List of top Questions asked in VITEEE- 2015

The matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 1 \end{pmatrix} \), then adj \( (A) \) is equal to

If a plane passing through the point \( (2, 2, 1) \) and is perpendicular to the planes \( 3x + 2y + 4z = 10 \) and \( 2x + y + 3z = 2 \), then the equation of the plane is

From a city population, the probability of selecting a male or smoker is \( \frac{7}{10} \), a male smoker is \( \frac{2}{5} \) and a male, if a smoker is already selected, is \( \frac{3}{5} \). Then, the probability of

At \( t = 0 \), the function \( f(t) = \sin \frac{t}{t} \) has

Using Rolle’s theorem, the equation \( a_0x^n + a_1x^{n-1} + \dots + a_n = 0 \) has at least one root between 0 and 1 if,

Which of the following inequality is true for \( x>0 \)?

The solution of \( \frac{d^2x}{dy^2} = k \), where \( k \) is a non-zero constant, vanishes when \( y = 0 \) and tends to finite limit as \( y \to \infty \), is

The equation of tangents to the hyperbola \( 3x^2 - 2y^2 = 6 \) which is perpendicular to the line \( x - 3y = 3 \) is

The limit of \( \int \frac{1}{\cos x} dx \) as \( b \to 0 \) is

The area of the region bounded by the curves \( x^2 + y^2 = 9 \) and \( x + y = 3 \) is

For any three vectors \( a, b, c \), \[ [a + b + c] = [a b c] = [a b c] \]

Let \( I = \int_{0}^{\frac{\pi}{2}} \log (\cos x) \, dx \)

If the mean and variance of a binomial distribution are 4 and 2, respectively. Then, the probability of at least 7 successes is

The shortest distance between the lines \[ \frac{x - 7}{3} = \frac{y + 4}{-16} = \frac{z - 6}{7} \] and \[ \frac{x - 10}{3} = \frac{y - 30}{8} = \frac{z - 6}{5} \] is

The normal at the point \( (a t^2, 2 a t) \) on the parabola meets the parabola again at the point \( (a t^2, 2 a t) \). The equation of the normal is

If \( a = i - j + 2k \) and \( b = 2i - j + k \), then the angle \( \theta \) between \( a \) and \( b \) is given by

The area bounded by the curves \( y = \cos x \) and \( y = \sin x \) between the ordinates \( x = 0 \) and \( x = \frac{\pi}{2} \) is

If \( a, b, c \) are three non-coplanar vectors, then \[ (a + b) \times (c + b) = (a - b) \times (c - b) = b \times c \]

If there is an error of \( m% \) in measuring the edge of a cube, then the percent error in estimating its surface area is

The given equation of rectangular hyperbola is \[ x^2 - y^2 = 6^2 \quad \text{(length of latus rectum is 16)} \] The asymptotes are parallel to each other

If \( (2, 7, 3) \) is one end of a diameter of the sphere \( x^2 + y^2 + z^2 - 6x - 12y - 2z + 20 = 0 \), then the coordinates of the other end of the diameter are

Given lines are \[ x = my + n, \, z = py + q \] and \[ x = m'y + n', \, z = p'y + q' \] Above equations can be rewritten as \[ x - n' = p', \quad m = 1, \, p = 1 \] Lines will be perpendicular if

A tetrahedron has vertices at \( O(0, 0, 0) \), \( A(1, -2, 1) \), \( B(2, 1, 1) \), and \( C(1, -1, 2) \). Then, the angle between the faces \( OAB \) and \( ABC \) is

If a line segment OP makes angles of \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \) with the X-axis and Y-axis, respectively, then the direction cosines are

If \( p, q \) are simple propositions with truth values \( T, F \), then the truth value of \( (\neg p \vee q) \wedge \neg r \) is