List of top Mathematics Questions

The value of the integral $ \int_{0}^{1} $ $ \frac{e^{5log_{e}x}-e^{4log_{e}x}}{e^{log_{e}x^3}-e^{log_{e}x^2}}dx $ is

$ \int \frac{x^3dx}{1+x^4} $ equals

If the straight lines $2x + 3y - 3 = 0$ and $x + ky + 7 = 0$ are perpendicular, then the value of $k$ is

If $a = 3, b = 4, c = 5$ each one of $a ,b$ & $c$ is perpendicular to the sum of the remaining then $| a + b + c | $ is equal to

The sum of coefficients of integral powers of $x$ in the binomial expansion $(1-2\sqrt x)^{50}$ is

If $y + 3x = 0$ is the equation of a chord of the circle, $x^2 + y^2 - 30x = 0$, then the equation of the circle with this chord as diameter is :

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^2$ = 8y. If the point $P$ divides the line segment $OQ$ internally in the ratio $1 : 3$, then the locus of $P$ is

Let $PQ$ be a double ordinate of the parabola, $y^2= - 4x$, where P lies in the second quadrant. If R divides $PQ$ in the ratio $2 : 1$, then the locus of R is :

Locus of the image of the point $(2, 3)$ in the line $\left(2x - 3y + 4\right) + k\left(x - 2y + 3\right) = 0, k \in R,$ is a

The matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 1 \end{pmatrix} \), then adj \( (A) \) is equal to

The solution of \( \frac{d^2x}{dy^2} = k \), where \( k \) is a non-zero constant, vanishes when \( y = 0 \) and tends to finite limit as \( y \to \infty \), is

From a city population, the probability of selecting a male or smoker is \( \frac{7}{10} \), a male smoker is \( \frac{2}{5} \) and a male, if a smoker is already selected, is \( \frac{3}{5} \). Then, the probability of

Which of the following inequality is true for \( x>0 \)?

At \( t = 0 \), the function \( f(t) = \sin \frac{t}{t} \) has

If a plane passing through the point \( (2, 2, 1) \) and is perpendicular to the planes \( 3x + 2y + 4z = 10 \) and \( 2x + y + 3z = 2 \), then the equation of the plane is

Using Rolle’s theorem, the equation \( a_0x^n + a_1x^{n-1} + \dots + a_n = 0 \) has at least one root between 0 and 1 if,

If the mean and variance of a binomial distribution are 4 and 2, respectively. Then, the probability of at least 7 successes is

Let \( I = \int_{0}^{\frac{\pi}{2}} \log (\cos x) \, dx \)

The shortest distance between the lines \[ \frac{x - 7}{3} = \frac{y + 4}{-16} = \frac{z - 6}{7} \] and \[ \frac{x - 10}{3} = \frac{y - 30}{8} = \frac{z - 6}{5} \] is

The limit of \( \int \frac{1}{\cos x} dx \) as \( b \to 0 \) is

For any three vectors \( a, b, c \), \[ [a + b + c] = [a b c] = [a b c] \]

The equation of tangents to the hyperbola \( 3x^2 - 2y^2 = 6 \) which is perpendicular to the line \( x - 3y = 3 \) is

The area of the region bounded by the curves \( x^2 + y^2 = 9 \) and \( x + y = 3 \) is

If \( a = i - j + 2k \) and \( b = 2i - j + k \), then the angle \( \theta \) between \( a \) and \( b \) is given by

If \( a, b, c \) are three non-coplanar vectors, then \[ (a + b) \times (c + b) = (a - b) \times (c - b) = b \times c \]