List of top Questions asked in KEAM

A ball is thrown up vertically at a speed of 6.0 m/s. The maximum height reached by the ball (Take \( g = 10 { m/s}^2 \)) is:
If the points \( (2, -3), (\lambda, -1) \) and \( (0, 4) \) are collinear, then the value of \( \lambda \) is equal to:
If \( B = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a \( 3 \times 3 \) matrix \( A \) and \( |A| = 4 \), then the value of \( \alpha \) is:

If 

then the value of \( x - y \) is:

The constant term in the expansion of \( \left( x^3 + \frac{1}{x^2} \right)^{10} \) is:
If \( _nP_r = 480 \) and \( _nC_r = 20 \), then the value of \( r \) is equal to:
The coefficient of \( x^3 \) in the binomial expansion of \( \left( \frac{1}{\sqrt{x}} - x \right)^6 \) is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
The numbers \( a, b, c, d \) are in G.P. with common ratio \( r \). If \( \frac{1}{a^3 + b^3} + \frac{1}{b^3 + c^3} + \frac{1}{c^3 + d^3} \) are also in G.P., then the common ratio is:
The second term of a G.P. is 4, then the product of the first three terms is:
If \( z_1 \) and \( z_2 \) are two complex numbers with \( |z_1| = 1 \), then \( \left| \frac{z_1 - z_2}{1 - z_1 \overline{z_2}} \right| \) is equal to:
If \( \left( \frac{1 - i}{1 + i} \right)^{10} = a + ib \), then the values of \( a \) and \( b \) are, respectively:
Let \( z \) be a complex number satisfying \( |z + 16| = 4|z + 1| \). Then:
Let \( X \) and \( Y \) be subsets of \( \mathbb{R} \). If \( f : X \rightarrow Y \) given by \( f(x) = -8(x + 5)^2 \) is one-to-one, then the codomain \( Y \) is:
If \( f(x) = \begin{cases} x^2 & \text{for } x < 0 \\ 5x - 3 & \text{for } 0 \leq x \leq 2 \\ x^2 + 1 & \text{for } x > 2 \end{cases} \), then the positive value of \( x \) for which \( f(x) = 2 \) is:
Let a relation \( R \) on the set of natural numbers be defined by \( (x, y) \in R \) if and only if \( x^2 - 4xy + 3y^2 = 0 \) for all \( x, y \in \mathbb{N} \). Then the relation is:
If A and B are two sets, such that A has 20 elements, \( A \cup B \) has 32 elements, and \( A \cap B \) has 10 elements, the number of elements in the set B is:
Lactose is composed of:
Which of the following is used as an insect attractant?
The reagent used for the conversion of but-2-ene to ethanol is:
The major products formed when one mole of \( \text{CH}_3\text{CH}_2\text{CH}(\text{CH}_3)\text{CH}_2\text{OCH}_2\text{CH}_3 \) is treated with one mole of HI are:
A tertiary alkyl halide (X), C\(_4\)H\(_9\)Br, reacted with alc.KOH to give compound (Y). Compound (Y) reacted with HBr in presence of peroxide to give compound (Z). The compounds (Y) and (Z) are respectively:
One mole of an alkene on ozonolysis gives a mixture of one mole pentan-3-one and one mole methanal. The alkene is:
The number of unpaired electrons in \([CoF_6]^{3-}\) is:

The decreasing order of stability of the following carbocations is: 
\( (i) \text{(CH}_3\text{)}_3\text{C}^+ \quad (ii) \text{(CH}_3\text{)}_2\text{C-CH}_2^+ \quad (iii) \text{CH}_3\text{CH}_2\text{-CH}_2^+ \)