List of top Mathematics Questions

Using the conditions from 32(b), prove that \(PR = 2AP\).

Prove that \(2 + 3\sqrt{5}\) is an irrational number given that \(\sqrt{5}\) is an irrational number.

Let P be a point on the parabola, \( x^2 = 4y \). If the distance of P from the centre of the circle, \( x^2 + y^2 + 6x + 8 = 0 \) is minimum, then the equation of the tangent to the parabola at P, is :

The value of x is maximum for

If \(a > 0, \, b > 0, \, c > 0\) and \(a, b, c\) are distinct, then \((a + b)(b + c)(c + a)\) is greater than

If \(|z_1| = 2, |z_2| = 3, |z_3| = 4\) and \(|2z_1 + 3z_2 + 4z_3| = 4\), then absolute value of \(8z_2z_3 + 27z_3z_1 + 64z_1z_2\) equals

Find the area of the region bounded by the curve \(y^2 = 8x\) and the line \(x = 2\).

If \( -1 + 7i \), \( -1 + xi \) and \( 3 + 3i \) are the three vertices of an isosceles triangle which is right angled at \( -1 + xi \), then the value of \( x \) is equal to

Evaluate the integral: \( \int \frac{1}{x^3} \sqrt{1 - \frac{1}{x^2}} \text{dx} = \)

The three vertices of a triangle are \( (0,0) \), \( (3,1) \) and \( (1,3) \). If this triangle is inscribed in a circle, then the equation of the circle is

The number of arrangements containing all the seven letter of the word ALRIGHT that begins with LG is

Consider the following statements :
(i) For every positive real number $x$, $x - 10$ is positive.
(ii) Let $n$ be a natural number. If $n^2$ is even, then $n$ is even.
(iii) If a natural number is odd, then its square is also odd.
Then

In triangles ABC and PQR, \( \angle A = \angle Q \) and \( \angle B = \angle R \), then \( AB : AC \) is equal to :

Find the general solution of the differential equation \(\dfrac{dy}{dx} + y\cot x = \csc x\).

What is the value of \( \sin^{-1}\left(\frac{1}{2}\right) + \cos^{-1}\left(\frac{1}{2}\right) \)?

Find the equation of the curve \( (x, y) \) if \( \cos^{-1}(x-2) = \sin^{-1}(y+1) \).

The distance between the foci of the ellipse \(\frac{(x + 2)^{2{9} + \frac{(y - 1)^{2}}{4} = 1\) is}

Identify the co-ordinates of the point where the line joining \( (1,1,1) \) and \( (2,2,2) \) intersects the plane \( x+y+z=9 \).

Calculate \( y(\log 2) \) if \( \dfrac{dy}{dx} = y + 5 \) and \( y(0) = 4 \).

Find the value of \( k \) if the function \( f(x) = k\sin x + 2\cos x \) is increasing for all \( x \)

The circle passing through the point (1, -2) and touching the x-axis at (3,0) also passes through the point

The axis of the parabola \(x^{2} + 6x + 4y + 5 = 0\) is

The value of \(k\), if the circles \(2x^{2} + 2y^{2} - 4x + 6y = 3\) and \(x^{2} + y^{2} + kx + y = 0\) cut orthogonally is