List of practice Questions

If the set of all \( a \in \mathbb{R} \), for which the equation \( 2x^2 + (a - 5)x + 15 = 3a \) has no real root, is the interval \( (\alpha, \beta) \), and \( X = \{ x \in \mathbb{Z} : \alpha<x<\beta \} \), then \( \sum_{x \in X} x^2 \) is equal to:

The molar mass of the water insoluble product formed from the fusion of chromite ore \(FeCr_2\text{O}_4\) with \(Na_2\text{CO}_3\) in presence of \(O_2\) is ....... g mol\(^{-1}\):

0.1 mole of compound S will weigh ...... g, (given the molar mass in g mol\(^{-1}\) C = 12, H = 1, O = 16)

The sum of sigma (σ) and pi (π) bonds in Hex-1,3-dien-5-yne is:

If \(A_2B \;\text{is} \;30\%\) ionised in an aqueous solution, then the value of van’t Hoff factor \( i \) is:

Given below are some nitrogen containing compounds:
Each of them is treated with HCl separately. 1.0 g of the most basic compound will consume ...... mg of HCl.
(Given Molar mass in g mol\(^{-1}\): C = 12, H = 1, O = 16, Cl = 35.5.)

Choose the correct statements:
(A) Weight of a substance is the amount of matter present in it.
(B) Mass is the force exerted by gravity on an object.
(C) Volume is the amount of space occupied by a substance.
(D) Temperatures below 0°C are possible in Celsius scale, but in Kelvin scale negative temperature is not possible.
(E) Precision refers to the closeness of various measurements for the same quantity. Choose the correct answer from the options given below:

The correct option with order of melting points of the pairs (Mn, Fe), (Tc, Ru) and (Re, Os) is:

The reaction \( \text{A}_2 + \text{B}_2 \to 2\text{AB} \) follows the mechanism: \[ \text{A}_2 \xrightarrow{k_1} \text{A} + \text{A} \, (\text{fast}), \quad \text{A} + \text{B}_2 \xrightarrow{k_2} \text{AB} + \text{B} \, (\text{slow}), \quad \text{A} + \text{B} \to \text{AB} \, (\text{fast}). \] The overall order of the reaction is:

1.24 g of \(AX_2\) (molar mass 124 g mol\(^{-1}\)) is dissolved in 1 kg of water to form a solution with boiling point of 100.105°C, while 2.54 g of AY_2 (molar mass 250 g mol\(^{-1}\)) in 2 kg of water constitutes a solution with a boiling point of 100.026°C. \(Kb(H)_2\)\(\text(O)\) = 0.52 K kg mol\(^{-1}\). Which of the following is correct?

Match List - I with List - II:

Choose the correct answer from the given below options

Match List - I with List - II:

List - I:
(A) Amylase
(B) Cellulose
(C) Glycogen
(D) Amylopectin

List - II:
(I) β-C1-C4 plant
(II) α-C1-C4 animal
(III) α-C1-C4 α-C1-C6 plant
(IV) α-C1-C4 plant

If \(a_0\) is denoted as the Bohr radius of the hydrogen atom, then what is the de-Broglie wavelength \( \lambda \) of the electron present in the second orbit of the hydrogen atom?

At temperature T, compound AB2 dissociates as \( AB_2 \rightleftharpoons A + \frac{1}{2} B_2 \), having degree of dissociation \( x \) (small compared to unity). The correct expression for \( x \) in terms of \( K_p \) and \( p \) is:

Match List - I with List - II:

List - I:

(A) \([ \text{MnBr}_4]^{2-}\)
(B) \([ \text{FeF}_6]^{3-}\)
(C) \([ \text{Co(C}_2\text{O}_4)_3]^{3-}\)
(D) \([ \text{Ni(CO)}_4]\)

List - II:

(I) d²sp³ diamagnetic
(II) sp²d² paramagnetic
(III) sp³ diamagnetic
(IV) sp³ paramagnetic

The product (P) formed in the following reaction is:

Given below are two statements:
Statement (I): The radius of isoelectronic species increases in the order: \[ \text{Mg}^{2+} < \text{Na}^{+} < \text{F}^{-} < \text{O}^{2-} \] Statement (II): The magnitude of electron gain enthalpy of halogens decreases in the order: \[ \text{Cl} > \text{F} > \text{Br} > \text{I} \] In light of the above statements, choose the most appropriate answer from the options given below:

The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which of the following is expected to be observed?

Total number of nucleophiles from the following is: \(\text{NH}_3, PhSH, (H_3C_2S)_2, H_2C = CH_2, OH−, H_3O+, (CH_3)_2CO, NCH_3\)

In the following substitution reaction:

The correct increasing order of stability of the complexes based on \( \Delta \) value is:

In a hydraulic lift, the surface area of the input piston is 6 cm² and that of the output piston is 1500 cm². If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is kJ.

The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank is cm. (Take g = 10 m/s²).

Two light beams fall on a transparent material block at point 1 and 2 with angle \( \theta_1 \) and \( \theta_2 \), respectively, as shown in the figure. After refraction, the beams intersect at point 3 which is exactly on the interface at the other end of the block. Given: the distance between 1 and 2, \( d = 4/3 \) cm and \( \theta_1 = \theta_2 = \cos^{-1} \frac{n_2}{2n_1} \), where \( n_2 \) is the refractive index of the block and \( n_1 \) is the refractive index of the outside medium, then the thickness of the block is cm.

Two light beams fall on a transparent material block

The coordinates of a particle with respect to origin in a given reference frame is \( (1, 1, 1) \) meters. If a force of \( \mathbf{F} = \hat{i} - \hat{j} + \hat{k} \) acts on the particle, then the magnitude of torque (with respect to origin) in the z-direction is: