List of top Mathematics Questions asked in VITEEE

If the line \( lx + my - n = 0 \) will be a normal to the hyperbola, then \( \frac{a^2}{l^2} + \frac{b^2}{m^2} = k \), where \( k \) is equal to?

If \( \cos \alpha + i \sin \alpha = b \), \( c = \cos \gamma + i \sin \gamma \) and \( b + c + a = 1 \), then \( \cos (\beta - \gamma) + \cos (\alpha - \beta) \) is equal to?

The greatest and the least value of \( z = x + iy \), where \( |z| = 1 \) and \( |x| \leq 3 \), are?

The minimum value of \( \frac{x}{\log x} \) is?

Two lines \( x - y + 1 = 1 \) and \( x - 3y - k = 2 \) intersect at a point, if \( k \) is equal to?

The equation of normal to the curve \( y = (1 + x) + \sin^{-1}(\sin x) \) at \( x = 0 \) is?

If \( x + y = 2 \cos \theta + 5 \sin \theta \), then \( x^2 + y^2 \) is equal to?

The triangle formed by the tangent to the curve \( y = x^2 + x + 1 \) at the point \( (1, 3) \) and the coordinate axes lies in the first quadrant. If its area is 2, then the value of \( b \) is?

The statement \( p \rightarrow q \) is equivalent to?

The value of from the Lagrange's mean value theorem for which \( f(x) = \sqrt{25 - x^2} \) in the interval \( [1,5] \) is?

The vertices of a triangle are \( A(0,4,1) \), \( B(2,-3,-1) \), and \( C(4,5,0) \), then the orthocenter of ABC is?

Let \( X \) denote the sum of the numbers obtained when two fair dice are rolled. The variance and standard deviation of \( X \) are?

A four digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd is?

If the integers \( m \) and \( n \) are chosen at random from 1 to 100, then the probability that a number of the form \( 7m + 7n \) is divisible by 5, equals to?

The length of longer diagonal of the parallelogram constructed on \( 5a + 2b \) and \( a - 3b \), if it is given that \( |a| = 2\sqrt{2} \), \( |b| = 3 \), and the angle between \( a \) and \( b \) is \( \frac{\pi}{4} \), is?

If \( r = a \times b \times c + \beta \cdot a + \gamma \cdot b + [a \, b \, c] = 2 \), then \( a + \beta + \gamma \) is equal to?

If \( a \), \( b \), and \( c \) are three non-coplanar vectors and \( p, q, r \) are reciprocal vectors, then \( (p + q + r) \) is equal to?

The solution of \( \frac{dy}{dx} = \frac{x^2 + y^2 + 1}{2xy} \), satisfying \( y(1) = 0 \), is given by?

If \( x \frac{dy}{dx} = x \cdot f(xy) \), then \( f(xy) \) is equal to?

The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is?

If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are reciprocal vectors, then $(la + mb + nc). (lp + mq + nr)$ is equal to

The triangle formed by the tangent to the curve $f (x) = x2 + bx - b$ at the point $(1,1)$ and the coordinate axes lies in the first quadrant. If its area is $2$, then the value of b is

If there is an error of $k\%$ in measuring the edge of a cube, then the percent error in estimating its volume is

Let $f ' (x),$ be differentiable $\forall \, x.$ If $f (1) = -2$ and $f '(x) \geq 2 \forall x \in [1, 6],$ then

If the points $(1, 2, 3)$ and $(2, -1, 0)$ lie on the opposite sides of the plane $2x + 3y - 2z = k,$ then