List of top Mathematics Questions

An ellipse passes through the foci of the hyperbola, $9x^2? 4y^2 = 36$ an and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\frac{1}{2},$ then which of the following points does not lie on the ellipse ?

If $y + 3x = 0$ is the equation of a chord of the circle, $x^2 + y^2 - 30x = 0$, then the equation of the circle with this chord as diameter is :

Let k be a non-zero real number. If

\( f(x) = \begin{cases} \dfrac{(e^x - 1)^2}{\sin\left(\frac{x}{k}\right)\log\left(1+\frac{x}{4}\right)}, & x \ne 0 \\[2ex] 12, & x = 0 \end{cases} \)

is a continuous function, then the value of \( k \) is:

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^2$ = 8y. If the point $P$ divides the line segment $OQ$ internally in the ratio $1 : 3$, then the locus of $P$ is

Let $PQ$ be a double ordinate of the parabola, $y^2= - 4x$, where P lies in the second quadrant. If R divides $PQ$ in the ratio $2 : 1$, then the locus of R is :

Locus of the image of the point $(2, 3)$ in the line $\left(2x - 3y + 4\right) + k\left(x - 2y + 3\right) = 0, k \in R,$ is a

The average age of 8 men is increased by 2 years when one of them whose age is 20 years is replaced by a new man. What is the age of the new man?

The approximate value of \((1.0002)^{3000}\) is

\((\mathbf{a} \cdot \hat{\mathbf{i}})(\mathbf{a} \times \hat{\mathbf{i}}) + (\mathbf{a} \cdot \hat{\mathbf{j}})(\mathbf{a} \times \hat{\mathbf{j}}) + (\mathbf{a} \cdot \hat{\mathbf{k}})(\mathbf{a} \times \hat{\mathbf{k}})\) is equal to

If \(A = \{(x,y): x^2 + y^2 = 25\}\) and \(B = \{(x,y): x^2 + 9y^2 = 144\}\); then \(A \cap B\) contains

The value of \(c\) prescribed by Lagrange's mean value theorem, when \(f(x) = \sqrt{x^2 - 4}\), \(a = 2\) and \(b = 3\), is

The mean deviation from the mean of the series \(a, a+d, a+2d, .........., a+2nd\), is

If \(f(x) = x e^{x(1-x)}\), then \(f(x)\) is

If \(\omega\) is an imaginary cube root of unity, then the value of \((1+\omega)(1+\omega^2)(1+\omega^3)(1+\omega^4)(1+\omega^5)..........(1+\omega^{3n})\) is

Let \(X\) denotes the number of times heads occur in \(n\) tosses of a fair coin. If \(P(X=4)\), \(P(X=5)\) and \(P(X=6)\) are in AP, then the value of \(n\) is

If there is a term containing \(x^{2r}\) in \(\left(x + \frac{1}{x^2}\right)^{n-3}\), then

The value of \(\sin^{-1}\left\{\cot\left(\sin^{-1}\sqrt{\frac{2-\sqrt{3}}{4}}\right) + \cos^{-1}\frac{\sqrt{12}}{4} + \sec^{-1}\sqrt{2}\right\}\) is

If \(\cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \theta\), then \(9x^2 - 12xy\cos\theta + 4y^2\) is equal to

If \(\tan(\sec^{-1}x) = \sin\left(\cos^{-1}\frac{1}{\sqrt{5}}\right)\), then \(x\) is equal to

The equation of the tangent to the curve \(y = (2x-1)e^{2(1-x)}\) at the point of its maximum, is

The proposition \((p \rightarrow \neg p) \wedge (\neg p \rightarrow p)\) is

The number of ways in which four letters can be selected from the word 'DEGREE', is

If PQRS is a convex quadrilateral with 3, 4, 5 and 6 points marked on sides PQ, QR, RS and PS respectively. Then, the number of triangles with vertices on different sides is

\(\lim_{x \to -1} \left( \frac{x^4 + x^2 + x + 1}{x^2 - x + 1} \right)^{\frac{1 - \cos(x+1)}{(x+1)^2}}\) is equal to

The term independent of \(x\) in the expansion of \(\left(x - \frac{1}{x}\right)^4 \left(x + \frac{1}{x}\right)^3\), is