List of top Mathematics Questions asked in VITEEE

If \[ \sin x + \cos x = \frac{1}{5} \] then \( \tan 2x \) is: 

The minimum value of the function \[ y = x^4 - 2x^2 + 1 \] in the interval \( \left[\frac{1}{2}, 2 \right] \) is:
In $\triangle ABC$, the midpoints of the sides $AB$, $BC$, and $CA$ are respectively $(1, 0, 0)$, $(0, m, 0)$, and $(0, 0, n)$. Then, $$ \frac{AB^2 + BC^2 + CA^2}{1^2 + m^2 + n^2} \text{ is equal to:} $$ 
Evaluate: \[ \tan (\cos^{-1} \frac{4}{5}) + \tan^{-1} \frac{2}{3} \]
Negation of the Boolean expression \[ p \Leftrightarrow (q \Rightarrow p) \] is:
If \[ R = \{ (x, y) : x \text{ is exactly } 7\text{cm taller than } y \} \] then \( R \) is:

The area of the region bounded by the ellipse $$\frac{x^2}{16} + \frac{y^2}{9} = 1$$ is: 

If \[ \frac{a^n + b^n}{a^{n-1} + b^{n-1}} \] is the arithmetic mean (A.M.) between \( a \) and \( b \), then the value of \( n \) is:

If 

then \( {Adj} (A) \) is equal to:

The integral \[ \int x^n (1 + \log x) \, dx \] is equal to: 

The number of distinct real roots of the equation: \[ x^7 - 7x - 2 = 0 \] is:
The shortest distance between the lines \( x = y + 2 = 6z - 6 \) and \( x + 1 = 2y = -12z \) is:
What is the approximate percentage increase in the production of Monopoly from 1993 to 1995?
The mean and variance of a random variable \( X \) having binomial distribution are 4 and 2, respectively. Find \( P(X = 1) \).

The determinant of the matrix:

is:

The number of nonzero terms in the expansion of \[ (1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9 \] is:
Evaluate: \[ \cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}} \]
If the function \[ f(x) = \begin{cases} 1, & x \leq 2 \\ ax + b, & 2 < x < 4 \\ 7, & x \geq 4 \end{cases} \] is continuous at \( x = 2 \) and \( x = 4 \), then the values of \( a \) and \( b \) are:
The domain of the function \[ f(x) = \frac{1}{\sqrt{9 - x^2}} \] is:
The general solution of the differential equation given by: \[ \tan^{-1} x + \tan^{-1} y = c \]
If \( n(A) = 4 \) and \( n(B) = 7 \), then the difference between the maximum and minimum value of \( n(A \cup B) \) is:

Consider a curve \( y = y(x) \) in the first quadrant as shown in the figure. Let the area \( A_1 \) be twice the area \( A_2 \). The normal to the curve perpendicular to the line \[ 2x - 12y = 15 \] does NOT pass through which point? 
 

If \[ f(x) = \frac{x + |x|}{x} \] then the value of \[ \lim_{x \to 0} f(x) \] is:
The sum of the first n terms of the series $$ 1^2 + 2 \cdot 2^2 + 3^2 + 2 \cdot 4^2 + 5^2 + 2 \cdot 6^2 + \cdots $$ is $$ \frac{n(n + 1)^2}{2} \quad \text{when n is even. When n is odd the sum is} $$ 

The variance of the data \( 2, 4, 6, 8, 10 \) is: