List of top Mathematics Questions

If $z= x +iy , x,y \in R , (x,y) \ne (0, -4)$ and $Arg \left( \frac{2z-3}{z+4i}\right) = \frac{\pi}{4}$ , then the locus of $z$ is
A box contains 4 white and 6 black balls. If 3 balls are drawn at random with replacement, what is the probability that at least one is white?
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
Consider the following lists.
List-I List-II
(A) $f(x) = \frac{|x+2|}{x+2} , x \ne -2 $ (I) $[\frac{1}{3} , 1 ]$
(B) $(x)=|[x]|,x \in [R$ (II) Z
(C) $h(x) = |x - [x]| , x \in [R$ (III) W
(D) $f(x) = \frac{1}{2 - \sin 3x} , x \in [R$ (IV) [0, 1)
(V) { -1, 1}
If the roots of the quadratic equation \( 2x^2 - 8x + 5 = 0 \) are \( p \) and \( q \), find the value of \( \frac{1}{p} + \frac{1}{q} \).
Two numbers are selected at random (without replacement) from the first 50 natural numbers. The probability that their sum is even is:
If $[x]$ is the greatest integer less than or equal to $x$ and $|x|$ is the modulus of $x$. then the system of three equations $2x + 3 | y | + 5[z] = 0, x + |y| - 2[z] = 4, x + |y| + |z| = 1$ has
If \( z \) is a complex number such that \( |z| = 5 \) and \( \text{Re}(z) = 3 \), then the value of \( z^2 \) is:
If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), find the inverse of matrix \( A \).
Let a circle pass through the point \( (1, 2) \) and touch the \( x \)-axis at \( (3, 0) \). Then the equation of the circle is:
A box contains 5 red balls and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?
$D = \left\{x\in\mathbb{R}: f\left(x\right) =\sqrt{\frac{x - \left|x\right|}{x - \left[x\right]}} \text{is defined} \right\}$ and $C$ be the range of the real function $g(x) = \frac{2x}{4 + x^{2}}$. Then $D \cap C$
Evaluate \(\lim_{x\rightarrow 5}\) f(x), where f(x) = |x|-5
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
If \[ \frac{(2 - i)\,x + (1 + i)}{2 + i} \;+\; \frac{(1 - 2i)\,y + (1 - i)}{1 + 2i} \;=\; 1 - 2i, \quad\text{then}\quad 2x + 4y =\;? \]
If the origin is shifted to the point \(\left(\frac{3}{2}, -2\right)\) by the translation of axes, then the transformed equation of \(2x^2 + 4xy + y^2 + 2x - 2y + 1 = 0\) is:
Solve the following pair of linear equations by the elimination method and the substitution method : 
(i) x + y = 5 and 2x – 3y = 4
(ii) 3x + 4y = 10 and 2x – 2y = 2 
(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7 
(iv)\( \frac{x}{2} + \frac{2y}{3} = -1 \) and \(x- \frac{y}{3} = 3\)
If \(f(x) =   \begin{cases}  x-2       & \quad 0\leq x\leq2\\     -2  & \quad -2\leq x\leq0   \end{cases}\) and \(h(x) = f(|x|) + |f(x)|, \int\limits^{k}_{0} h(x) dx\) is equal to _____.(k>0)
Find the number of rational numbers in the expansion of \((2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}\).
Three urn A, B, C, A has 7 red and 5 black balls, B has 5 red and 7 black balls, C has 6 red and 6 black balls. One urn is selected and black ball is taken out. Find probability that the selected urn is A.
Find \(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{\sin^2x}{1+2^x} \;dx\)
\(f(x)=\frac{2x^2-3x+8}{2x^2+3x+8}\), Then sum of maximum and minimum values of f(x) is:
The coefficient of x7 in (1-x-x2+x3)6
If (z)2+|z|=0 and if α is sum of roots and β is product of non-zero roots, then find 4(α2+β2)
If the length of focal chord of y2 = 12x is 15 and if the distance of the focal chord from origin is p then 10p2 is equal to: