List of top Mathematics Questions

If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) and \( A + B + C = \pi \), then which of the following is true?
Let a, b, c be three distinct positive real numbers such that (2a)logea = (bc)logeb and bloge2 = alogec. Then 6a + 5bc is equal to _____.
If the roots of the quadratic equation \( x^2 - 6x + k = 0 \) have a difference of 2, find the value of \( k \).
If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), find the inverse of matrix \( A \).
If \( z = 1 + i \), find the modulus of \( z^2 \).
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?
The mean of 5 numbers is 10, and their variance is 16. If one number is increased by 5, what is the new mean?
Find the area of the triangle with vertices at (0, 0), (3, 0), and (0, 4).
If $ \log_2(x + 1) = 3 $, what is the value of $ x $?
The equation of the circle with center at $ (2, -3) $ and radius $ 5 $ 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?

If \(\sin \theta = \frac{3}{5}\) and $ \theta $ is in the first quadrant, what is $ \tan \theta $?

If the roots of the quadratic equation $ 2x^2 - 3x + 1 = 0 $ are $ \alpha $ and $ \beta $, what is the value of $ \alpha^2 + \beta^2 $?
Let \( f(x) = 2x^3 - 3x \neq 4 \). Then the inverse function \( f^{-1}(x) \) is:
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
Let a circle pass through the point \( (1, 2) \) and touch the \( x \)-axis at \( (3, 0) \). Then the equation of the circle is:
If \( \tan \theta = \frac{3}{4} \) and \( \theta \) is in the first quadrant, find the value of \( \sin \theta + \cos \theta \).
Find the distance between the points \( (3, 4) \) and \( (7, 1) \) in the Cartesian plane.
If \( A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \), find the determinant of \( A \).
Evaluate \( \int_{0}^{1} (2x + 1) \, dx \).
Given the linear equation \(2x + 3y – 8 = 0\), write another linear equation in two variables such that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines (iii) coincident lines
Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the AP:
 adn\(a_n\)
(i)738….
(iI)-18…100
(iii)…-318-5
(iv)-18.92.5…3.6
(v)3.50105…
Which of the following is correct for A - B?

Express the following in the form \(\frac{p }{ q}\) , where p and q are integers and q ≠ 0. 

(i) 0.6(ii) 0.47 (iii) 0.001.

Write the following in decimal form and say what kind of decimal expansion each has : 

(i) \(\frac{36}{100}\)  (ii) \(\frac{1}{11}\) (iii) \(4\frac{1}{8}\)

(iv) \(\frac{3}{13}\)  (v) \(\frac{2}{11}\)  (vi) \(\frac{329}{400}\)