List of practice Questions

In \(\triangle ABC\), if \(a + c = 5b\), then \(\cot\dfrac{A}{2} \cdot \cot\dfrac{C}{2} =\)
If \[ \binom{p}{q} = \binom{p}{q} \quad \text{and} \quad \sum_{i=0}^m \binom{10}{i} \binom{20}{m-i} \text{ is maximum, then find } m. \]
If $a = \ln \left( \frac{1}{z^2} \right)$ and $z$ is any non-zero complex number such that $|z| = 1$, then which of the following is the correct expression for $a$?
If \( ax^2 + bx + e>0 \) for all \( x \in \mathbb{R} \) and the expressions \( cx^2 + ax + b \) and \( ax^2 + bx + c \) have their extreme values at the same point \( x \), then for the expression \( cx^2 + ax + b \), find the correct statement regarding its extreme value.
If \( x^2 - 5x + 6 \) is a factor of \( f(x) = x^4 - 17x^3 + kx^2 - 247x + 210 \), find the other quadratic factor of \( f(x) \).
What are x and y in the following set of reactions?
Which of the following is not an example of an antacid?
When ethyl bromide and \textit{n}-propyl bromide are allowed to react with Na metal in dry ether, the number of different alkanes formed is:
Consider the following sequence of reactions:
isopropyl benzene
The incorrect statement about compound \( z \) is:
Which of the following complexes exhibit geometrical isomerism?
[label=\Roman*.]
The IUPAC name of the following compound is
7-Bromo-5-ethyl-2-methyldec-5-en-4-ol
Identify the correct statements from the following (only one):
I) Sulphur sol is an example of multimolecular colloid.
II) Starch sol is an example of associated colloid.
III) Artificial rubber is an example of macromolecular colloid.
Which of the following statements is incorrect with reference to alkaline earth metals?
Consider the following statements:
Statement-I: The order of electronegativity of B, Al, In, Tl is \(B>Tl>Al>In\)
Statement-II: Boric acid is a weak protic acid
Consider the following:
Assertion (A): CO is poisonous to living beings
Reason (R): CO binds to hemoglobin forming carboxyhaemoglobin, which is less stable than oxygen-hemoglobin complex.
Consider the following reaction sequence:
Vinylbenzene \(\xrightarrow{KMnO_4 + KOH, \Delta}\) X \(\xrightarrow{NaOH + CaO, \Delta}\) Y
'Y' can also be formed from
At 273 K the maximum work done when pressure on 10 g of hydrogen is reduced from 10 atm to 1 atm under isothermal, reversible conditions is
A Zener diode of breakdown voltage 20 V is connected as shown in the given circuit. The current through Zener diode is
A Zener diode of breakdown voltage 20 V
A capacitor of capacitance 2\(\mu\)F is charged to 50 V and then disconnected from the source. Later the gap between the plates of the capacitor is filled with a dielectric material. If the energy stored in the capacitor is decreased by 25% of its initial value, then the dielectric constant of the dielectric material is
A wire of resistance 100 \(\Omega\) is stretched so that its length increases by 20%. The stretched wire is then bent in the form of a rectangle whose length and breadth are in the ratio 3 : 2. The effective resistance between the ends of any diagonal of the rectangle is
The magnetic field at a distance of 10 cm from a long straight thin wire carrying a current of 4 A is
A closely wound solenoid of 1200 turns and area of cross-section 5 cm\(^2\) carries a current. If the magnetic moment of the solenoid is 1.2 J T\(^{-1}\), then the current through the solenoid is
If a refrigerator of coefficient of performance (COP) 5 has a freezer at a temperature of -13 °C, then the room temperature is
From the figure shown for a thermodynamic system, match the curves with their respective thermodynamic processes (P - Pressure and V - Volume)
thermodynamic system,
Curve | Process I | a) Adiabatic
II | b) Isobaric
III | c) Isochoric
IV | d) Isothermal
Two sound waves of wavelengths 99 cm and 100 cm produce 10 beats in a time of \( t \) seconds. If the speed of sound in air is 330 m/s, then the value of \( t \) in seconds is