List of top Mathematics Questions asked in VITEEE

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

Let \( f(x) = 25x^{24}(1 - x)^{75} \), on the interval \( [0, 1] \), then \[ f'(x) = 25x^{24}(1 - x)^{75} - 75x^{25}(1 - x)^{74} = 25x^{24}(1 - x)^{74}[(1 - x) - 3x] \]

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

If \( |z| \geq 3 \), then the least value of \( |z + 4| \) is

If \( \text{line} \, y = mx + c \) is a normal to the ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \] then \( c^2 \) is equal to

The correct result of the equation \( 3x^2 + 2x + 7y^2 - 14y + 4 \) is

Correct result is as follows: \[ P \, (\neg \, Q) \, \equiv (P \, \vee \, Q) \, \implies (P \, \vee \, Q) \, \implies \, R \, \implies \, S \]

The structure \( (N_3) \) satisfies the closure property, associativity and commutativity but the identity element 0 does not belong to \( N \).

If \( l = x^2 + y^2 + z^2 \) is a normal to the ellipse \[ \frac{x^2}{16} + \frac{y^2}{9} = 1, \] then

The integral \( \int \frac{dx}{\cos x + \sqrt{5} \sin x} \) equals

If \( A, B, C \) are three events associated with a random experiment, then \( P(A \,|\, B) \) is

The differential equation \( (3x + 4y + 1) dx + (4x + 5y + 1) dy = 0 \) represents a family of

The probability of getting a double six in one throw of two dice

If the complex number \( z \) lies on a circle with center at the origin and radius \( \frac{1}{4} \), then the complex number \( 1 + z \) lies on a circle with radius

If \( A = \begin{pmatrix} 1 & 2
3 & 1 \end{pmatrix} \), then rank \( A \) is

If \( \Delta r = \left| \sum_{r=1}^{n} r \right| \), then \( \sum_{r=1}^{n} \Delta r \) is equal to

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

If $N$ is a set of natural numbers, then under binary operation $a ?b =a + b, (N, ?)$ is

On the interval $[0, 1]$, the function $x^{25}(1 - x)^{75}$ takes its maximum value at the point

The normal at the point $(at_1^2 ,\, 2at_1)$ on the parabola meets the parabola again in the point $(at_1^2 ,\, 2at_2)$ , then

The two lines $x = my + n, z = py + q$ and $x = m'y + n',\, z = p'y + q'$ are perpendicular to each other, if

If p, q, r are simple propositions with truth values T, F, T, then the truth value of $\left(\sim p \vee q\right) \wedge \sim r \Rightarrow p $ is

If $|z| \ge 3$, then the least value of $\left|z+\frac{1}{4}\right|$ is