List of practice Questions

The modulus of the conjugate of \( z = \frac{-2 + i}{(1 - 2i)^2} \) is:
If \( z_1 = 2 + 5i \), \( z_2 = -1 + 4i \) and \( z_3 = i \), then
\[ \frac{|z_1 - z_3|}{|z_3 - z_2|} = ? \]
The locus of the variable point \( z = x + iy \) whose amplitude is always equal to \( \theta \), is:
If \( \alpha \) is the real root and \( \beta \), \( \gamma \) are the other roots of the equation \( x^3 - a^3 = 0 \, (a>0) \), then the number of common points of the curves given by \( |z - \beta| = \frac{\sqrt{3a}}{2} \) and \( |z - \gamma| = \frac{\sqrt{3a}}{2} \) is:
For \( x \in \mathbb{R} \), the minimum value of \( \frac{x^2 + 2x + 5}{x^2 + 4x + 10} \) is:
If \( f(0) = 0, f(1) = 1, f(2) = 2 \) and \( f(x) = f(x-2) + f(x-3) \) for \( x = 3, 4, 5, \dots \), then find \( f(10) \).
If \( f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x} \) for \( x \in \mathbb{R} \), then find \( f(2023) \).
If \( A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix} \), then \( A^{-1} \) = ?
The rank of the matrix \( A = \begin{bmatrix} 1 & 1 & 3 \\ 2 & 2 & 1 \\ 1 & 1 & 1 \end{bmatrix} \) is:
A man spends 60% of his income and saves the remaining. His income increases by 28% and his expenditure also increases by 30%. Find the percentage increase in his savings.
If A is a non singular square matrix of order 3 such that \(A^3 = 4A^2\) then value of |A| is:
Derivative of \(2x^2\) with respect to \(5x^4\) is:
If \(\frac{d}{dx}(2\frac{d^2y}{dx^2})^3= 7\), then the sum of order and degree of the differential equation is:
A random variable has the following probability distribution
\(X=x_i\)2345
\(P(X=x_i)\)4kk5k2k
The value of P(X <3) is:
If A=\(\begin{bmatrix} 2&3 \\ -1&1\end{bmatrix}\)and \(A^2-3A+kI = 0\) then the value of k is:
The value of the determinant \(\begin{vmatrix}cos^2θ&cosθsinθ&0 \\-sinθ&cosθ&0 \\ 0&0&1 \end{vmatrix}\) is equal to
If \(x = e^{y+e^y+.... to \space ∞}, x> 0\) then \(\frac{d^2y}{dx^2}\) is:
The value of \(\int\limits_{-1}^1x^2 [x] dx\) is:
The value of \(\int\limits_{-3}^2x^2 |2x| dx\) is:
Le L be the set of all lines in a plane and R be the relation in L. defined as R = {(\(L_1, L_2\)): \(L_1\) is perpendicular to \(L_2\)} then R is:
A) Reflexive
B) Symmetric
C) Neither reflexive nor transitive
D) Transitive
E) Neither reflexive nor symmetric
Choose the correct answer from the options given below:
Consider the non-empty set consisting of children in a family and a relation R is defined as aRb if a is a brother of b. Then R is:
The value of the expression sin \([cot^{-1}(cos (tan^{-1}1))]\) is:
There are two values of a for which the determinant, \(\Delta =\begin{bmatrix}1& -2& 5\\[0.3em]0& a& 1\\[0.3em] 0& 4& 2a\\[0.3em] \end{bmatrix} = 86\), then the sum of these values of a is:
If A is a skew-symmetric matrix of order n. then
If, A = \(\begin{bmatrix}a& d& l\\[0.3em]b& e& m\\[0.3em]c& f& n\\[0.3em] \end{bmatrix}\)and B = \(\begin{bmatrix}l& m& n\\[0.3em]a& b& c\\[0.3em]d& e& f\\[0.3em]  \end{bmatrix}\), then