List of practice Questions

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

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

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

The sum of the first 24 terms of the series 9+13+17+...... is equal to

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

The modulus of \((\frac{1+i}{1-i})^{75}-(\frac{1-i}{1+i})^{75}\)is

If \(z^4=7-5i\), then \(\text{Im}((\bar{z})^4)\) is equal to

The value of \(\left[ \frac{5i}{(1-i)(2-i)(3-i)} \right]^{50}\)is equal to

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

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

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