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Q. 4 If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that

(i) (A \cup B)′ = A′ \cap B′

(ii) (A \cap B)′ = A′ \cup B′

Q. 5 Draw appropriate Venn diagram for each of the following :

(i) (A ∪ B)′

(ii) A′ ∩ B′

(iii) (A ∩ B)′

(iv) A′ ∪ B′

Q. 6 Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60\degree, what is A′?

Q.7 Fill in the blanks to make each of the following a true statement :

(i) A \cup A′ = \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot

(ii) \phi ' \capA = \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot

(iii) A \cap A′ =\cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot

(iv) U′ \cap A =\cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot

Q. 16 In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

Q. 15 In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:

(i) the number of people who read at least one of the newspapers.

(ii) the number of people who read exactly one newspaper.

Q. 14 In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

Q. 13 In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

Q. 12 Find sets A, B and C such that A \cap B, B \cap C and A \cap C are non-empty sets and A  \cap B \cap C = \phi

Q. 11 Let A and B be sets. If A \cap X =B \cap X = \phiand A \cup X = B \cup X for some set X, show that A =B.

AlF3 is soluble in HF only in the presence of KF. It is due to the formation of

Option: 1

K3[AlF3H3]


Option: 2

K3[AlF6]


Option: 3

AlH3


Option: 4

K[AlF3H]


Jahn-Teller effect is not observed in high spin complexes of:

Option: 1

d7


Option: 2

d8


Option: 3

d4


Option: 4

d9


  A student measures the time period of 100 oscillations of a simple pendulum four times.

 The data set is 90 s, 91 s, 95 s and 92 s.  If the minimum division in the measuring clock is 1 s,

  then the reported mean time should be :

Option: 1

 92 \pm 2 sec


Option: 2

92 \pm 5 sec


Option: 3

92 \pm 1.8 sec


Option: 4

92 \pm 3sec


A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases. The ratio of emf's is :

Option: 1

5 : 1


Option: 2

5 : 4


Option: 3

3 : 4


Option: 4

3 : 2


The diagrams below show regions of equipotentials.

A positive charge is moved from A to B in each diagram.

Option: 1

Maximum work is required to move q in figure (c).


Option: 2

In all the four cases the work done is the same.


Option: 3

Minimum work is required to move q in figure (a).


Option: 4

Maximum work is required to move q in figure (b).


In the given figure a = 15 \frac{m}{s^2}represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R = 2.5{\rm m} at a given instant of time. The speed of the particle is

Option: 1

4.5{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}


Option: 2

5.0{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}


Option: 3

5.7{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}


Option: 4

6.2{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}


Which one of the following is mineral of iron?

Option: 1

Malachite


Option: 2

Cassiterite


Option: 3

Pyrolusite


Option: 4

Magnetite


In a CE transistor amplifier, the audio signal voltage across the collector resistance of 2 k\Omega is 2 V. If the base resistance is 1 k\Omega and the current amplification of the transistor is 100, the input signal voltage is:

Option: 1

0.1 V


Option: 2

1.0 V


Option: 3

1 mV


Option: 4

10 mV


When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index:

Option: 1

equal to that of glass


Option: 2

less than one


Option: 3

greater than that of glass


Option: 4

less than that of glass


A ray of light is incident at an angle of incidence i, on one face of prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is \mu, the angle of incidence i is nearly equal to:

Option: 1

\mu A


Option: 2

\frac{\mu A}{2}


Option: 3

\frac{A}{\mu}


Option: 4

\frac{A}{2 \mu}


What is the figure given below showing in particular?

Option: 1

Ovarian cancer


Option: 2

Uterine cancer


Option: 3

Tubectomy


Option: 4

Vasectomy


Compared to those of humans, the erythrocytes in frog are

Option: 1

Without nucleus but with haemoglobin


Option: 2

nucleated and with haemoglobin


Option: 3

very much smaller and fewer


Option: 4

nucleated and without haemoglobin.


The anion of acetylacetone (acac) forms Co(acac)_{3} chelate with Co^{3+}. The rings of the chelate are

Option: 1

three membered


Option: 2

five membered


Option: 3

four membered


Option: 4

six membered


Treatment of cyclopentanone 

 

with methyl, lithium gives which of the following species?

Option: 1

Cyclopentanonyl radical


Option: 2

Cyclopentanonyl biradical


Option: 3

Cyclopentanonyl anion


Option: 4

Cyclopentanonyl cation


Reaction of phenol with chloroform in presence of dilute sodium hydroxide finally introduces which one of the following functional group ?

Option: 1

-CH2Cl


Option: 2

-COOH


Option: 3

-CHCl2


Option: 4

-CHO


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