List of top Mathematics Questions

The values of constants \( a \) and \( b \), so that \[ \lim_{x \to \infty} \left( \frac{x^2 + 1}{x + 1} - ax - b \right) = 0 \] are:

The sum of the coefficients of \( (6a - 5b)^n \), where \( n \) is a positive integer, is:

The projection of the vector \( \mathbf{i} - 2\mathbf{j} + \mathbf{k} \) on the vector \( 4\mathbf{i} - 4\mathbf{j} + 7\mathbf{k} \) is:

If \( a, b, c \) are three non-zero vectors such that \( a + b + c = 0 \) and \( m = a \cdot b + b \cdot c + c \cdot a \), then:

Evaluate \[ \int_{ \frac{\pi}{4} }^{ \frac{3\pi}{4} } \frac{1}{1 + \cos x} \, dx \]

If D is the set of all real x such that \( 1 - e^{(1/x)} \) is positive, then D is equal to:

Evaluate \[ \int \frac{x^2 + 4}{x^4 + 16} \, dx \]

Find the value of the limit \[ \lim_{x \to 0} \frac{\sqrt{1 - \cos x}}{x} \]

If one AM 'A' and two GM \( p \) and \( q \) are inserted between two given numbers, then find the value of \[ \frac{p^2}{q} + \frac{q^2}{p} \]

A line passes through \( (2, 2) \) and is perpendicular to the line \( 3x + y = 3 \). What is its y-intercept?

The number of common tangents to the circles \( x^2 + y^2 = 4 \) and \( x^2 + y^2 - 6x - 8y = 24 \) is:

If \( x^2 + 2x + 7<6 \), \( x \in \mathbb{R} \), then:

If \( R \) be a relation from \( A = \{1, 2, 3, 4\} \) to \( B = \{1, 3, 5\} \) such that \( (a, b) \in R \) if \( a<b \), then ROR is:

For a GP, \( a_n = 3(2^n) \), \( n \in \mathbb{N} \), Find the common ratio.

If \( x + y = (1 + i \sqrt{3})^{100} \), then find \( (x, y) \):

The number of ways of painting the faces of a cube of six different colours is:

If \( a, b, c \) are in HP, then \( \frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} \) will be in:

To the lines \( ax^2 + 2hxy + by^2 = 0 \), the line \( ax^2 + 2h(a+b)xy + b^2y^2 = 0 \) are:

Equation of the bisector of the acute angle between lines $3x + 4y + 5 = 0$ and $12x -5y - 7 = 0$ is

The value of $7 \log\left(\frac{16}{15} \right) +5 \log\left(\frac{25}{24}\right) + 3 \log\left(\frac{81}{80}\right) $ is equla to

$\displaystyle\lim_{x\to0} \frac{\sin x}{x}$ is equal to

A bag contains $3$ white and $5$ black balls. One ball is drawn at random. Then the probability that it is white is:

The length of the latus rectum of the parabola $169\left[(x-1)^{2}+(y-3)^{2}\right]=(5 x-12 y+ 17) ^{2}$ is:

If $2 i + j - k$ and $i -4 j +\lambda k$ are perpendicular to each other, then $\lambda$ is equal to:

If rth and (r + 1)th terms in the expansion of $(p + q)^n$ are equal, then $\frac {(n+1)q} {r(p+q)} $ is