List of practice Questions

Evaluate the following expression: \[ \frac{1}{81^n} - \binom{2n}{1} . \frac{10}{81^n} + \binom{2n}{2} . \frac{10^2}{81^n} - .s + \frac{10^{2n}}{81^n} = ? \]

If \( x \) is a positive real number and the first negative term in the expansion of \[ (1 + x)^{27/5} \text{ is } t_k, \text{ then } k =\ ? \]

If \( \omega_1 \) and \( \omega_2 \) are two non-zero complex numbers and \( a, b \) are non-zero real numbers such that \[ |a\omega_1 + b\omega_2| = |a\omega_1 - b\omega_2|, \] then \( \dfrac{\omega_1}{\omega_2} \) is:

If \( \alpha, \beta \) are the roots of \( x^2 - 5x - 68 = 0 \) and \( \gamma, \delta \) are the roots of \( x^2 - 5\alpha x - 6\beta = 0 \), then \( \alpha + \beta + \gamma + \delta = \) ?

Benzyl amine can be prepared from which of the following reactions?

If \( f : \mathbb{R} \to A \), defined by \( f(x) = \cos x + \sqrt{3}\sin x - 1 \), is an onto function, then \( A = \)

Which of the following represents nucleoside of RNA?

Which one of the statements regarding X is not correct?
3-Hydroxybutanoic acid → 3-Hydroxypentanoic acid → X X is:

Identify the essential amino acids from the following:
A) Leucine
B) Tyrosine
C) Cysteine
D) Histidine

The following graph is obtained for a first-order reaction (A → P). The activation energy (E\(_a\) in kJ/mol\(^{-1}\)) and heat of reaction (ΔH in kJ/mol\(^{-1}\)) for this reaction are respectively

Identify the correct statements from the following:
A) Among alkali metal ions, Li⁺ has the highest hydration enthalpy.
B) Boiling point of alkali metals increases from Li to Cs.
C) Density of K is less than that of Na and Rb.
D) Li has strong tendency to form superoxide.

Identify the correct statements from the following:
I) CO reduces the oxygen carrying ability of blood.
II) Producer gas contains CO and N₂.
III) C-O bond length in CO₂ is 115 pm.

The mass of a mixture containing NaCl and NaBr is 4.0 g. If Na is 20% of the total mixture, the composition of NaCl in the mixture is

In a common emitter transistor amplifier the resistance of collector is 3 kΩ. If the current amplification factor is 100 and the base resistance is 2 kΩ, then the power gain of the transistor is

When current in a coil changes from 2 A to 5 A in a time of 0.3 s, if the emf induced in the coil is 40 mV, then the self-inductance of the coil is

The ratio of de Broglie wavelengths associated with thermal neutrons at temperatures 127°C and 352°C is

The ratio of the time periods of the revolution of the electrons in the second and third excited states of hydrogen atom is

A capacitor of capacitance 2 μF is charged with the help of a 60 V battery. After disconnecting the battery, if this capacitor is connected in parallel with another uncharged capacitor of capacitance 1 μF, then the potential difference across the plates of the 2 μF capacitor is

If a proton of kinetic energy 8.35 MeV enters a uniform magnetic field of 10 T at right angles to the direction of the field, then the force acting on the proton is

When an object is placed in front of a convex mirror at a distance 'u' from the pole of the mirror such that the size of the image is 'n' times that of the object, then the object distance 'u' is

A narrow slit of width 2 mm is illuminated with monochromatic light of wavelength 500 nm. If the distance between the slit and the screen is 1 m, then first minima are separated by a distance of

If the ratio of universal gas constant and specific heat capacity at constant volume of a gas is given by 0.67, then the gas is

The internal energy of 4 moles of a monoatomic gas at a temperature of 77°C is