List of top Mathematics Questions

Let $x$ be a real number such that $5<|x - 1|<15$. Then

The coefficient of $\dfrac{1}{x^2}$ in the binomial expansion of $\left(3x - \dfrac{1}{3x}\right)^4$ is:

If $(x \;\; 3 \;\; -1)\begin{pmatrix} 1 & 1 & 1 \\ -1 & 0 & 1 \\ 1 & 0 & -1 \end{pmatrix}\begin{pmatrix} 2 \\ 3 \\ 1 \end{pmatrix} = 0$, then the values of $x$ are:

Evaluate the determinant $\begin{vmatrix} 11 & 1 & 1 \\ 1 & 21 & 1 \\ 1 & 1 & 31 \end{vmatrix}$:

Let $P = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 10 & 100 & -1 \end{pmatrix}$. Then $P^{4052}$ is equal to:

If $A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$ and $(\alpha I + \beta A)^2 = A$, where $I$ is $2 \times 2$ unit matrix, then $\alpha^2 - \beta^2 =$:

$\displaystyle \int \frac{x^4 - 1}{x + 1} \, dx$ is equal to:

$\displaystyle \int_{-6}^{0} \left[t^3 + 9t^2 + 27t + 29 + (t+3)\cos(t+3)\right] dt$ is equal to:

If $I = \displaystyle \int_{-1}^{1} \frac{x^4}{1 - x^4} \cos^{-1}\left(\frac{2x}{1+x^2}\right) dx$, then $2I$ is equal to:

$\displaystyle \int \frac{\sin t + \cos t}{13 + 36\sin^2 t} \, dt$ is equal to:

$\displaystyle \int_{0}^{1} \left[\tan^{-1}\left(\frac{1}{1+x+x^2+x^3}\right) + \tan^{-1}(1+x+x^2+x^3)\right] dx$ is equal to:

PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.

D is the mid-point of side BC of \(\triangle ABC\). CE and BF intersect at O, a point on AD. AD is produced to G such that \(OD = DG\). Prove that OBGC is a parallelogram.

The dimensions of a window are 156 cm \(\times\) 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Two dice are rolled together. The probability of getting an outcome \((x, y)\) where \(x>y\), is

A camping tent in hemispherical shape of radius \(1.4\) m, has a door opening of area \(0.50\) \(\text{m}^2\). Outer surface area of the tent is

Arc \(PQ\) subtends an angle \(\theta\) at the centre of the circle with radius \(6.3 \text{ cm}\). If \(\text{Arc } PQ = 11 \text{ cm}\), then the value of \(\theta\) is

The HCF of 960 and 432 is :

The value of x for which \( 2x, (x + 10) \) and \( (3x + 2) \) are the three consecutive terms of an A.P. is :

In the given figure, \(\Delta AHK \sim \Delta ABC\). If \(AK = 10 \text{ cm}\), \(BC = 3.5 \text{ cm}\) and \(HK = 7 \text{ cm}\), find the length of \(AC\).

Prove by vector method an angle in a semi-circle is a right angle.

A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as \(60^{\circ}\). If \(AB = 5\sqrt{3}\) m, then length of the wire is

If \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} - 3\hat{k} \), find the magnitude of \( \vec{a} \times \vec{b} \).

Three fair dice are rolled simultaneously. Let a, b, c be the numbers on the top of the dice. Then the probability that \( \min(a, b, c) = 6 \) is: