List of top Mathematics Questions

If $ f(x) = e^{2x} \sin x $, find $ f'(x) $.
If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.
The value of $ \sin^2 30^\circ + \cos^2 60^\circ $ is:
Evaluate: $$ \lim_{x \to 0} \frac{\sqrt{1 + x} - \sqrt{1 - x}}{x} $$
A box contains 5 red balls and 4 green balls. Two balls are drawn one after another without replacement. What is the probability that the second ball is green, given that the first ball drawn was red?
Let $ f(x) = |x^2 - 4x + 3| + |x^2 - 5x + 6| $. The minimum value of $ f(x) $ is:
If a point $ P(x, y) $ satisfies the condition that its distance from the point $ (3, -2) $ is equal to its distance from the line $ y = 2x + 1 $, then the locus of point $ P $ is:
If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \), where \( A + B + C = \pi \), then what is the value of \( \tan A \tan B + \tan B \tan C + \tan C \tan A \)?
If \( A = \begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \\ \end{vmatrix} \), then the value of \( A \) is:
Solve the inequality: \( \log_2(x^2 - 5x + 6) >1 \)
Two numbers are selected at random (without replacement) from the first 6 natural numbers. What is the probability that the difference of the numbers is less than 3?
If \( z = x + iy \) is a complex number such that \( |z - 1| = |z + 1| \), then the locus of \( z \) represents:
If \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \) and \( \vec{b} = 2\hat{i} - \hat{j} + 2\hat{k} \), then find the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \).
If one root of the quadratic equation \( ax^2 + bx + c = 0 \) is double the other, then what is the correct relation among the coefficients?
Find the sum of the infinite geometric series: $$ S = 8 + 4 + 2 + \cdots $$ if it converges.
If $$ A = \begin{pmatrix} 2 & 3 \\ 1 & k \end{pmatrix} $$ and $\det(A) = 7$, find the value of $ k $.
If $\log_2 (x-1) + \log_2 (x-3) = 3$, find the value(s) of $ x $.
Find the equation of the tangent to the curve $ y = x^3 - 3x + 1 $ at the point where $ x = 2 $.
How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
If $\sin \theta = \frac{3}{5}$ and $\theta$ lies in the first quadrant, find $\cos \theta$.
The quadratic equation $ x^2 - 5x + k = 0 $ has equal roots. Find the value of $ k $.
The sum of the first 20 terms of the arithmetic progression 7, 10, 13, ... is:
If \( \tan A + \cot A = 2 \), then the value of \( \tan^2 A + \cot^2 A \) is:
If the distance between the points \( (2, -1) \) and \( (k, 3) \) is 5, then the possible values of \( k \) are:
The equation of the circle passing through the points (1,2), (4,3), and (2,–1) is: