List of top Questions asked in VITEEE- 2011

In a group \( (G^*) \), the equation \( x * a = b \) has a:

If the roots of the equation \( x^2 + ax + b = 0 \) are \( c \) and \( d \), then one of the roots of the equation \[ x^2 + (2c + a)x + c^2 + ac + b = 0 \] is:

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

Find the value of \( (7.995)^{1/3} \) correct to four decimal places.

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 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:

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

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

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

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

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

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

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:

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

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

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

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

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

For the reaction \( 2A + B \rightleftharpoons C \), \( \Delta H = x \) cal, which one of the following conditions would favour the yield of C on the basis of Le-Chatelier's principle?

The EMF of the cell, \[ \text{Mg}^{2+}(0.01M) \parallel \text{Sn}^{2+}(0.1M) \parallel \text{Sn at 298K} \] is:

Heat of formation, \( \Delta H_f \), of an explosive compound like NC\( _3 \) is:

For the reaction, \[ C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(l) \] at constant temperature, \( \Delta H = \Delta E \) is: