List of top Mathematics Questions

The distance between the parallel lines $5x + 12y - 3 = 0$ and $5x + 12y + 10 = 0$ is:

If the straight lines $x + 2y - 9 = 0$, $3x + 5y - 5 = 0$ and $ax + by - 1 = 0$ are concurrent, then the straight line $22x - 35y = 1$ passes through the point:

If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ passes through the origin, has radius 3, and its center lies on the line $x + y = 4$, then $g + f =$

If the angle between the pair of lines $x^2 - 2cxy - 7y^2 = 0$ is $\frac{\pi}{3}$, then the value of $c^2$ is:

In a binomial distribution, the mean is 4 and the variance is 3. Then the number of trials $n$ is:

A random variable $X$ has the following probability distribution:
$X = x$: 0, 1, 2, 3, 4, 5
$P(X=x)$: $k$, $3k$, $5k$, $7k$, $9k$, $11k$
Then the value of $k$ is:

When the origin is shifted to $(2, 3)$ by translation of axes, the coordinates of a point $P$ become $(1, -2)$. The original coordinates of $P$ are:

If $A$ and $B$ are two events such that $P(A) = 0.4$, $P(B) = 0.8$ and $P(B|A) = 0.6$, then $P(\bar{A} \cap B) =$

A bag contains 5 red and 4 black balls. Three balls are drawn at random from the bag. The probability that two of them are red and one is black is:

If the mean deviation of the numbers $1, 1+d, 1+2d, \dots, 1+100d$ from their mean is 255, then $d =$

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all three apply for the same house is:

If $\vec{a} = \vec{i} + \vec{j} + \vec{k}$, $\vec{b} = 4\vec{i} + 3\vec{j} + 4\vec{k}$ and $\vec{c} = \vec{i} + \alpha\vec{j} + \beta\vec{k}$ are linearly dependent vectors and $|\vec{c}| = \sqrt{3}$, then:

The variance of the first $n$ even natural numbers is:

In a triangle $ABC$, if $a = 13$, $b = 14$, $c = 15$, then the area of the triangle is:

If $\sinh x = \frac{3}{4}$, then $\cosh 2x =$

Let $\vec{a}$ and $\vec{b}$ be two unit vectors. If the angle between them is $\theta$, then $\cos(\theta/2) =$

If $\vec{a} = 2\vec{i} + 3\vec{j} - \vec{k}$, $\vec{b} = -\vec{i} + 2\vec{j} - 4\vec{k}$ and $\vec{c} = \vec{i} + \vec{j} + \vec{k}$, then $(\vec{a} \times \vec{b}) \cdot (\vec{a} \times \vec{c}) =$

The maximum value of $3 \sin x + 4 \cos x + 5$ is:

If $\tan^{-1}(x) + \tan^{-1}(y) + \tan^{-1}(z) = \frac{\pi}{2}$, then $xy + yz + zx =$

The number of terms in the expansion of $(x + y + z)^{10}$ is:

If $\frac{3x + 4}{(x-1)(x-2)^2} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{(x-2)^2}$, then $A + B + C =$

If $\sin \theta + \cos \theta = \sqrt{2} \cos \theta$, then $\cos \theta - \sin \theta =$

If $\alpha, \beta$ are the roots of the quadratic equation $x^2 - 2x + 4 = 0$, then the value of $\alpha^n + \beta^n$ is:

If the roots of the equation $x^3 - 7x^2 + 14x - 8 = 0$ are in geometric progression, then the common ratio can be:

If the number of permutations of $n$ different things taken all at a time is $5040$, then $n =$