List of top Mathematics Questions

The number of trials conducted in a binomial distribution is 6. If the difference between the mean and variance of this variate is \(\frac{27}{8}\), then the probability of getting at most 2 successes is:
If \(A(\cos \alpha, \sin \alpha)\), \(B(\sin \alpha, -\cos \alpha)\), and \(C(1, 2)\) are the vertices of \(\triangle ABC\), then find the locus of its centroid.
A and B are two independent events of a random experiment and \(P(A)>P(B)\). If the probability that both A and B occur is \(\frac{1}{6}\) and neither of them occurs is \(\frac{1}{3}\), then the probability of the occurrence of B is:
A company representative is distributing 5 identical samples of a product among 12 houses in a row such that each house gets at most one sample. The probability that no two consecutive houses get one sample is:
Line \(L_1\) passes through the points \(\mathbf{i} + \mathbf{j}\) and \(\mathbf{k} - \mathbf{i}\). Line \(L_2\) passes through the point \(\mathbf{j} + 2\mathbf{k}\) and is parallel to the vector \(\mathbf{i} + \mathbf{j} + \mathbf{k}\). If \(\mathbf{x}i + \mathbf{y}j + \mathbf{z}k\) is the point of intersection of the lines \(L_1\) and \(L_2\), then find \((y - x) =\)
In a triangle \(ABC\), if \(r_1 : r_2 = 3 : 4\) and \(r_1 : r_3 = 2 : 3\), then find the ratio \(a : b : c\).
Let \(\mathbf{a} = \mathbf{i} + 2\mathbf{j} - \mathbf{k}\) and \(\mathbf{b} = 6\mathbf{i} - \mathbf{j} + 2\mathbf{k}\) be two vectors. If \[ |\mathbf{a} \times \mathbf{b}|^2 + |\mathbf{a} . \mathbf{b}|^2 = f(x,y)(x+y) - 46 = 0, \] then what does this represent?
Evaluate: \(\tanh^{-1}\left(\frac{1}{3}\right) + \coth^{-1}(3) =\)
In \(\triangle ABC\), if the line joining the circumcentre and incentre is parallel to \(BC\), then find \( \cos B + \cos C \).
Evaluate: \(\tan\left(2\tan^{-1}\left(-\frac{1}{3}\right) + \tan^{-1}\left(\frac{1}{7}\right)\right) =\)
If \[ \frac{2x^4 - 3x^2 + 4}{(x^2 + 1)(x^2 + 2)} = a + \frac{px + q}{x^2 + 1} + \frac{mx + n}{x^2 + 2}, \] then $\frac{n}{q} =$
The coefficient of $x^{10}$ in the expansion of $\left(x + \frac{2}{x} - 5 \right)^{12}$ is
The number of ways of dividing 15 persons into 3 groups containing 3, 5 and 7 persons so that two particular persons are not included into the 5 persons group is
Evaluate \[ (4 \cos^2 \frac{\pi}{20} - 1)(4 \cos^2 \frac{3\pi}{20} - 1)(4 \cos^2 \frac{5\pi}{20} - 1)(4 \cos^2 \frac{7\pi}{20} - 1)(4 \cos^2 \frac{9\pi}{20} - 1). \]
Assertion (A): $S_3 = 55 \times 2^9$
Reason (R): $S_1 = 90 \times 2^8$ and $S_2 = 10 \times 2^8$
If $\cos 80^\circ + \cos 40^\circ - \cos 20^\circ = k$, then $\frac{4k}{3} =$
If A and B are the values such that $(A + B)$ and $(A - B)$ are not odd multiples of $\frac{\pi}{2}$ and $2\tan(A+B) = 3 \tan(A-B)$, then $\sin A \cos A =$
The number of distinct quadratic equations $ax^2 + bx + c = 0$ with unequal real roots that can be formed by choosing the coefficients $a, b, c$ (with $a \ne 0$) from the set $\{0,1,2,4\}$ is
The product of all the real roots of the equation $|x^2 - 5||x| + 6 = 0$ is
After the roots of the equation $6x^3 + 7x^2 - 4x - 2 = 0$ are diminished by $h$, if the transformed equation does not contain $x$ term, then the product of all possible values of $h$ is
If the difference of the roots of the equation $x^2 - 7x + 10 = 0$ is same as the difference of the roots of the equation $x^2 - 17x + k = 0$, then a divisor of $k$ is
The number of integers greater than 6000 that can be formed by using the digits 0, 5, 6, 7, 8 and 9 without repetition is
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $5x^3 - 4x^2 + 3x - 2 = 0$, then $\alpha^3 + \beta^3 + \gamma^3$ equals
If $A = \begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$ and $\alpha, \beta, \gamma$ are the roots of the equation represented by $|A - xI| = 0$, then $\alpha^2 + \beta^2 + \gamma^2 =$
If B is the inverse of a third order matrix A and det B = k, then $(\text{adj}(\text{adj} A))^{-1}=$