List of top Mathematics Questions

If a dice is thrown twice, then the number of sample events is
A solution of \(2\cos^2 x - 3\cos x + 1 = 0\) is
If \(\cos^ 4\theta - \sin^ 4\theta = \frac{1}{2}\),then \(θ=\)
\(\sqrt{\frac{1 + \sin\theta}{1 - \sin\theta}} + \sqrt{\frac{1 - \sin\theta}{1 + \sin\theta}}=\)
The value of \((1 + \cos x)(1 + \cot^2 x)(1 - \cos x)\) =
If A, B and C are angles in a triangle then\(\tan\left(\frac{A + B}{2}\right) \tan\left(\frac{C}{2}\right) \tan + \tan\left(\frac{B + C}{2}\right) \tan\left(\frac{A}{2}\right) + \tan\left(\frac{C + A}{2}\right) \tan\left(\frac{B}{2}\right)\) =
BC is a tower, B is its base. A is a point on a horizontal line passing through B, the angle of elevation of C from A is 60°. From another point D on AB, the angle of elevation is found to be 30°, then BD =
\(\frac{(\sin 30^\circ \cdot \sec 60^\circ + \cos 30^\circ \cdot \csc 60^\circ)}{(\sec 45^\circ \cdot \cot 45^\circ \cdot \csc 45^\circ)}=\)
A square of side 7 cm encloses a circle touching all its four sides. Then the area enclosed between the square and the circle is
The diameter of a sphere is equal to the height of the cone of equal volume. If r and R are the radii of cone and sphere respectively, then r2 =
A man is standing between two lamp posts on a horizontal line dividing the distance between them in the ratio 1:2. The height of man is 2 m. It is noticed that shadow of the man with respect to first lamp post just touches the foot of second lamp post. If the distance between the posts is 30 m, find the height of the first post.
The diagonals of a quadrilateral ABCD intersect at a point O such that AO. DO = BO.CO. Then the quadrilateral is definitely a
An equilateral triangle ABC is such that the side BC is parallel to X-axis. Then the slopes of its sides AB, BC, CA respectively are
The perimeter of the quadrilateral ABCD formed by A(-3, 1), B(0, 5), C(4, 8), D(1, 4) taken in that order is
Q is a point on the line BD dividing the segment internally. AB, PQ and CD are drawn perpendicular to BD. If AB = a, PQ = b and CD = c, then
In a trapezium \(ABCD AB || CD\), the diagonals AC and BD intersect at ‘P’. If \(AB: CD = 2:1\), then area of \(△CPD: \)area of \(△APB = \)
Which of the following combinations of sides and/or angles cannot form a right-angled triangle?
The first non-zero Fourier coefficient in the expansion of \( \sin^3(x) \) is:
The unit vectors \( \hat{\theta} \) and \( \hat{\phi} \) (where \( \theta \) and \( \phi \) are the polar and azimuthal angles, respectively), in the spherical coordinate system, under the operation of inversion (i.e., reflection through the origin) have:
The only possible real eigenvalue of a Skew-Hermitian matrix is:
The matrix \( A = \begin{bmatrix} -2 & 1 & 2
1 & 2 & 1
2 & 1 & -2 \end{bmatrix} \) is:
Evaluate the integral:
\[ \int_{0}^{\infty} e^{-x} \delta(\lambda^2 - 4)dx \]
A box contains $30$ toys of same size in which $10$ toys are white and all the remaining toys are blue. A toy is drawn at random horn the box and it is replaced in the box after noting down its colour. If $5$ toys are drawn in tills way, then the probability of getting atmost $2$ white toys is
If $f(x)=(2k + 1)x - 3 - ke^{-x } + 2e^x$ is monotonically increasing for all $x \in R$, then the least value of $k$ is
Let x be an $n \times 1$ matrix. Let O and I be the zero, and identity matrices of order n, respectively. Define $P = - \frac{xx^T}{x^Tx}$ is the transpose of x. Then which of the following options is always CORRECT?