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AP EAMCET Mock Test - 10 - JEE MCQ


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30 Questions MCQ Test AP EAMCET Mock Test Series - AP EAMCET Mock Test - 10

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AP EAMCET Mock Test - 10 - Question 1

A metallic sphere A of radius 'a' carries a charge Q. It is brought in contact with an uncharged sphere B of radius 'b'. The charge on sphere A now will be

Detailed Solution for AP EAMCET Mock Test - 10 - Question 1

Charge will flow from A to B until their potentials become equal. If charge q flows from A to B, then 
or, Q - q = a/b, which gives q = 
Hence, charge left on A = Q - q = Q - 
Hence, the correct choice is (d).

AP EAMCET Mock Test - 10 - Question 2

Three rods of same dimensions have thermal conductivities 3K, 2K and K, with their ends at 100°C, 50°C and 0°C respectively. They are arranged as shown in the diagram. The temperature of the junction J in steady-state is:

Detailed Solution for AP EAMCET Mock Test - 10 - Question 2

Let T = temperature of the junction J
L = length and A = area of each rod
Heat conducted in first rod = heat conducted by second rod + heat conducted by third rod

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AP EAMCET Mock Test - 10 - Question 3

The diagram shows five isosceles right angled prisms. A light ray incident at 90o at the first face emerges at same angle with the normal from the last face. which of the following relations will hold regarding the refractive indices?

Detailed Solution for AP EAMCET Mock Test - 10 - Question 3

AP EAMCET Mock Test - 10 - Question 4

Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is–

Detailed Solution for AP EAMCET Mock Test - 10 - Question 4

Ratio of masses is 1:5.
Ratio of acceleration is 5:1.
Ratio of distances covered is  5:1.
Distance to be covered  =(12R−R−2R)=9R
Distance moved by smaller sphere

AP EAMCET Mock Test - 10 - Question 5

A radioactive material decays by simultaneous emission of two particles with half-lives 1620 years and 810 years respectively. The time in years after which one-fourth of material remains, is

Detailed Solution for AP EAMCET Mock Test - 10 - Question 5

Since, from Rutherford - Soddy law, the number of atoms left after half-lives is given by

Where, N0 is the original number of atoms.
The number of half-lives, 

Relation between effective disintegration constant (λ) and half life (T)


Effective half life,

AP EAMCET Mock Test - 10 - Question 6

The potential energy of a 1 kg particle, free to move along the x-axis, is given by V(x) = J. The total mechanical energy of the particle is 2 J. Then, the maximum speed (in m/s) is

Detailed Solution for AP EAMCET Mock Test - 10 - Question 6

dv/dx = x3 - x = 0
⇒ x(x2 - 1) = 0
⇒ x = 0, ±1
 = (3x2 - 1) = Positive for x = ±1
i.e. V is minimum at x = ±1
⇒ Vmax = - J
⇒ Kmax = 2 -  =  J
 × 1 × v2 = 
⇒ v = 3/√2 m/sec

AP EAMCET Mock Test - 10 - Question 7

When one of the slits in Young's experiment is covered with a transparent sheet of thickness 3.6 x 10-3 cm, the central fringe shifts to a position originally occupied by the 30th bright fringe. If λ = 6000 Å, then the refractive index of the sheet is

Detailed Solution for AP EAMCET Mock Test - 10 - Question 7

AP EAMCET Mock Test - 10 - Question 8

If the velocity of a particle is  find the acceleration of the particle at t = 1 s.

Detailed Solution for AP EAMCET Mock Test - 10 - Question 8

Given,
velocity of the particle is 
time instance is 1 sec.
The acceleration of the particle is the rate of change of velocity with respect to time thus, acceleration is given by,

Acceleration of the particle remains constant at all times.

AP EAMCET Mock Test - 10 - Question 9

The species having pyramidal shape is :

Detailed Solution for AP EAMCET Mock Test - 10 - Question 9

The shape of a molecule depends upon the hybridisation and number of lone pair(s) on the central atom of the molecule. The hybridisation in a molecule can be determined by the total steric number around the central atom, which is equal to the sum of sigma bonds and lone pair(s) of electrons on the central atom. 
The number of sigma bonds and lone pairs can be determined from the Lewis structure of the molecule.
OSF2
The Lewis structure of the molecule can be represented as under :


Number of sigma bonds = 3
Number of lone pair = 1
Total steric number = 3 + 1 = 4
The hybridistion of a molecule with a steric effect of 4 is sp3. A hybridisation of sp3 is expected to have a tetrahedral geometry, but the presence of a lone pair on the sulphur atom comes into play (VSEPR theory). 
The geometry of a molecule with three sigma bond pairs and one lone pair, according to the VSEPR theory, can be represented as under:

Lone Pair − Bond Pair repulsion > Bond Pair − Bond Pair repulsion
Due to a greater repulsion between the lone pair and bond pair, the bond angle between the lone pair and each S−FS-F bond is more than the bond angles of the F−S−O and O−S−FF-S-O and O-S-F bonds. Thus, the molecule OSF2OSF2 has a trigonal pyramidal geometry.  

SO2
The Lewis structure of the molecule can be represented as under :

Number of sigma bonds = 2
Number of lone pair = 1
Total steric count = 2 + 1 = 3
A steric count of 3 has a hybridisation of sp2. So, the molecule is expected to have a trigonal planar shape, but due to the presence of a lone pair of electrons on the sulphur atom, the geometry changes to a bent structure as follows:

BrF3
The Lewis structure of the molecule can be represented as under :

Number of sigma bonds = 3

Number of lone pairs = 2
Due to the presence of three sigma bonds, and two lone pairs of electrons, BrF3BrF3 shows a trigonal bipyramidal geometry with a distorted T−T-shaped structure.

SiO2−3

The Lewis structure of the molecule can be represented as under :

Number of sigma bond pairs = 3

Numebr of lone pair = 0

Total steric number = 3 + 0 = 3

Hybridisation → sp2
Since there are no lone pairs on the silicon atom, the molecule shows a geometry of trigonal planar, as per its hybridisation. 

AP EAMCET Mock Test - 10 - Question 10

Acid hydrolysis of which of the following compounds yields two different organic compounds?

Detailed Solution for AP EAMCET Mock Test - 10 - Question 10

Acid hydrolysis of an ester gives two different organic compounds.

AP EAMCET Mock Test - 10 - Question 11

In the extraction of copper from its sulphide ore, the metal is formed by the reduction of Cu2O with

Detailed Solution for AP EAMCET Mock Test - 10 - Question 11

Cu from sulphide ore is obtained in a Bessemer's convertor as follows:


Copper pyrite ore CuFeS2 also contains FeS which is removed as follows:

Roasting converts FeS to FeO, which combines with silica flux to form slag.

AP EAMCET Mock Test - 10 - Question 12

If the enthalpy of oxidation of methanol to formaldehyde and water is -163 kJ, then what is the enthalpy of the formation of CH3OH? (Given: Enthalpy of formation of HCHO (l) is -116 kJ and enthalpy of formation of H2O (l) is -286 kJ.)

Detailed Solution for AP EAMCET Mock Test - 10 - Question 12

AP EAMCET Mock Test - 10 - Question 13

The following equilibria are given:
a. N2 + 3H2  2NH3; K1
b. N2 + O2  2NO; K2
c. H2 + O H2O; K3
The equilibrium constant for the reaction,
2NHO2  2NO + 3H2O in terms of K1, K2 and K3 will be

Detailed Solution for AP EAMCET Mock Test - 10 - Question 13

From the given equations, we have
K1 = 
K2 = 
K3 = 
For the given reaction,
K = 

K = 

AP EAMCET Mock Test - 10 - Question 14

Which of the following relations is correct?

Detailed Solution for AP EAMCET Mock Test - 10 - Question 14

The Gibbs free energy change at a constant temperature and pressure is given as:

where, ΔH is the change in the enthalpy of the process and ΔS is the change in the entropy of the process.

For the process to be spontaneous, ΔG must be negative.

AP EAMCET Mock Test - 10 - Question 15

Calculate the value of ΔG for the reaction given below at 800°C:

Using the following data given (at same temperature),

Detailed Solution for AP EAMCET Mock Test - 10 - Question 15

For the reaction

ΔGo for the reaction
2ZnS + 3O2 → 2ZnO + 2SO2
Can be obtained by adding eqn. (1), (2) and (3)
⇒ ΔGo = 293 − 480 − 544 = −731 kJ

AP EAMCET Mock Test - 10 - Question 16

Detailed Solution for AP EAMCET Mock Test - 10 - Question 16

AP EAMCET Mock Test - 10 - Question 17

If m1, m2 are slopes of the two tangents that are drawn from (2, 3) to the parabola y2 = 4x, then the value of [(1/m1) + (1/m2)] is

AP EAMCET Mock Test - 10 - Question 18

Suppose ω is an imaginary cube root of unity. If (1+ω2)m = (1+ω4)m, then the least positive integral value of m is

Detailed Solution for AP EAMCET Mock Test - 10 - Question 18

The given equation reduces to (−ω)m    = (−ω2)m 

⇒ ωm  = 1 

⇒ m = 3

AP EAMCET Mock Test - 10 - Question 19

 

is equal to

AP EAMCET Mock Test - 10 - Question 20

If b,c and sinB are given such that ∠B is acute and b<c sinB, then

Detailed Solution for AP EAMCET Mock Test - 10 - Question 20

When two sides and angle opposite to one of then be given. In this case, the triangle is not always uniquely determined. It is quite possible to have no triangle, one triangle and two triangles with this type of data.
So, it is called an ambiguous case.
Let b, c and B are given parts.
When B is acute and b < c sin B, then there is no triangle
By Cosine Law
b2 = c2 + a2 - 2ac cos B
⇒ a2 - 2ac cos B = b2 - c2
⇒ a2 - 2ac cos B + c2 cos2 B
= b2 - c2 + c2 cos2 B
⇒ (a - c cos B)2 = b2 - c2 (1 - cos2 B)
= b2 - c2 sin2 B


This equation helps us to determine a, when b, c and B are being given. We observe that:
When b < c sin B, then a is imaginary and so there is no solution.

AP EAMCET Mock Test - 10 - Question 21

Which is logically equivalent to "If today is Sunday, Matt cannot play hockey."?

Detailed Solution for AP EAMCET Mock Test - 10 - Question 21

Statements are logically equivalent to their contrapositives.

AP EAMCET Mock Test - 10 - Question 22

The derivative of an odd function is an

AP EAMCET Mock Test - 10 - Question 23

If the pair of lines ax2+ 2hxy + by2 + 2gx + 2fy + c = 0 intersect on the y-axis then

AP EAMCET Mock Test - 10 - Question 24

If A and B are two matrices such that AB = B and BA = A, then A2+ B2 =

AP EAMCET Mock Test - 10 - Question 25

Which of the following is the converse of the statement: "If x > 4, then x + 2 > 5"?

Detailed Solution for AP EAMCET Mock Test - 10 - Question 25

To form the CONVERSE of a statement, the "If" and the "then" sections of the statement switch places.

AP EAMCET Mock Test - 10 - Question 26

The locus of x2+y2+z=0 is

AP EAMCET Mock Test - 10 - Question 27

In equation 2|x+1|-2x=|2x-1|+1 the values of x are

AP EAMCET Mock Test - 10 - Question 28

If |a|=3, |b|=4, |c|=5 and a+b+c=0, the angle between a and b is

AP EAMCET Mock Test - 10 - Question 29

If |z| = 4 and arg z = (5π/6), then the value of z is

AP EAMCET Mock Test - 10 - Question 30

Which of the following statement is false?

Detailed Solution for AP EAMCET Mock Test - 10 - Question 30

The determinant of skew-symmetric matrix of odd order is always zero
Therefore the inverse of skew-symmetric matrix does not exist

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