List of top Mathematics Questions

After the coordinate axes are rotated through an angle \(\frac{\pi}{4}\) in the anticlockwise direction without shifting the origin, if the equation \(x^2 + y^2 - 2x - 4y - 20 = 0\) transforms to \(ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0\) in the new coordinate system, then
\[ \begin{vmatrix} a & h & g \\ h & b & f \\ g & f & c \end{vmatrix} \]
The mean and variance of a binomial distribution are \(x\) and \(5\) respectively. If \(x\) is an integer, then the possible values for \(x\) are
If \( X \sim B(9, p) \) is a binomial variate satisfying the equation \( P(X = 3) = P(X = 6) \), then \( P(X < 3) = \)?
A bag contains 5 balls of unknown colors. There are equal chances that out of these five balls, there may be 0 or 1 or 2 or 3 or 4 or 5 red balls. A ball is taken out from the bag at random and is found to be red. The probability that it is the only red ball in the bag is:
A die is thrown twice. Let A be the event of getting a prime number when the die is thrown first time and B be the event of getting an even number when the die is thrown second time. Then \(P(A/B) =\)
A four member committee is to be formed from a group containing 9 men and 5 women. If a committee is formed randomly, then the probability that it contains atleast one woman is
There are 8 boys and 7 girls in a class room. If the names of all those children are written on paper slips and 3 slips are drawn at random from them, then the probability of getting the names of one boy and two girls or one girl and two boys is
Let \(x_1, x_2, \ldots, x_{11}\) be the observations satisfying \(\sum_{i=1}^{11} (x_i - 4) = 22\) and \(\sum_{i=1}^{11} (x_i - 4)^2 = 154\). If the mean and variance of the observations are \(\alpha\) and \(\beta\), then the quadratic equation having the roots \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\) is:
If \( \overline{a} = \overline{i} - 2\overline{j} - 3\overline{k} \), \( \overline{b} = -2\overline{i} + 3\overline{j} + 4\overline{k} \), \( \overline{c} = 5\overline{i} - 4\overline{j} + 3\overline{k} \), and \( \overline{d} = 3\overline{i} + \overline{j} + 5\overline{k} \) are four vectors, then \( (\overline{a} \times \overline{b}) \cdot (\overline{c} \times \overline{d}) = \)
If \( \overline{a} \) is a unit vector, then \( |\overline{a} \times \overline{i}|^2 + |\overline{a} \times \overline{j}|^2 + |\overline{a} \times \overline{k}|^2 = \)
If \( \overline{a} = 2\overline{i} - 3\overline{j} + 5\overline{k} \) and \( \overline{b} = -\overline{i} + 3\overline{j} + 3\overline{k} \) are two vectors, then the vector of magnitude 28 units in the direction of the vector \( \overline{a} - \overline{b} \) is:
If the median AD of the triangle ABC is bisected at E and BE meets AC in F, then AF : AC =
In \( \triangle ABC \), if \( a = 8 \), \( b = 10 \), \( c = 12 \), then \( \frac{r}{R} = \)
\(\operatorname{Tanh}^{-1}(\sin\theta) =\)
The number of solutions of \( \tan^{-1} 1 + \frac{1}{2} \cos^{-1} x^2 - \tan^{-1}\left(\frac{\sqrt{1+x^2} + \sqrt{1-x^2}}{\sqrt{1+x^2} - \sqrt{1-x^2}}\right) = 0 \) is
The general solution satisfying both the equations \(\sin x = -\frac{3}{5}\) and \(\cos x = -\frac{4}{5}\) is:
If \(\cos\theta = -\frac{3}{5}\) and \(\theta\) does not lie in second quadrant, then \(\tan\frac{\theta}{2} =\)
If \( \sqrt{3} \cos \theta + \sin \theta > 0 \), then the range of \( \theta \) is:
\( \csc 48^\circ + \csc 96^\circ + \csc 192^\circ + \csc 384^\circ = \)
If \( \frac{3x+1}{(x-1)(x^2+2)} = \frac{A}{x-1} + \frac{Bx+C}{x^2+2} \), then \( 5(A-B) = \)?
\( 1 + \frac{4}{15} + \frac{4 \cdot 10}{15 \cdot 30} + \frac{4 \cdot 10 \cdot 16}{15 \cdot 30 \cdot 45} + \cdots \infty \)
If \(C_0, C_1, C_2, \dots, C_n\) are the binomial coefficients in the expansion of \((1 + x)^n\), then \((C_0 + C_1) - (C_2 + C_3) + (C_4 + C_5) - (C_6 + C_7) + \dots = \)
The number of ways in which a committee of 7 members can be formed from 6 teachers, 5 fathers and 4 students in such a way that at least one from each group is included and teachers form the majority among them, is:
The number of ways of forming the ordered pairs (p, q) such that p>q by choosing p and q from the first 50 natural numbers is:
If all possible 4-digit numbers are formed by choosing 4 different digits from the given digits $ 1, 2, 3, 5, 8 $, then the sum of all such 4-digit numbers is: