List of practice Questions

Angle between the circles \( x^2 + y^2 - 4x - 6y - 3 = 0 \) and \( x^2 + y^2 + 8x - 4y + 11 = 0 \) is:
If the slope of one of the lines in the pair of lines \( 8x^2 + axy + y^2 = 0 \) is thrice the slope of the second line, then \( a = \) ?
If the vectors \( a\hat{i} + \hat{j} + 3\hat{k} \), \( 4\hat{i} + 5\hat{j} + \hat{k} \), and \( 4\hat{i} + 2\hat{j} + 6\hat{k} \) are coplanar, then \( a \) is:
In a triangle ABC, if \( (r_1 + r_2) \csc^2 \frac{C}{2} = \)
If \(\sinh x = \dfrac{\sqrt{21}}{2}\) then \(\cosh 2x + \sinh 2x = \)
The set of all real values \( a \) for which \[ -1<\frac{2x^2 + ax + 2}{x^2 + x + 1}<3 \] holds for all real values of \( x \) is:
A short magnet oscillates with a time period of 0.1 s at a place where the horizontal magnetic field is 24 \(\mu T\). A downward current of 18 A is established in a vertical wire kept at a distance of 20 cm east of the magnet. The new time period of oscillations of the magnet is:
A metallic wire loop of side \( 0.1 \) m and resistance of \( 10 \Omega \) is moved with a constant velocity in a uniform magnetic field of \( 2 \text{ Wm}^{-2} \) as shown in the figure. The magnetic field is perpendicular to the plane of the loop. The loop is connected to a network of resistors. The velocity of loop so as to have a steady current of \( 1 \) mA in loop is:
A metallic wire loop of side 0.1 m and resistance
The principal quantum number \( n \) corresponding to the excited state of \( He^+ \) ion, if on transition to the ground state two photons in succession with wavelengths \( 1026 \text{\AA} \) and \( 304 \text{\AA} \) are emitted: \((R = 1.097 \times 10^7 \text{ m}^{-1})\)
Which physical quantity is measured in barn?
Which one of the following is not classified as pulse modulation?
Two statements are given below:
Statement I: Nitrogen has more ionization enthalpy and electronegativity than beryllium.
Statement II:\( CrO_3 \), \( B_2O_3 \) are acidic oxides.
Correct answer is:
The ratio of ground state energy of \( \text{Li}^{2+}, \text{He}^{+}, \text{H} \) is:
At \( T(K) \) for one mole of an ideal gas, the graph of \( P \) (on y-axis) and \( V^{-1} \) (on x-axis) gave a straight line with slope of \( 32.8 \) L atm mol\(^{-1} \). What is the temperature (in K)? \((R = 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1})\)
Identify the correct statements from the following:
i. Reaction of hydrogen with fluorine occurs even in dark.
ii. Manufacture of ammonia by Haber process is an endothermic reaction.
iii. HF is an electron-rich hydride.
In which of the following reactions, hydrogen is one of the products?
Two statements are given below:
Statement I: SnF\(_4\), PbF\(_4\) are ionic in nature.
Statement II: GeCl\(_2\) is more stable than GeCl\(_4\).
The correct answer is:
Species A, B, C, D formed in the following bond cleavages respectively are
bond cleavages
Two statements are given below.
Statement I: The reaction Cr$_2$O$_3$ + 2Al → 2Cr + Al$_2$O$_3$ (ΔG° = -421 kJ) is thermodynamically feasible.
Statement II: The above reaction occurs at room temperature.
The correct answer is
Assertion (A): Carboxylic acids are more acidic than phenols.
Reason (R): Resonance structures of carboxylate ion are equivalent, while resonance structures of phenoxide ion are not equivalent.
In the reaction sequence, Y is: \[ CH_3CO_2H \xrightarrow{\text{(1) NH}_3, \text{(2)} \Delta} P \xrightarrow{\text{Br}_2/\text{NaOH}} Y \]
What is the major product 'Z' in the following sequence?
major product ’Z’ in the following sequence
Consider the following reactions. \[ \text{C}_2\text{H}_2 + \text{H}_2\text{O} \xrightarrow[\text{333 K}]{\text{Hg}^{2+}/\text{H}^+} [X] \xrightleftharpoons{\text{Isomerization}} Y \] Y cannot be obtained from which of the following reactions?
Polymers that can be softened on heating and hardened on cooling are called
The number of –OH groups in open chain and ring structures of D-glucose are respectively