List of top Questions asked in KEAM

The quadratic equation whose roots are three times the roots of the equation \( 2x^2 + 3x + 5 = 0 \), is

If \(x\) is real number, then \( \frac{x}{x^2 - 5x + 9} \) must lie between

If \( z = 1 + i \), then the argument of \( z^2 e^{z-i} \) is

If \( \mathrm{Re}(1+iy)^3 = -26 \), where \(y\) is a real number, then the value of \( |y| \) is

If \( z = x + iy \) is a complex number such that \( |z| = \mathrm{Re}(z) + 1 \), then the locus of \(z\) is

Let \( i^2 = -1 \). Then \( \left(i^{10} - \frac{1}{i^{11}}\right) + \left(i^{11} - \frac{1}{i^{12}}\right) + \left(i^{12} - \frac{1}{i^{13}}\right) + \left(i^{13} - \frac{1}{i^{14}}\right) + \left(i^{14} + \frac{1}{i^{15}}\right) \) is equal to

The set \( (A \setminus B) \cup (B \setminus A) \) is equal to

In a class of 80 students numbered 1 to 80, all odd numbered students opt for Cricket, students divisible by 5 opt for Football, and those divisible by 7 opt for Hockey. The number of students who do not opt any of the three games is

Match the following

Let \( X \) and \( Y \) be two non-empty sets such that \( X \cap A = Y \cap A = \emptyset \) and \( X \cup A = Y \cup A \) for some non-empty set \( A \). Then

Let the six numbers \( a_1, a_2, a_3, a_4, a_5, a_6 \) be in A.P., and \( a_1 + a_3 = 10 \). If the mean of these six numbers is \( \frac{19}{2} \) and their variance is \( \sigma^2 \), then \( 8\sigma^2 \) is equal to:

If \( f(1)=1 \), \( f(2n)=f(n) \) and \( f(2n+1)=(f(n))^2 - 2 \) for \( n=1,2,3,\ldots \), then the value of \( f(1)+f(2)+\cdots+f(25) \) is equal to

Which one of the following monomers form biodegradable polymer?

Which one of the following is an allylic halide?

Which one of the following undergoes iodoform test?

Which one of the following is used as a test for aliphatic primary amines?

When methanamine is treated with benzoyl chloride, the major product is

In DNA, the consecutive deoxynucleotides are connected by

Out of the following isomeric alcohols containing five carbon atoms, the alcohol that exhibits optical isomerism is

When methane is heated with dioxygen in the presence of Mo$_2$O$_3$ catalyst, the organic product obtained is

Isomers which can be interconverted through rotation about C–C single bond are

Among the following, the ambident nucleophile is

Which one of the following compounds shows cis-trans isomerism?

The chelating ligand used to remove excess of copper and iron in chelate therapy is

Glycerol can be separated from spent-lye in soap industry by