List of top Mathematics Questions asked in KEAM

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

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 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

If ¹¹P_r=7920 and ¹¹C_r = 330, then the value of r is equal to

If z₁ and z₂ are two different complex numbers with |z₂|=1, then \(|\frac{1-\bar{z_1}z_2}{z_1-z_2}|\)is equal to

In an A.P. there are 18 terms and the last three terms of the A.P. are 67, 72, 77. Then the first term of the A.P. is

If -1+7i, -1+xi and 3+3i are the three vertices of an isosceles triangle which is right angled at -1+xi, then the value of x is equal to

If n^th term of a series is n+(-1)^n-1, n = 1,2,3,..., then the sum of first 40 terms of the series is

If the first term of a G.P. is 3 and the sum of second and third terms is 60, then the common ratio of the G.P. is

The principal argument of the complex number \(z=\frac{8+4i}{1+3i}\) is equal to

The minimum value of |z+1|+|z-2| is equal to

Let ⊙ be a binary operation on Q - {0} defined by a⊙b=\(\frac{a}{b}\). Then 1⊙(2⊙(3⊙4)) is equal to

Let f: R→R be defined by f(x) = cos x. Then

Let \(f(x) =   \begin{cases}     x+2       & for\ x\lt\ 1 \\     4x-1  & for\ 1\leq x \leq3 \\ x^2+5 & for\ x\gt3   \end{cases}\). Then

If n(A∪B)=97, n(A∩B) = 23 and n(A-B)=39, then n(B) is equal to

For any two positive rational numbers m and n, a binary operation * is defined by \(m*n=\frac{m+n}{3}\), then \(\frac{7}{2}*\frac{5}{2}\) is equal to

The general solution of the differential equation 4xy+12x+(2x²+3)y' = 0 is

If \(\frac{z}{i}=11-13i\), then \(z+\bar z\) is equal to

Let X be the set {1, π, {42, √2}, {1,3}}. Which of the following statement(s) is/are true? Ρ : π ∈X , Q :{1,3} ⊆ X , R : {1,7} ⊆ X 

If the inequality -13 ≤ x ≤ 5 is expressed in the form |x-a|≤b, then the values of a and b are respectively

The solution set of the inequality 5(4x+6) <25x+10 is

Let \(\begin{vmatrix} x-1&2&1\\2&x-1&2\\1&x+2&x-1 \end{vmatrix}=ax^3+bx^2+cx+d\), where a,b,c and d are constants. Then the value of d is

The matrix \(\begin{bmatrix} -2&1&0\\3&4&1\\-4&\lambda&0 \end{bmatrix}\) is non-singular for \(\lambda\ne\)

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