List of top Mathematics Questions

If \( |\mathbf{\bar{f}}| = 10\), \( |\mathbf{\bar{g}}| = 14\) and \( |\mathbf{\bar{f}} - \mathbf{\bar{g}}| = 15\), then \( |\mathbf{\bar{f}} + \mathbf{\bar{g}}| =\)
If five-digit numbers are formed from the digits 0, 1, 2, 3, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 is
The equation of the circle whose diameter is the common chord of the circles \(x^2 + y^2 - 6x - 7 = 0\) and \(x^2 + y^2 - 10x + 16 = 0\) is:
If \(y = t^2 + t^3\) and \(x = t - t^4\), then \(\frac{d^2y}{dx^2}\) at \(t = 1\) is:
If \( p_1 \) and \( p_2 \) are the perpendicular distances from the origin to the tangent and normal drawn at any point on the curve \( x^{2/3} + y^{2/3} = a^{2/3} \) respectively. If \( k_1 p_1^2 + k_2 p_2^2 = a^2 \), then \( k_1 + k_2 = \)
The acute angle between the curves \(x^2 + y^2 = x + y\) and \(x^2 + y^2 = 2y\) is:
Determine the order and degree of the differential equation \( \frac{d^3y}{dx^3} = \left[1 + \left(\frac{dy}{dx}\right)^2\right]^{5/2} \):
Find the integrating factor of the differential equation \( \sin x \frac{dy}{dx} - y \cos x = 1 \):
The general solution of the differential equation \( (x \sin \frac{y}{x}) dy = (y \sin \frac{y}{x} - x) dx \) is:
Evaluate the integral \( \int \frac{dx}{x(x^4 + 1)} \):
If \( l_1 \) and \( l_2 \) are the lengths of the perpendiculars drawn from a point on the hyperbola \( 5x^2 - 4y^2 - 20 = 0 \) to its asymptotes, then \( \frac{l_1^2 l_2^2}{100} = \)
If a directrix of a hyperbola centered at the origin and passing through the point \( (4, -2\sqrt{3}) \) is \( \sqrt{5}x = 4 \) and \( e \) is its eccentricity, then \( e^2 = \)
The number of numbers lying between 1000 and 10000 such that every number contains the digits 3 and 7 only once without repetition is:
The number of ways in which 17 apples can be distributed among four guests such that each guest gets at least 3 apples is:
The domain of the real valued function \( f(x) = \sqrt{2 + x} + \sqrt{3 - x} \) is:
Two natural numbers are chosen at random from 1 to 100 and are multiplied. If \(A\) is the event that the product is an even number and \(B\) is the event that the product is divisible by 4, then \(P(A \cap \bar B) = \)
If the chord of the ellipse \( \frac{x^2}{4} + \frac{y^2}{9} = 1 \) having \((1,1)\) as its middle point is \( x + \alpha y = \beta \), then:
In \(\triangle ABC\), \(bc - r_2 r_3 = \)
If \(2.4^{2n+1} + 3^{3n+1}\) is divisible by \(k\) for all \(n \in \mathbb{N}\), then \(k\) is:
Evaluate the integral \( \int_{-\frac{1}{24}}^{\frac{1}{24}} \sec(x) \log\left(\frac{1-x}{1+x}\right) \, dx \):
If \((\alpha + \beta)\) is not a multiple of \(\frac{\pi}{2}\) and \(3 \sin(\alpha - \beta) = 5 \cos(\alpha + \beta)\), then \[ \tan\left(\frac{\pi}{4} + \alpha\right) + 4\tan\left(\frac{\pi}{4} + \beta\right) = \]
If \([x]\) is the greatest integer function, then evaluate the integral \( \int_{0}^{5} [x] \, dx \):
The angle between the diagonals of the parallelogram whose adjacent sides are \(2i + 4j - 5k\) and \(i + 2j + 3k\) is
Equation of a tangent line of the parabola \(y^2 = 8x\), which passes through the point \((1, 3)\) is:
A person is known to speak false once out of 4 times. If that person picks a card at random from a pack of 52 cards and reports that it is a king, then the probability that it is actually a king is