List of top Questions asked in KEAM

The mass percentage of glucose in acetonitrile when 6 g of glucose is dissolved in 294 g of acetonitrile is:
The type of d-d transition of the electron occurs in \([Ti(H_2O)_6]^{3+}\) is:
The increasing order of field strength of ligands in the spectrochemical series is:
Which of the following is used in the treatment of lead poisoning?
The number of unpaired electrons in \([CoF_6]^{3-}\) is:
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:
The minimum value of \( f(x) = 7x^4 + 28x^3 + 31 \) is:
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:
A coordination compound of cobalt acts as an antipericious anemia factor is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
If two vectors \( \vec{a} = \cos \alpha \hat{i} + \sin \alpha \hat{j} + \sin \frac{\alpha}{2} \hat{k} \) and \( \vec{b} = \sin \alpha \hat{i} - \cos \alpha \hat{j} + \cos \frac{\alpha}{2} \hat{k} \) are perpendicular, then the values of \( \alpha \) are:
The second term of a G.P. is 4, then the product of the first three terms is:
If \( \left( \frac{1 - i}{1 + i} \right)^{10} = a + ib \), then the values of \( a \) and \( b \) are, respectively:
If \( 2z = 7 + i\sqrt{3} \), then the value of \( z^2 - 7z + 4 \) is:
An electric appliance draws 3A current from a 200 V, 50 Hz power supply. The amplitude of the supply voltage is nearly:
The value of \( \tan \left[ \tan^{-1} \left( \frac{3}{4} \right) + \tan^{-1} \left( \frac{2}{3} \right) \right] \) is:
The coefficient of \( x^3 \) in the binomial expansion of \( \left( \frac{1}{\sqrt{x}} - x \right)^6 \) is:
The common ratio of a G.P. is \( \frac{1}{2} \). If the product of the first three terms is 64, then the sum of the first 10 terms is:
If one end of a diameter of the circle \( x^2 + y^2 - 4x - 6y + 11 = 0 \) is \( (3, 4) \), then the coordinate of the other end of the diameter is:
If the acceleration due to gravity on the surface of a planet is 2.5 times that on Earth and radius, 10 times that of the Earth, then the ratio of the escape velocity on the surface of a planet to that on Earth is:
Which of the following statements is incorrect about Bohr's model of the atom?
The oscillating magnetic field in a plane electromagnetic wave is given by \(B_y = (8 \times 10^{-6}) \sin[2 \pi \times 10^{11} t + 200 \pi x] \) tesla. Then the wavelength of the electromagnetic wave (in cm) is:
The coefficient of linear expansion of aluminum is \( 2.5 \times 10^{-5} \, {K}^{-1} \). Its coefficient of volume expansion in \( {K}^{-1} \) is:
A tuning fork vibrating at 300 Hz, initially in air, is then placed in a trough of water. The ratio of the wavelength of the sound waves produced in air to that in water is (Given that the velocity of sound in water and in air at that place are 1500 m/s and 350 m/s respectively):
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: