List of top Mathematics Questions asked in KCET

The mean of 100 observations is 50 and their standard deviation is 5. Then the sum of squares of all observations is
If n is even and the middle term in the expansion of \((x^2+\frac{1}{x})^n\) is 924 x6, then n is equal to
If \(\lim\limits_{x \rightarrow 0} \frac{\sin(2+x)-\sin(2-x)}{x}\)= A cos B, then the values of A and B respectively are
The distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt2\). Its equation is
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is
If A is a skew symmetric matrx, then \(A^ {2021}\) is
If \(\vec{\alpha}=\hat{i}-3\hat{j},\vec{\beta}=\hat{i}+2\hat{j}-\hat{k}\) then express If |a×b|+|a.b|=36 and |a|=3 then |b| is equal to\(\vec{\beta}\) in the form \(\vec{β}=\vec{β_1}+\vec{β_2}\) where \(\vec{β}_1\) is parellel to \(\vec{\alpha}\) and \(\vec{β}_2\) is perpendicular to \(\vec{\alpha}\) then \(\vec{β_1}\) is given by
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 \([x]\) is the greatest integer function not greater than x, then \(\int [x]\)\(dx\) is equal to
If A = {1,2,3........,10} then number of subsets of A containing only odd number is
\(\sqrt{2 + \sqrt{2 + \sqrt{2 + 2\cos(8\theta)}}}\)=
The value of \(\sin \frac{5\pi}{12} \sin \frac{\pi}{12}\) is
The degree measure of \(\frac{\pi}{32}\) is equal to
The trigonometric function y = tan x in the II quadrant
The domain of the function \(f(x) = \frac{1}{\log(1-x)} + \sqrt{x+2}\) 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 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
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
Find the mean number of heads in three tosses of fair coin:
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
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 co-ordinates of the foot of the perpendicular drawn from the origin to the plane 2x - 3y + 4z = 29 are