List of top Mathematics Questions asked in VITEEE

If \( (-4, 5) \) is one vertex and \( 7x - y + 8 = 0 \) is one diagonal of a square, then the equation of second diagonal is:
Which of the following is an infinite set?
Let \[ \int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{3}{3} \, g(x) + C \] then
The domain of the function \[ \sqrt{2x - 5x^2 + 6} + \sqrt{2x + 8 - x^2} \] is:
If \( \mathbf{a} = 2i - 2j + k \) and \( \mathbf{c} = -i + 2k \), then \( \mathbf{a} \times \mathbf{c} \) is equal to:
\( P = Q \) can also be written as:
Radius of the circle \( (x + 5)^2 + (y - 3)^2 = 36 \) is:
The shortest distance between the lines \( x = y + 2 \), \( z = 6x - 6 \) and \( x + 1 = 2y = -12z \) is:
If \( f(x) = \frac{x}{1 + x^2} + \frac{x}{(1 + x^2)^2} + \cdots \) to infinity, then at \( x = 0, f(x) \)
If the tangent at \( P(1, 1) \) on \( y^2 = x(2 - x) \) meets the curve again at \( Q \), then \( Q \) is:
The value of \( c \) in Rolle’s Theorem for the function \( f(x) = e^x \sin x, x \in [0, \pi] \) is:
The equations \( 2x + 3y + 4 = 0 \), \( 3x + 4y + 6 = 0 \), and \( 4x + 5y + 8 = 0 \) are:
A die is thrown $10$ times, the probability that an odd number will come up at least one time is
Let \( f \) be the function defined by \[ f(x) = \begin{cases} x^2 - 1, & x \neq 1 \\ x^2 - 2|x-1|^{-1}, & x = 1 \end{cases} \] The function is continuous at:

The equation of the plane which bisects the angle between the planes \[ 3x - 6y + 2z + 5 = 0 \quad \text{and} \quad 4x - 12y + 32z - 3 = 0 \] \(\text{which contains the origin is:}\)

If \[ \left( \frac{a}{b} \right)^2 + \left( \frac{b}{a} \right)^2 = 676, \quad \left| \mathbf{b} \right| = 2, \quad \text{then} \left| \mathbf{a} \right| \(\text{ is equal to:}\)

If \[ \int \frac{\sin x}{\sin(x - \alpha)} dx = Ax + B \log \sin(x - \alpha) + C, \] \(\text{then the value of}\) \( (A, B) \) is:

If \( y = \tan^{-1} \left( \frac{4x}{1+5x^2} \right) + \tan^{-1} \left( \frac{2 + 3x}{3 - 2x} \right) \), then \( \frac{dy}{dx} = \):
The value of \( x \) in the interval \( [4, 9] \) at which the function \[ f(x) = \sqrt{x} \] \text{satisfies the mean value theorem is:}
The value of the integral \[ \int_1^3 |x| + |x - 1| \, dx \] \text{is:}
Let \( e^{1/c}, e^{b/c}, e^{1/a} \) are in A.P. with a common difference \( d \). Then \( e^{1/c}, e^{b/c}, e^{1/a} \) are in:
If the second term in the expansion \[ \left( \frac{3}{\sqrt{4a + \sqrt{a}}} \right)^n \] \text{is} \( 14a^{5/2} \), then \( nC_3 \) is:
It is given that the events \( A \) and \( B \) are such that \[ P(A) = \frac{1}{4}, \quad P(A|B) = \frac{1}{2}, \quad P(B|A) = \frac{2}{3}. \] \text{Then \( P(B) \) is:}
The solution of the differential equation \[ \left(1 + x \sqrt{x^2 + y^2}\right) dx + \left( \sqrt{x^2 + y^2} - 1 \right) y dy = 0 \]
The integrating factor of \[ \frac{dy}{dx} - y = x^4 - 3x \] \text{is:}