List of top Mathematics Questions asked in KEAM

The value of the determinant \(\begin{vmatrix} 4&4^2&4^3\\3&3^2&3^3\\2&2^2&2^3 \end{vmatrix}\)is
If \(\begin{vmatrix} 1&2&1\\0&x&-3\\2&-1&x \end{vmatrix}=0\), then the value of x are
Let \(A+B=\begin{bmatrix} 4&1&4\\1&4&4 \end{bmatrix}\)and \(B=\begin{bmatrix} 1&0&-2\\-1&3&0 \end{bmatrix}\), then A=
If \(AB=\begin{bmatrix} 4&3\\5&4 \end{bmatrix}\) and \(A^{-1}=\begin{bmatrix} 3&-2\\-1&1 \end{bmatrix}\), then B=
If p and q are positive integers such that \(^{p+q}P_2=42\ and\ ^{p-q}P_2=20\), then the values of p and q respectively
The number of 3-digit numbers that can be formed from the digits 0, 2, 3, 5, 7 is (repetition is allowed)
A set contains 9 elements. Then the number of subsets of the set which contains at most 4 clements is
The first term of a G.P. is 3 and the common ratio is 2. Then the sum of first eight terms of the G.P. is
A covid-19 vaccination reduces the probability of getting covid-19 infection from 0.4 to 0.1. In a city, 45% people are vaccinated. Then the probability that a non-vaccinated person chosen at random in the city gets covid-19 infection is
The number of ways a committee of 3 women and 5 men can be formed from a panel of 8 men and 5 women is
In an A.P. the difference between the last and the first terms is 632 and the common difference is 4. Then the number of terms in the A.P. is
If the 10th and 12th terms of an A.P. are respectively 15 and 21, then the common difference of the A.P. is
If the first term of a G.P. is 1 and the sum of 3rd and 5th terms is 90, then the positive common ratio of the G.P. is
If a1, a2, a3,..., an are in A. P. with a1 = 3, an, = 39 and a1+a2+...+an = 210, then the value of n is equal to
The value of \(\displaystyle\sum_{k=5}^{36}\frac{1}{k^2-k}\) is equal to
Let tn, n = 1,2,3,... be the nth term of the A.P. 5, 8, 11,.... Then the value of n for which tn = 305 is
The value of \(\sqrt{(- 25)} + 3\sqrt{(- 4)} + 2\sqrt{(- 9)}\) is equal to
The area of the triangle on the complex plane formed by the points z, z+iz and iz is 128. Then the value of |z| is
The imaginary part of \(z=\frac{2+i}{3-i}\) is
If the real part of the complex number \(z=\frac{p+2i}{p-i}\), \(p\isin\R, p\gt0\ is\ \frac{1}{2}\), then the value of p is equal to
Let z1, z2 and z3 be three distinct points in the complex plane such that the segment joining z1 and z2 is perpendicular to the segment joining z1 and z2. If |z1-z2|=5 and|z1-z3|=12 then|z2-z3| is equal to
If z=2-i√3, then |z4| is equal to
Let a=2-3i be a root of the equation z2-4z+k=0 , where k is a real number. If β is the other root, then the value of α2 +β2 is
Let f(x) = x2 and \(g(x) = \sqrt{9+x}\). Then the value of \((f^\circ g-g^\circ f)(4)\) is equal to
Let f(x) = [x], x ∈ R, where [x] denotes the greatest integer ≤ x. Then the images of the elements -4.6 and 2.7 are respectively