JEE question bank, practice MCQ , Notes, Lectures

1 P � Block Elements

Which of the following species have undistorted octahedral structures?

a) SF₆
b) PF₆^-
c) SiF₆^2-
d) SeF₆

Select the correct answer using the codes given below

1) b, c and d

2) a. b and c

3) a, c and d

4) a, b and d

Option 1

Option 2

Option 3

Option 4 Solution:

Solution:

2 Electrostatic Potential

1000 drops of water of radius 1 cm each carrying a charge of 10 esu combine to form a single drop. The capacitance increases thereby

1) 1 time
2) 10 times
3) 100 times
4) 1000 times

Option 1

Option 2 Solution:

Solution:

$$n^{\frac{1}{3}}r =R$$

$$n^{\frac{1}{3}}C\,_{small\,drop}\,^{=C\,_{bigger \,drop }}$$

$$\left(10\right)^{3\times\frac{1}{3}}C\,_{small\,drop}\,^{=C\,_{bigger\,drop}}$$

Option 3

Option 4

3 Probability

On a busy road in a city the number of persons sitting in the cars passing by were observed during a particular interval of time. Data of $$60$$ such cars is given in the following table.

No. of persons in the car	$$1$$	$$2$$	$$3$$	$$4$$	$$5$$
No of Cars	$$22$$	$$16$$	$$12$$	$$6$$	$$4$$

Suppose another car passes by after this time interval. Find the probability that it has at least $$4$$ persons in it

1) $$\dfrac {1}{6}$$
2) $$\dfrac {1}{12}$$
3) $$\dfrac {1}{10}$$
4) None of these

Option 1 Solution:

Solution

$$P$$(at least $$4$$) $$=\dfrac{(4+5)}{Total}$$

$$=\dfrac{6+4}{60}=\dfrac{1}{6}$$

Option 2

Option 3

Option 4

4 Polymers

Nylon-66 is a

1) Natural polymer
2) Condensation polymer
3) Addition polymer
4) Substitution polymer

Option 1

Option 2 Solution:

SOLUTION

Nylon 6,6 or polyamide is a substance obtained from the repeated condensation reaction of Hexamythyline di amine and adipic acid which when undergoes polymerisation gives rives polyamide and water molecules

Nylon 6,6 is a condensation product of adipic acid and hexamethylenediamine

Nylon 6 is a condensation product of only one monomer caprolactum.

Nylon 6,6 is stronger and more resistant to heat as compared to Nylon 6.
Nylon 6,6 is used for making carpets, tyre ropes etc. due to its strength and toughness.
Nylon 6 on the other hand is used for making clothes, nets, threads etc.

Option 3

Option 4

5 Laws of Motion

A block of mass 1 kg slides down on a rough inclined plane of inclination 60^o starting from its top. If the coefficient of kinetic friction is 0.5 and length of the plane is 1 m, then work done against friction is (Take g = 9.8 m/s²)

1) 9.82 J

2) 4.94 J

3) 2.45J

4) 1.96 J

Option 1

Option 2

Option 3 Solution:

Solution :

W = mmgcosθ.S

=5 x 1 x 9.8 x 1/2= 2.45 J.

Option 4

6 Classification of Elements and Periodicity

The ions O²⁻, F⁻, Na⁺, Mg²⁺ and Al³⁺ are isoelecronic. Their ionic radii show:

1) a significant increase from O²⁻ to Al³⁺
2) a significant decrease from O²⁻ to Al³⁺
3) an increase from O²⁻ to F⁻ and then decrease from Na⁺ to Al³⁺
4) an decrease from O²⁻ to F⁻ and then increase from Na⁺ to Al³⁺

Option 1

Option 2 Solution:

SOLUTION

As all the given species are iso electronic, the ionic radii decreases with increasing atomic number as effective nuclear charge increases. Hence from O²⁻ to Al³⁺, the size decreases significantly

Option 3

Option 4

7 Thermal Properties Of Matter

Four rods with different radii r and length / are used to connect two heat reservoirs at different temperature. Which one will conduct most heat ?

1) $$r = 1 \, cm, l = 1 \, m $$
2) $$r = 1 \, cm , l = \frac{1}{2} m$$
3) $$r = 2 \, cm, l = 2 \, m $$
4) $$r = 2 \, cm , l = \frac{1}{2} m$$

Option 1

Option 2

Option 3

Option 4 Solution:

Solution:

$$H = \frac{KAd\theta}{L} \propto \frac{A}{L } = \frac{\pi r^{2}}{L} $$

$$ \left(\frac{A}{L}\right)_{1} = \frac{\pi\left(1\right)^{2}}{1} = 2\pi\,\, units \hspace10mm \left(\frac{A}{L}\right)_{2} = \frac{\pi\left(2\right)^{2}}{\frac{1}{2}} = 8\pi \,\, units.$$

$$ \left(\frac{A}{L}\right)_{3} = \frac{\pi\left(1\right)^{2}}{1} = \pi \,\, units \hspace10mm \left(\frac{A}{L}\right)_{_4 }= \frac{\pi\left(2\right)^{2}}{2} = 2\pi\,\, units$$

So rod (2) will conduct most heat per second.|

8 Matrices

If A=[a_ij] is a square matrix of even order such that [a_ij]=i²−j², then

1) A is a skew-symmetric matrix and |A| = 0
2) A is skew-symmetric matrix and |A| is a square
3) A is symmetric matrix and |A| = 0
4) none of these

Option 1

Option 2 Solution:

Solution

Given $$\displaystyle \left [ a_{ij} \right ]=i^{2}-j^{2}$$
$$\Rightarrow a_{ii}=0$$ for all i.

Also, for $$i \ne j, a_{ij}=i^{2}-j^{2}=-(j^{2}-i^{2})=-a_{ji}$$
$$\Rightarrow a_{ij}=-a_{ji}$$

Hence, A is skew-symmetric matrix.
For order 2, $$A=\begin{bmatrix} 0 & -3 \\ 3 & 0 \end{bmatrix}$$
$$|A|=9\ne 0$$

Hence, A is a skew-symmetric matrix and |A| is a square

Option 3

Option 4

9 Binomial Theorem

The coefficient of three consecutive of (1 + χ)ⁿ⁺⁵ are in the ratio 5 : 10 : 14. Then, n is equal to

1) 1
2) 3
3) 4
4) 6

Option 1

Option 2

Option 3

Option 4 Solution:

SOLUTION

10 Electromagnetic Induction

A solenoid of length 30 cm with 10 turns per�centimetre and area of cross-Section 40�cm² completely surrounds another�co-axial solenoid of same length, area of Cross-section 20�cm^2�with 40 turns per centimetre. The�mutual inductance of the

1) 10 H
2) 8 H
3) 3mH
4)�30 mH

�

Option 1

Option 2

Option 3 Solution:

Solution

Mutual inductance of the system,
M=μ0n1n₂A₂l
Where�A₂is�the area of inner solenoid.
n1=10cm⁻¹=1000m⁻¹
n2=40cm⁻¹=4000m⁻¹
l=30cm=30�10m⁻¹
A2=20cm²=20�10⁻⁴m²
∴M=4π�10⁻⁷�1000�4000�20�10⁻⁴�30�10⁻²
=301.44�10⁻⁵H=3mH

Option 4

JEE

EXAM PREP

Question Bank

Solution

Solution

Solution

MOCK TEST