List of practice Questions

The length of transverse and conjugate axes in a hyperbola are 6 and 8, respectively. The eccentricity of the hyperbola, rounded off to TWO decimal places, is .......

The vibrational frequency (expressed in wavenumber) of \( ^1H^{35}Cl \) is 2990.6 cm\(^{-1}\). Assuming that the force constant is the same in both cases, vibrational frequency (in cm\(^{-1}\)) of \( ^2D^{35}Cl \) is .............

The median of Y in the following data is .............
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline \text{Serial number} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Y & 22 & 12 & 10 & 14 & 16 & 20 \\ \hline \end{array} \]

In the following reaction, the values of \( \Delta H \) and \( \Delta S \) at temperature 25 °C are -13.7 kcal/mole and -16.0 cal/(K·mole), respectively.
The value of \( \Delta G \) (in kcal/mole) of the reaction, rounded off to TWO decimal places, is ...............

The solution to the integral \( \int_0^1 2y\sqrt{1 + y^2} \, dy \), rounded off to TWO decimal places, is ............

Which of the following is(are) CORRECT?

Which of the following gas(es) function(s) as signaling molecule(s) in the human nervous system?

Consider two bodies with equal masses of \( 10^{12} \) kg each and R distance apart. Let G be the gravitational constant and \( V_0 \) be a constant with dimensions of energy. Which of the following represent(s) gravitational potential energy (V) between the bodies, such that Newton's law of gravitation is valid?

Which of the following curve/straight line equations will pass through the origin when plotted on a graph?

Protozoa are

Which of the following is(are) CORRECT?

Which of the following is(are) involved in the activation of cytotoxic T cells?

Which of the following is(are) TRUE about photosynthesis?

IR spectrum of a compound \( C_5H_{10}O \) shows a band at 1715 cm\(^{-1}\). The same compound showed two signals, a triplet and a quartet, in its NMR spectrum. Identify the compound from the following.

In the following reaction, X is an intermediate and Y is one of the end products.

Which one of the following compounds is the end product Y?

Which one of the following compounds is the simplest alkane that is optically active?

The following carboxylic acids have a general formula, R-COOH.
(i) HCOOH
(ii) CH\(_3\) - COOH
(iii) ClCH\(_2\) - COOH
(iv) CF\(_3\) - COOH
Which one of the following represents the decreasing order of their respective pK\(_a\) values?

Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
Assertion [a]: The difference in the respective melting points of butter and coconut oil is caused by the degrees of saturation of the corresponding fatty acid chain.
Reason [r]: Unsaturated fatty acid chains in fats/lipids become solid more easily because they are relatively straight and thus able to pack together more closely than saturated chains.

Consider monoatomic ideal gas molecules of equal mass \( m \) in thermal equilibrium, at temperature \( T \). Which one of the following equations is correct? (the angular brackets denote average, \( k_B \) is Boltzmann constant, \( v \) is velocity, and \( v_x \) is the x-component of velocity)

Match the RNAs in Group I with their corresponding function in Group II
Group I Group II
(P) snRNA (1) rRNA processing
(Q) piRNA (2) RNA splicing
(R) snoRNA (3) Selected mRNAs degradation
(S) siRNA (4) Germ line protection from transposable elements

If a coin is tossed three times, what is the probability that NO two successive tosses show the same face?

Which one of the following ions has the maximum number of unpaired electrons?

Match the enzymes in Group I with the corresponding substrate in Group II
Group I Group II
(P) Amylase (1) Protein
(Q) Pepsin (2) Fat
(R) Lipase (3) RNA
(S) Ribozyme (4) Starch

For an ideal gas at room temperature, choose the CORRECT representation(s) of Boyle's Law.
(P = Pressure, V = Volume, T = Temperature)

The curve \( y = x^4 - 4x^3 + 4x^2 - 4 \) has tangents parallel to the x-axis at the following points \( (x, y) \)