List of top Mathematics Questions asked in KCET

If A is a skew symmetric matrx, then \(A^ {2021}\) is

If \(|\vec{a}|=2\) and \(|\vec{b}|=3\) and the angle between \(\)\(\vec{a}\) and \(\vec{b}\) is 120°, then the length of the vector \(|\frac{1\vec{a}}{2}-\frac{1\vec{b}}{3}|^2\) is

If A = {1,2,3........,10} then number of subsets of A containing only odd number is

The trigonometric function y = tan x in the II quadrant

If 3x + i(4x-y) = 6-i, where x and y are real numbers, then the value of x and y are respectively

Let the relation R is defined in N by \(a \mathbb{R} b\), if \(3a+2b = 27\) , then R is

The function \(f(x) = \log(1+x) - \frac{2x}{2+x}\) is increasing on

The function \(f(x) = 4 \sin^3 x - 6 \sin^2 x + 12 \sin x + 100\) is strictly

The value of \(\sin \frac{5\pi}{12} \sin \frac{\pi}{12}\) is

\(\sqrt{2 + \sqrt{2 + \sqrt{2 + 2\cos(8\theta)}}}\)=

Find the mean number of heads in three tosses of fair coin:

The domain of the function \(f(x) = \frac{1}{\log(1-x)} + \sqrt{x+2}\) is

If A and B are two independent events such that \(P(\overline{A}) = 0.75\), \(P(A \cup B) = 0.65\) and \(P(B) = x\), then find the value of x:

A pandemic has been spreading all over the world. The probabilities are 0.7 that there will be a lockdown , 0.8 that the pandemic is controlled in one month if there is a lockdown and 0.3 that it is controlled in one month if there is no lockdown. the probability that the pandemic will be controlled in one month is

The distance of the point whose position vector is \(\mathbf{2\hat{i} + \hat{j} - \hat{k}}\) from the plane vector \(\vec{r} \cdot (\hat{i} - 2\hat{j} + 4\hat{k}) = 4\) is

If A and B are the two events such that \(P(A) = \frac{1}{2}\), \(P(B) = \frac{1}{3}\) and \(P(A|B) = \frac{1}{4}\), then \(P(A' \cap B')\) is

Suppose that the number of elements in set A is p, the number of elements in set B is q and the number of elements in \(A \times B\) is 7 then \(p^2 + q^2 =\)

A dietician has to develop a special diets using two foods X and Y. Each packet (containing 30g) of food. X contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Y contains 3units of calcium , 20 unit of iron, 4 units of cholesterol and 3 units of vitamin A.The diet requires atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. The corner points of the feasible region are

The corner points of the feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5), then the minimum value of z = 4x + 6y occurs at

The co-ordinates of the foot of the perpendicular drawn from the origin to the plane 2x - 3y + 4z = 29 are

The angle between the pair of lines \(\frac{x+3}{3} = \frac{y-1}{5} = \frac{z+3}{4}\) and \(\frac{x+1}{1} = \frac{y-4}{4} = \frac{z-5}{2}\) is

If \(|\vec{a}\times\vec{b}|\) + \(|\vec{a}.\vec{b}|^2=36\) and \(|\vec{a}|=3\) then \(|\vec{b}|\) is equal to

The sum of the degree and order of differential equation \(\left(1 + y_1^2\right)^{\frac{2}{3}} = y_2\) is

If y(x) be the solution of the differential equation \(x \log(x) \frac{dy}{dx} + y = 2x \log(x), \quad y(e)\) is equal to

The solution of the differential equation \(\frac{dy}{dx} = (x+y)^2\) is