List of top Mathematics Questions

If the centroid of the triangle ABC with vertices A(5,-4), B(7,8) and C(a,b) is G(7,6), then (b-a) is

\(\sqrt{\dfrac{1+\cos\theta}{1-\cos\theta}} =\)

Find the value of 45^ 30^ + 60^ 45^ - 5 90^2 0^

In an arithmetic progression, the sum of the first 10 terms is 210 and the sum of the next 10 terms is 610. What is the common difference of the arithmetic progression?

If the sum of the zeroes of the polynomial (p(x)=2x^3-3kx^2+4x-5) is 6, then the value of k is

Two cars A and B start from the same point and travel the same distance. The ratio of their speeds is 3: 4. Car A takes 30 minutes more than car B to complete the journey. If car B takes 't' minutes, then what is the value of 't' (in minutes)?

A solid metal cylinder has a radius r and height h. It is melted down and recast into a new cylinder where the radius is reduced by 5

Find the value of the following algebraic expression: \[ \frac{(0.64)^{3}-(0.36)^{3}}{(0.64)^{2}+(0.64)(0.36)+(0.36)^{2}} = \]

If () and () are the roots of the quadratic equation (2x^2-3x-1=0), then find the value of (^4+^4).

Let (N) denote the set of all natural numbers and (kN = kx x N) for any (k N). Then (8N 12N =)

The angle between two radii of a circle is (60^). Find the area of a sector (in sq.cm.) of radius 7 cm.

If (_2128=a), (_3813=b), then (a-2b=)

A number when divided successfully by 2, 3, and 5 leaves remainders 1, 2, and 3 respectively. If the number is less than 200 and also divisible by 7 after adding 4 to it, then that number is

Among the following differential equations, the equation having order 2 and degree 3 is:

The general solution of the differential equation \( \frac{dy}{dx} + y \tan x = - \tan x \log(\cos x) \) (\(0 < x < \pi/2\)) is:

A circle passes through the ends of the latus rectum of parabola \( y^2=12x \) and has its centre at the vertex. The area inside the circle and outside the parabola in the \( 1^{st} \) quadrant is:

The integral \( \int_{0}^{\pi} |x \cos 2x| dx \) is equal to:

Consider the differential equations \(\frac{dy}{dx}(x+y+1)=1\) and \(\frac{dx}{dy}=3y+2x^2\).
Which of the following is correct regarding these two differential equations?

The integral \( \int \frac{\cos x - \sin x}{10 + \sin 2x} dx \) is equal to:

The integral \( \int_{\sqrt{2}}^{2} \frac{x}{(x^3 - x^2 + x - 1)(x+1)} dx \) is equal to:

The integral \( \int_{0}^{1} x^{5/2} (1-x)^{3/2} dx \) is equal to:

The length of the tangent drawn at the point \(P(1, 3\sqrt{3})\) on the curve is \(\frac{x^2}{3} + \frac{y^2}{27} = 4\):

If \(x > 0\), then \(\int \frac{1}{\sqrt{x^4 + 2x^3 + 2x^2}} dx =\)

The function \(f(x) = \frac{x}{2} + \frac{2}{x}\) has a local minimum at

The integral \( \int \frac{\cos^3 x}{(1+\sin x)^4} dx \) is equal to: