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\(A = \{1, 2, 3\}\)

\(B = \{4,5,6\}\)

\(1) \,A\times B = \{(1, 4),(1,5),(1,6), (2,4),(2, 5), (2, 6),(3,4),(3, 5),(3,6)\}\) 

\(2) \,B\times A = \{(4, 1), (4, 2),(4, 3),(5, 1),(5, 2),(5,3),(6,1),(6, 2)(6,3)\}\).

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

f(x)=x²-4/x-2

NOW FOR THIS FUNCTION THE DOMAIN WOULD BE 

X-2>0=x>2 or Simple We can say {R}->2

Thanks regards 

(1) As given, 0.2 mole of CO₂ gas.

Mass = number of moles x molar mass

1 mole of CO₂ = 44 g

0.2 moles of CO₂ = 44 x 0.2 = 8.8g

(2) As given, 3.01  x 10²³ molecules of water.

1 mole of H₂O contains 6.023 x 10²³ molecules.

6.023 x 10²³ molecules of H₂O = 18g

3.01 x 10²³ molecules of H₂O = \(\frac{18\times3.01\times10^{23}}{6.0253\times10^{23}}\) = 8.99g.

(3) As given, 2.24 L SO₂

1 mole of gas ocupies 22.4 L volume at N.T.P.

22.4 L of SO₂. gas = 64g

2.24 L of SO₂. gas = \(\frac{64\times2.24}{22.4}\) = 6.4g

(4) As given, 20 g calcium

Mass of calcium = 20g

Thus, the highest mass is possesses by 20 g calcium and option(4) is correct.

The no. of terms in the answer is 49.

• First you should agree that;

no. of 4's = no. of the fractional parts

• The first fraction \(\frac{1}{2}\) can be written as( \(\frac{1}{1}-\frac{1}{2}\)) .
• The denominator of \(\frac{1}{1}\) ,i.e.,1 indicates that it is 1st fraction.
• Similarly, in the second fraction \(\frac{1}{6}\) can be written as (\(\frac{1}{2}-\frac{1}{3}\) ). 
• Here also, the denominator of \(\frac{1}{2}\) ,i.e., 2 indicates that it is 2nd term.
• Hence in( \(\frac{1}{49}-\frac{1}{50}\)) , the denominator of \(\frac{1}{49}\) ,i.e. , 49 indicates that it is 49th term
• And hence the total no. of fraction = 49 = no. of 4's.
• So total 49 times 4 are 49×4

5th shell is more closer.No doubt its energy may be more.

Answer is (c) Planning

When p-n junction is operated under a reverse bias condition a very small reverse current (about few μA) flows due to drifting of minority charge carriers, which is independent of the applied potential up to a critical voltage.

When the reverse voltage across the p-n junction reaches a critical voltage, the reverse current suddenly rises to a large value. It is due to sudden increase in the number of minority charge carriers, resulting from breakdown of the diode. 

If the p-n junction is lightly doped, the avalanche breakdown occurs due to ionisation by collision. 

If the p-n junction is heavily doped, the zener breakdown occurs at even low voltages due to field emission.

Work done in moving a charge q on path abcda is :

\(= q\vec E.(\vec{ab})+q\vec E.(\vec{bc})+q\vec E.(\vec{cd})+q\vec E.(\vec{da})\)

= qE(ab) cos90˚+ qE (bc) cos0˚ + qE(cd) cos90˚ + qE (da) cos180˚ 

= qE(bc) – qE(da) 

= 0 [since, bc = da].

Here, 

\(\vec E\) = 3 × 103 \(\hat i\) N/C

(i.e field is along + direction of x-axis). 

Surface are, 

s = (10cm)² = 10^-2m² 

When plane is parallel to yz plane, 

θ = 0° 

∴ ϕ_E (electric flux) = Es cosθ 

= 3× 10³ × 10⁻² × cos 0° 

= 30 Nm²/C.

With in the elastic limit stress directly proportional to the strain.

Stress ∝ strain; Stress = k × strain; k = Stress/strain

Where k is modulus of elasticity.

Yes, Rubber, type metal, cast iron are contract on heating.

The difference in the velocities of air results in the pressure difference between the lower and upper faces and there is a net upward force on the ball. This dynamic lift due to spinning is called magnus effect.