List of top Mathematics Questions asked in KEAM

The value of \(\cos^{-1}(\cos(\frac{7\pi}{6}))\) is equal to

The solutions of the equation \(cos\theta=2-3sin(\frac{\theta}{2})\ in\ the\ interval\ 0\leq\theta\leq\pi\ are\)

If \(\theta \isin(-\pi,0)\ and\ cos\theta=\frac{-12}{13}, then\ \sin(\frac{\theta}{2})=\)

The period of the function \(g(x)=5\cot(\frac{\pi}{3}x+\frac{\pi}{6})+2\) is equal to

The range of the function f(x) = 2sin(3x) +1 is equal to

If \( \alpha \) and \( \beta \) are two acute angles of a right triangle, then \[ (\sin \alpha + \sin \beta)^2 + (\cos \alpha + \cos \beta)^2 = \] 

If \(\cos\theta=\frac{5}{11}\) and \(\tan\theta\lt0\), then the value of \(\sin\theta\) is equal to

Consider the following statements:
(i) For every positive real number X, x-10 is positive.
(ii) Let n be a natural number. If n² is even, then n is even.
(iii) If a natural number is odd, then its square is also odd.
Then

The set of all x satisfying the inequality |3x+4| ≤ 7 is

The solution set of the inequality \(-2\leq\frac{3x+2}{2}\lt7\) is

If A is non-singular matrix and if \(A^{-1}=\frac{1}{2}\begin{bmatrix} -10&-4\\2&1\end{bmatrix}\), then adj(A)=

If A=[2 0 6] and \(B=\begin{bmatrix} 3&\ \ 5\\7&-2\\6&\ \ 6 \end{bmatrix}\), then AB=

The value of x satisfying the equation \(\begin{vmatrix} x&\ \ 4&\ \ 0\\2&-2&-x\\1&\ \ 1&\ \ 1 \end{vmatrix}=0\) are

Let \(\begin{vmatrix} 2&1&-2\\1&1&-1\\1&0&\ \ 3 \end{vmatrix}\)and let B=|A|adj(A). Then |B|=

Let \(A= \begin{bmatrix} 3&4\\ 1&-2 \end{bmatrix}\) and let \(AB= \begin{bmatrix} -5&41\\ 5&-13 \end{bmatrix}\). Then |B^T| =

If ⁿC₅ + ⁿC₆ = ⁵¹C₆, then the value of n is equal to

Let (3+x)¹⁰ = a₀+a₁(1+x)+a₂(1+x)²+..... a₁₀(1+x)¹⁰, where a₁, a₂, ... a₁₀ are constants. Then the value of a₀+a₁+a₂+.... a₁₀ is equal to

In the binomial expansion of (x - 2y²)⁹, the coefficient of x⁶y⁶ is equal to

The number of subsets containing exactly 4 elements of the set {2, 4, 6, 8, 10, 12, 14, 16, 18) is equal to

The number of numbers greater than 6000 that can be formed from the digits 3, 5, 6, 7 and 9 (no digit is repeated in a number) is equal to

The number of arrangements containing all the seven letter of the word ALRIGHT that begins with LG is

Let \(t_n=\frac{1}{n}\displaystyle\sum^{n}_{k=1}\left(\frac{k}{n} \right)^2\)for n=1,2,3…. Then t₁₀ is equal to

Let S_n be the sum of the first n terms of the series a₁+a₂+...a_n+… If S_n=n²+4n, then the n^th term a_n is

The 11^th term of the geometric series \(\displaystyle\sum^{20}_{r=0}2\times(-2)^r\) is equal to