List of top Questions asked in VITEEE- 2019

Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is:

The equation of the chord of the hyperbola \( 25x^2 - 16y^2 = 400 \) that is bisected at point \( (5, 3) \) is:

Value of \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1 + \sqrt{\cot x}} dx \]

A wire 34 cm long is to be bent in the form of a quadrilateral of which each angle is 90°. What is the maximum area which can be enclosed inside the quadrilateral?

If \( \sin y = x \sin(a + y) \), then \( \frac{dy}{dx} \) is equal to:

The conic represented by \[ x = 2(\cos t + \sin t), \quad y = 5(\cos t - \sin t) \] \text{is}

The area under the curve \( y = | \cos x - \sin x | \), where \( 0 \leq x \leq \frac{\pi}{2} \), and the x-axis is:

Evaluate \[ \int \left( 27e^{9x} + e^{12x} \right)^{1/3} dx \]

The solution of \( \sin x = \frac{-\sqrt{3}}{2} \) is:

The equation \( y^2 + 3 = 2(2x + y) \) represents a parabola with the vertex at:

If \( a \), \( b \), and \( c \) are in A.P., then the value of: \[ |x + 1| + |x + 2| + |x + 3| + |x + b| + |x + c| \]

The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder, in cm\(^3\)/min, when the radius is 2 cm and the height is 3 cm is:

Evaluate \( \lim_{x \to 2} \frac{\sqrt{x+7} - 3}{\sqrt{x-3} - 2} \):

At how many points between the interval \( (-\infty, \infty) \) is the function \( f(x) = \sin x \) is not differentiable?

If vector equation of the line \( \frac{x-2}{2} = \frac{2y-5}{-3} = z+1 \), is \[ \mathbf{r} = \left( 2\hat{i} + \frac{5}{2} \hat{j} - k \right) + \lambda \left( 2\hat{i} - \frac{3}{2} \hat{j} + p \hat{k} \right) \] then \( p \) is equal to:

If \[ A = \begin{bmatrix} 0 & c & -b \\ -c & 0 & a \\ b & -a & 0 \end{bmatrix}, \quad B = \begin{bmatrix} a^2 & ab & ac \\ ab & b^2 & bc \\ ac & bc & c^2 \end{bmatrix}, \] then \( AB \) is equal to:

If the lines \( 3x - 4y + 4 = 0 \) and \( 6x - 8y - 7 = 0 \) are tangents to a circle, then radius of the circle is:

A circle has radius 3 and its center lies on the line \( y = x - 1 \). The equation of the circle, if it passes through (7, 3), is:

If \( \omega = \frac{-1 + \sqrt{3}i}{2} \), then \( (3 + \omega + 3\omega^2) \) is:

The position vector of A and B are: \[ 2\hat{i} + 2\hat{j} + \hat{k} \quad \text{and} \quad 2\hat{i} + 4\hat{j} + 4\hat{k} \] The length of the internal bisector of \( \triangle AOB \) is:

The system of linear equations: \[ x + y + z = 0, \quad 2x + y - z = 0, \quad 3x + 2y = 0 \] \text{has:}

A coordination complex compound of cobalt has the molecular formula containing five ammonia molecules, one nitro group and two chlorine atoms for one cobalt atom. One mole of this compound produces three mole ions in an aqueous solution; on reacting with excess of \( \text{AgNO}_3 \), \( \text{AgCl} \) is precipitated. The ionic formula for this complex would be:

An endothermic reaction with high activation energy for the forward reaction is given by the diagram:

The volume of a closed reaction vessel in which the following equilibrium reaction occurs is halved: \[ 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) \] \text{As a result,}

If \( \tan \theta = \sqrt{n} \) for some non-square natural number \( n \), then sec \( 2\theta \) is: