List of top Mathematics Questions asked in KCET

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

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

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 \(p^2 + q^2 =\)

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

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:

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

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 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

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

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

\(\int\limits_{0}^1\frac{xe^x}{(2+x)^3}\ dx\) is equal to

Evaluate \(\int\limits_{2}^3x^2\ dx\) as the limit of a sum

\(\int\limits_{0}^{\frac{\pi}{2}}\frac{\cos x\sin x}{1+\sin x}\ dx\) is equal to

Area of the region bounded by the curve \(y = tan x\), the x- axis and the line \(x = \frac{\pi}{3}\) is

If \(\frac{dy}{dx} + \frac{y}{x} = x^2\) then \(2y (2) - y (1) =\)

If \(\int \frac{dx}{(x+2)(x^2 + 1)} = a \log |1+x^2| + b \tan^{-1} x + \frac{1}{5} \log |x+2| + c\), then

If \([x]\) is the greatest integer function not greater than x, then \(\int [x]\)\(dx\) is equal to

If \(e^y + xy = e\) the ordered pair \(\left(\frac{dy}{dx},  \frac{d^2y}{dx^2}\right)\) at \(x = 0\) is equal to

\(\int \frac{\cos(2x) - \cos(2\alpha)}{\cos(x) - \cos(\alpha)} \, dx\) is equal to

\(\int\limits_{0}^{\frac{\pi}{2}}\sqrt{\sin \theta}\cos^3\theta\ d\theta\) is equal to

The co-ordinates of the point on the \(\sqrt{x} + \sqrt{y} = 6\) at which the tangent is equally inclined to the axes is