List of top Mathematics Questions

If \( X \sim B(4, p) \) and \( 2 P(X = 3) = 3 P(X = 2) \), then the value of \( p \) is:

The particular solution of the differential equation \[ \left( y + x \frac{dy}{dx} \right) \sin y = \cos x \quad \text{at} \quad x = 0 \, \text{is:} \]

If \( A(0, 4, 0) \), \( B(0, 0, 3) \), and \( C(0, 4, 3) \) are the vertices of \( \Delta ABC \), then its incenter is:

The probability distribution of a discrete r.v. \( X \) is: \[ \begin{array}{c|ccccc} X = x & 0 & 1 & 2 & 3 & 4 \\ P(X = x) & k & 2k & 4k & 2k & k \\ \end{array} \] Then, the value of \( P(X \leq 2) \) is:

If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if:

If the angle between the lines whose direction ratios are \( 4, -3, 5 \) and \( 3, 4, k \) is \( \frac{\pi}{3} \), then \( k = \)

If one of the lines given by \( kx^2 + xy - y^2 = 0 \) bisects the angle between the co-ordinate axes, then values of \( k \) are:

If \( \frac{x}{x-y} = \log \left( \frac{a}{x-y} \right) \), then \( \frac{dy}{dx} = \)

The rate of decay of mass of a certain substance at time \( t \) is proportional to the mass at that instant. The time during which the original mass of \( m_0 \) gram will be left to \( m_1 \) gram is
\[ k \text{ is constant of proportionality} \]

The equation of the line passing through the points \( (3, 4, -7) \) and \( (6, -1, 1) \) is:

If the error involved in making a certain measurement is continuous random variable \( X \) with probability density function \( f(x) = k (4 - x^2) \) for \( -2 \leq x \leq 2 \), and \( f(x) = 0 \) otherwise, then \[ P(|-1<X<1|) \]

If \( | \vec{a} \, \vec{b} \, \vec{c} | = 3 \), then the volume of the parallelepiped with \( 2\vec{a} + \vec{b} \), \( 2\vec{b} + \vec{c} \), \( 2\vec{c} + \vec{a} \) as coterminous edges is:

Evaluate the integral: \[ \int_{-1}^{1} \left[ \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right] dx \]

Evaluate the integral: \[ \int \left[ \frac{1 - \log x}{1 + (\log x)^2} \right]^2 dx \]

The co-ordinates of the foot of the perpendicular from the point \( (0, 2, 3) \) on the line
\[ \frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3} \]

The equation of a circle passing through the origin and making x-intercept 3 and y-intercept -5 is:

Which of the following have the same value:
(a) \( \sin 120^\circ \)
(b) \( \cos 930^\circ \)
(c) \( \tan 840^\circ \)
(d) \( \cot(-1110^\circ) \)

Evaluate the integral: \[ \int_0^{\frac{\pi}{2}} \frac{dx}{1 + \cos x} \]

Evaluate the sum of the series: \[ \frac{1^2}{2} + \frac{1^2 + 2^2}{3} + \frac{1^2 + 2^2 + 3^2}{4} + \frac{1^2 + 2^2 + 3^2 + 4^2}{5} + \cdots \quad \text{upto 8 terms} \]

If \(A(3,2,-1)\) and \(B(1,4,3)\), then the equation of the plane which bisects the segment \(AB\) perpendicularly is

ABCD is a parallelogram. \(P\) is the midpoint of \(AB\). If \(R\) is the point of intersection of \(AC\) and \(DP\), then \(R\) divides \(AC\) internally in the ratio

Two dice are thrown together. The probability that the sum of the numbers is divisible by 2 or 3 is

\(y = mx + \dfrac{2}{m}\) is the general solution of

In a triangle \(ABC\) with usual notations, \[ \frac{\cos A - \cos C}{a - c} + \frac{\cos B}{b} = \]

The approximate value of \( \log_{10}99 \) is (Given \( \log_{10}e = 0.4343 \))