List of top Mathematics Questions

The absolute value of the tangent of the difference of the angles made by the lines \( 4x^2 - 24xy + 11y^2 = 0 \) with the X-axis is:
If p and q are the x and y intercepts respectively of the line passing through the points \( (a \cos \alpha, b \sin \alpha) \) and \( (a \cos \beta, b \sin \beta) \), then:
If the y-intercept of the perpendicular bisector of the line segment joining P(1,4) and Q(k,3) is -4, then a possible value of k is:
If a Bernoulli trial is conducted n times, then which one of the following is not suitable to use Poisson distribution?
If the mean and variance of a binomial variable X are 2.4 and 1.44 respectively, then the parameters \( n \) and \( p \) are respectively:
A pair of dice is thrown. Then the probability that either of the dice shows 2 when their sum is 6 is:
If A and B simultaneously toss one coin each every time, each 50 times, then the probability of not getting a tail on both the coins is:
If \( S \) is the sample space of a random experiment \( \xi \) and \( P \) is a probability function defined on the power set \( P(S) \) of \( S \), then which one of the following is not satisfied by \( P \)?
If A and B are any two events of a sample space, then set-theoretic description for the event "Exactly one of the events A, B to occur" is:
The locus of the point which is equidistant from the point \( (1, 1) \) and the line \( x + y + 1 = 0 \) is:
Let \( L \) be the line passing through the points \( i\hat{i} - 9\hat{k} \) and \( 7j\hat{k} \), and \( \pi \) be the plane passing through the point \( 6i + j \) and perpendicular to the vector \( i + j + k \). If \( \theta \) is the angle between \( L \) and \( \pi \), then \( \sin \theta = \):
If \( \vec{OA} = 2i - j + k \), \( \vec{OB} = -3i - k \), and \( \vec{OC} = -2i + 2j - 3k \), then a unit vector perpendicular to the plane containing \( A, B, C \) is:
Let \( \vec{b} = 3i - 2j + k \) and \( \vec{c} = i - j - k \) be two vectors. If \( \vec{a} \) is a vector such that \( \vec{a} + \vec{b} + \vec{c} = 0 \), then \( | \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} | \) is:
If each of the observations \( x_1, x_2, \dots, x_n \) is increased or decreased by \( k \), where \( k \) is a positive number, then the variance of the data thus obtained:
Assertion (A): The function \( f(x) = \begin{cases} 1 - \cos x, & x<0 \\ \sin x, & x \geq 0 \end{cases} \) is continuous at \(x = 0\). Reason (R): \(\lim_{x \to 0} \sin x = 0\)
Which one of the following is a homogeneous differential equation?
The area (in square units) bounded by \[ x = 4, \quad y = -4, \quad \text{and} \quad y = x \quad \text{is:} \]
The particular solution of the differential equation \[ (1 + y^2) \, dx - xy \, dy = 0, \quad y(1) = 0 \quad \text{represents:} \]
The positive value of \( x \) satisfying the equation \[ \int_0^x (1 - t) \, dt = \frac{1}{2} \] is:
Evaluate the following integral: \[ \int (x^3 + x^2 m + x^m) (2x^{2m} + 3x^m + 6x^m) \, dx \]
Evaluate the integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin x \cdot \sin^2 x \cdot \cos x \, dx \]
If \( a \in \mathbb{Z}^+ \), \([x]\) is the greatest integer not more than \( x \) and \[ \int_0^a \left\lfloor x \right\rfloor \, dx = 127, \text{ then } a = ? \]
If \( c \) and \( d \) are arbitrary constants, then \[ y = e^{2x} \left( \cosh \sqrt{2} x + d \sinh \sqrt{2} x \right) \] is the general solution of the differential equation:
The maximum value of \( x^4 y^4 \) when \( a^2 x^4 + b^2 y^4 = c^6 \) is:
If \( (a^2 - 1)x + ay + (3 - a) = 0 \) is a normal to the curve \( xy = 1 \), then the interval in which ‘a’ lies is: