physics -Basic Mathematics(basic-L1)

What is the approximate value of 'e'?

• e = 1.987

• e = 2.496

• e = 2.7183

• e = 3.336

Answer explanation

The approximate value of 'e' is 2.7183, so the correct choice is e = 2.7183.

Which of the following is correct expression ?

• log(ab) = loga + logb

• log(ab) = loga - logb

• log(ab) = loga.logb

• log(ab) = loga/logb

Answer explanation

The correct expression is log(ab) = loga + logb, which follows the logarithmic property of addition when multiplying two numbers.

Which of the following is the correct expression ?

• log(ab) = loga+logb

• log(ab) = loga.logb

• log(a/b) = loga-logb

• log(ab) = loga/logb

Answer explanation

The correct expression is log(ab) = loga-logb because when you multiply two numbers in logarithms, it becomes subtraction.

Which of the following is the correct value of ln(e)?

• π

• 1

• 0

• 2

Answer explanation

The correct value of ln(e) is 1 because the natural logarithm of e is always equal to 1.

Find the value of log6 ( if log3=0.4771 , log2=0.3010).

• 0.6020

• 0.3010

• 0.7781

• 0.4771

Answer explanation

To find log6, we use the change of base formula: log6 = log(6)/log(10). Given log3=0.4771 and log2=0.3010, we can calculate log6 as log6 = log(2*3)/log(10) = (log2 + log3)/log(10) = (0.3010 + 0.4771)/0.3010 = 0.7781.

What is the value of log300? (if log3 = 0.4771)

• 3.4771

• 2.4771

• 2.4770

• 0.4771

Answer explanation

The value of log300 can be calculated by using the property of logarithms: log(a*b) = log(a) + log(b). Therefore, log300 = log(3*100) = log3 + log100 = 0.4771 + 2 = 2.4771.

What is value of log10^-5?

• -5

• 0

• 1

• 10

Answer explanation

The value of log10^-5 is -5. In logarithms, a negative exponent results in the reciprocal of the base raised to the positive exponent. Therefore, log10^-5 = log(1/10^5) = -5.

Which of the following expression is correct?

• sin(A+B) = sin(A)cosB+cosAsinB

• sin0^o = 1

• cos0^o = 0

Answer explanation

The correct expression is sin(A+B) = sin(A)cosB+cosAsinB, as per trigonometric identities.

Which of the following is the correct option?

• sin2A = cosAsinA

• sin2A = sinAcosA

• sin2A = 2sinAcosA

• sin2A = 2sinA

Answer explanation

The correct option is sin2A = 2sinAcosA because the double angle identity for sine is sin2A = 2sinAcosA.

Which of the following is the correct option

• sinA = 2sin(A/2).cos(A/2)

• sinA =

  cos(A/2).sin(A/2)

Answer explanation

The correct option is sinA = 2sin(A/2).cos(A/2) as it matches the given correct answer choice.