List of top Mathematics Questions

If the equation of an ellipse is \(3x^2+2y^2+6x-8y+5=0\), then which of the following are true?

The equation of the common tangents to the two hyperbolas \(\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\) and \(\dfrac{y^2}{a^2}-\dfrac{x^2}{b^2}=1\), are

If \(3\sin\theta+5\cos\theta=5\), then the value of \(5\sin\theta-3\cos\theta\) is equal to

The value of
\[ \lim_{n\to\infty}\left[\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\cdots+\frac{1}{n(n+1)}\right] \] is equal to

A rod of length \(l\) slides with its ends on two perpendicular lines. Then, the locus of its mid point is

The equation of straight line through the intersection of the lines \(2x+y=1\) and \(3x+2y=5\) and passing through the origin is

The line joining \((5,0)\) to \((10\cos\theta,10\sin\theta)\) is divided internally in the ratio \(2:3\) at \(P\). If \(\theta\) varies, then the locus of \(P\) is

If \(2x+y+k=0\) is a normal to the parabola \(y^2=-8x\), then the value of \(k\) is

The chances of defective screws in three boxes \(A,B,C\) are \(\dfrac{1}{5},\dfrac{1}{6},\dfrac{1}{7}\) respectively. A box is selected at random and a screw drawn from it at random is found to be defective. The probability that it came from box \(A\), is

For what values of \(m\) can the expression
\[ 2x^2+mxy+3y^2-5y-2 \] be expressed as the product of two linear factors?

The value of \(\dfrac{\cos\theta}{1+\sin\theta}\) is equal to

If \(z=\dfrac{1-i\sqrt{3}}{1+i\sqrt{3}}\), then \(\arg(z)\) is

If \(B\) is a non-singular matrix and \(A\) is a square matrix, then \(\det(B^{-1}AB)\) is equal to

If \(f(x), g(x)\) and \(h(x)\) are three polynomials of degree 2 and
\[ \Delta(x)= \begin{vmatrix} f(x) & g(x) & h(x)\\ f'(x) & g'(x) & h'(x)\\ f''(x) & g''(x) & h''(x) \end{vmatrix} \] then \(\Delta(x)\) is a polynomial of degree

Let \(S\) be a set containing \(n\) elements. Then, number of binary operation on \(S\) is

The number of solutions of the equation \(\sin(e^x)=5+x-5^x\), is

If \(a^x=b^y=c^z=d^u\) and \(a,b,c,d\) are in GP, then \(x,y,z,u\) are in

If \(z\) satisfies the equation \(|z|=z-1+2i\), then \(z\) is equal to

If \(F\) is function such that \(F(0)=2,\ F(1)=3\), and
\[ F(x+2)=2F(x)-F(x+1)\ \text{for}\ x\geq 0, \] then \(F(5)\) is equal to

From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is

The value of $\cos^{-1}x + \cos^{-1} \left(\frac{x}{2} + \frac{1}{2} \sqrt{3-3x^{2}}\right) ; \frac{1}{2} \le x \le 1 $ is

The slope of the tangent to the hyperbola $2x^2 - 3y^2 = 6$ at $(3, 2)$ is

The solution of differential equation $2x \frac{dy}{dx} - y = 3$ represents a family of

If $I_{m}=\int\limits_{1}^{e}(\ln x)^{m} d x$, where $m \in N$, then $I_{10}+10 I_{9}$ is equal to -