + x), then f(4) equals

If A is a skew symmetric matrix, then A^t

Correct evaluation of \(\smallint \frac{x}{{\left( {x - 2} \right)\left( {x - 1} \right)}}dx\)

If \(\mathop {\lim }\limits_{n \to \infty }\)\(\sum\limits_{k = 1}^n {\left( {{{\left( {\frac{{3k}}{n}} \right)}^2} + 2} \right)\frac{3}{n}} \) = \(\int\limits_0^6 {f(x)}\) dx, then

A coin is tossed twice. If E and F denote occurrence of head on first toss and second toss respectively, then what is P(E ∪ F) equal to?

What is \(\rm \displaystyle\int e^x \left(\sqrt x + \frac{1}{2 \sqrt x} \right) dx\) is equal to ?

The area enclosed between the curves y² = x and y = |x| is:

Let f be a differentiable function such that f(1) = 2 and f'(x) = f(x) for all x ∈ R. If h(x) = f(f(x)), then h'(1) is equal to 

The plane 2x - 3y + 6z - 11 = 0 makes an angle sin^-1 (∝) with X-axis . the value of ∝ is equal to

The magnitude of the projection of the vector \(2\hat i + 3\hat j + \hat k,\) on the vector perpendicular to the plane containing the vectors \({\rm{\hat i}} + {\rm{\hat j}} + {\rm{\hat k\;and\;\hat i}} + 2{\rm{\hat j}} + 3{\rm{\hat k}}\), is:

Find the distance between the straight line \(\frac{{x - 3}}{1} = \frac{{y - 4}}{{\;2}} = \frac{{z - 5}}{1}\) and the plane x - y + z - 5 = 0 ?

The minimum value of 3𝑥 + 5𝑦 such that,

3x + 5y ≤ 15

4x + 9y ≤ 8

13x + 2y ≤ 2

x ≥ 0, y ≥ 0

is ___________.

What is the area of one of the loops between the curve y = c sin x and x-axis?

Two models, P, and Q, of a product, earn profits of Rs.100 and Rs.80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, the objective function Z is subjected to the constraints as?

Find the area under the curve y = x + 2 , x-axis and y-axis.

What is the probability that the roots of the equation x² + x + n = 0 are real, where n ϵ N and n < 4?

Five coins are tossed at a time. then, the probability of obtaining at least one head is

X is a random variable with distribution function as \({f_x}\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2\pi }}&{-\pi\leq x \leq\pi }\\ {0,}&{else{\rm{ }}where} \end{array}} \right.\)distributed between (-π, π). Then E [sin x] is ____________. 

If the lines \(\rm {x -x_1\over a}={y-y_1\over b}={z-z_1\over c}\) and \(\rm {x -x_2\over p}={y-y_2\over q}={z-z_2\over r}\) are lies on a plane, then 

Let X be a random variable that is uniformly chosen from the set of positive odd numbers less than 100. The expectation, E[X], is