List of top Mathematics Questions

If \( P(B) = \frac{3}{5} \), \( P(A \mid B) = \frac{1}{2} \), and \( P(A \cup B) = \frac{4}{5} \), then the value of \( P(A \cup B)' + P(A' \cup B) \) is:
Bag P contains 6 red and 4 blue balls, and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
The probability of getting a sum greater than 7 when a pair of dice are thrown is:
If \( \alpha_1, \alpha_2, \alpha_3 \) are the roots of the equation \( x^3 + 3x + 2 = 0 \), then \( \alpha_1^5 + \alpha_2^5 + \alpha_3^5 \) is:
If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax - b = 0 \), and \( \alpha^2 + \beta^2 \) and \( \alpha^3 + \beta^3 \) are the roots of \( Ax^2 + Bx + C = 0 \), then \( C = \ldots \)
If \( P(x) = 0 \) is a polynomial of least degree with integer coefficients and \( \sqrt{2} + \sqrt{3}i \) is one of its roots, then that equation is:
If $ \alpha, \beta, \gamma $ are the roots of the equation $ x^3 + 3x^2 + 4x + 5 = 0 $, then the cubic equation whose roots are $ 1 + 4\alpha, 1 + 4\beta, 1 + 4\gamma $ is:
If the sum of the coefficients of even powers of \( x \) in the expansion of \( (1 - x + x^2)^{2n} \) is 3281, then \( n \) is:
If the equation \( x^4 + ax^3 + bx^2 + cx + d = 0 \) has three equal roots, then the root is:
If $ 3 + i $ and $ 2 - \sqrt{3} $ are the roots of the equation $ f(x) = a_0 + a_1 x + a_2 x^2 + ... + a_n x^n $, where $ a_0, a_1, ..., a_n \in \mathbb{Z} $, then the least value of $ n $ and the value of $ a_0 $ are respectively:
If \( \alpha, \beta, \gamma \) are the roots of \( x^3 + 2x + 5 = 0 \), then \( \sum \frac{\beta + \gamma}{\alpha^2} \) is:
The degree of the polynomial \( \left( x + \sqrt{x^4 - 1} \right)^9 + \left( x - \sqrt{x^4 - 1} \right)^9 \) is:
The minimum value of \( f(x) = \frac{x^2 - 2x + 3}{x^2 - 4x + 7} \) is:
If \( x^2 + x - 6 \) is a factor of \( 2x^3 + x^2 + ax + b \), then \( 6a + 13b = \) ?
If the sum of the cubes of the roots of the equation \( x^3 - ax^2 + bx - c = 0 \) is zero, then \( a^3 + 3c = \):
If \( -1 \) is a twice repeated root of the equation \( ax^3 + bx^2 + cx + 1 = 0 \), then \( ax^3 + bx^2 + cx + 1 = 0 \) represents:
If \( 3 \cdot {}^5C_0 + 8 \cdot {}^5C_1 + 13 \cdot {}^5C_2 + 18 \cdot {}^5C_3 + 23 \cdot {}^5C_4 + 28 \cdot {}^5C_5 = k \cdot 2^5 \), then \( k = \)
For a binomial distribution with mean 6 and variance 2, \( P(X \ge 2) = \)
If \( C_j \) stands for \( \binom{n}{j} \), then: \[ \frac{C_1}{C_0} + 2 \times \frac{C_2}{C_1} + 3 \times \frac{C_3}{C_2} + ... + n \times \frac{C_n}{C_{n-1}} \]
If a point R$(4,y,z)$ lies on the line joining $P(2,-3,4)$ and $Q(8,0,10)$, then distan of R from origin is
The transformed equation of $2x^2 + 3y^2 - z^2 - 8x + 18y + 2z + 9 = 0$ when the axes are translated to the point $(2,-3,1)$ is

If a straight line is equally inclined at an angle $ \theta $ with all the three coordinate axes, then $ \tan \theta =$

If the foot of the perpendicular drawn from $(0,0,0)$ to a plane is $(1,2,3)$, then the equation of the plane is

The vector equation of any plane passing through the line of intersection of the planes $ \bar{r} \cdot \bar{n}_1 = q_1 $ and $ \bar{r} \cdot \bar{n}_2 = q_2 $ is given by $ \bar{r} \cdot (\bar{n}_1 + \lambda \bar{n}_2) = q_1 + \lambda q_2 $ for $ \lambda \in \bar{R} $. The vector equation of a plane passing through the point $ 2\bar{i} - 3\bar{j} + \bar{k} $ and the line of intersection of the planes $ \bar{r} \cdot (\bar{i} - 2\bar{j} + 3\bar{k}) = 5 $, $ \bar{r} \cdot (3\bar{i} + \bar{j} - 2\bar{k}) = 7 $ is