List of practice Questions

Which of the following happens when NH\(_4\)OH is added gradually to the solution containing 1M A\(^{2+}\) and 1M B\(^{3+}\) ions? Given: K\(_{sp}\)[A(OH)\(_2\)] = 9 \(\times\) 10\(^\text{-10}\) and K\(_{sp}\)[B(OH)\(_3\)] = 27 \(\times\) 10\(^\text{-18}\) at 298 K.

Match the LIST-I with LIST-II: 

 


Choose the correct answer from the options given below :

An electron is made to enters symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the field region with a horizontal component of velocity \(10^6\) m/s. If the magnitude of the electric field between the plates is 9.1 V/cm, then the vertical component of velocity of electron is (mass of electron = \(9.1 \times 10^{-31}\) kg and charge of electron = \(1.6 \times 10^{-19}\) C):
2.8 \( \times 10^{-3} \) mol of \( \text{CO}_2 \) is left after removing \( 10^{21} \) molecules from its ‘\( x \)’ mg sample. The mass of \( \text{CO}_2 \) taken initially is: Given: \( N_A = 6.02 \times 10^{23} \, \text{mol}^{-1} \)
From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ‘M’, is :

Match the LIST-I with LIST-II 


 

Let \( a_1, a_2, a_3, \dots \) be a G.P. of increasing positive terms. If \( a_1 a_5 = 28 \) and \( a_2 + a_4 = 29 \), then the value of \( a_6 \) is equal to:
The d-electronic configuration of an octahedral Co(II) complex having a magnetic moment of 3.95 BM is:

The product of all solutions of the equation \(e^{5(\log_e x)^2 + 3 = x^8, x > 0}\) , is :

Let \( A = \{1, 2, 3, \dots, 10\} \) and \( B = \left\{ \frac{m}{n} : m, n \in A, m <n \text{ and } \gcd(m, n) = 1 \right\} \). Then \( n(B) \) is equal to :
What amount of bromine will be required to convert 2 g of phenol into 2, 4, 6-tribromophenol? (Given molar mass in g mol\(^{-1}\) of C, H, O, Br are 12, 1, 16, 80 respectively)
The correct set of ions (aqueous solution) with the same colour from the following is:

The correct stability order of the following species/molecules is:
 


 

Let A and B be the two points of intersection of the line \( y + 5 = 0 \) and the mirror image of the parabola \( y^2 = 4x \) with respect to the line \( x + y + 4 = 0 \). If \( d \) denotes the distance between A and B, and \( a \) denotes the area of \( \Delta SAB \), where \( S \) is the focus of the parabola \( y^2 = 4x \), then the value of \( (a + d) \) is:

Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \( f(x + y) = f(x) f(y) \) for all \( x, y \in \mathbb{R} \). If \( f'(0) = 4a \) and \( f \) satisfies \( f''(x) - 3a f'(x) - f(x) = 0 \), where \( a > 0 \), then the area of the region R = {(x, y) | 0 \(\leq\) y \(\leq\) f(ax), 0 \(\leq\) x \(\leq\) 2\  is :

Standard electrode potentials for a few half-cells are mentioned below: \[ \begin{array}{|c|c|} \hline \text{Half-cell} & \text{Standard Electrode Potential}
\hline \text{Cu}^{2+} / \text{Cu} & +0.34 \, \text{V}
\text{Zn}^{2+} / \text{Zn} & -0.76 \, \text{V}
\text{Ag}^+ / \text{Ag} & +0.80 \, \text{V}
\text{Mg}^{2+} / \text{Mg} & -2.37 \, \text{V}
\hline \end{array} \] Which one of the following cells gives the most negative value of \( \Delta G^\circ \)?

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance \( R_p = 1 \, \Omega \) as shown in the figure. An external resistance of \( R_e = 2 \, \Omega \) is connected via the sliding contact.
The current \( i \) is : 

 

Given below are two statements: Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In light of the above statements, choose the correct answer from the options given below.
Let \( f(x) \) be a real differentiable function such that \( f(0) = 1 \) and \( f(x + y) = f(x)f'(y) + f'(x)f(y) \) for all \( x, y \in \mathbb{R} \). Then \( \sum_{n=1}^{100} \log_e f(n) \) is equal to :
The complex that shows Facial - Meridional isomerism is:
Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of \(16((sec^{-1}x)^{2}+(cosec^{-1}x)^{2})\) is:

A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is:

 

Given below are two statements:
Statement I: Fructose does not contain an aldehydic group but still reduces Tollen’s reagent.
Statement II: In the presence of base, fructose undergoes rearrangement to give glucose.
In the light of the above statements, choose the correct answer from the options given below.
The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is _____.
Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of bigger body is 400 K. If the energy radiate from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding to be negligible):