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Class 12 Maths Mcqs

Q:

Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F) then value of P(S|F)
is __________

A) 0 B) -1
C) 1 D) 2
 
Answer & Explanation Answer: C) 1

Explanation: We know that P(S|F) = P(S?F) / P(F). (By formula for conditional probability)
Which is equivalent to P(F) / P(F) = 1, hence the value of P(S|F) = 1.

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488
Q:

Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F), then value of P(F|F)
is __________

A) 0 B) -1
C) 1 D) 2
 
Answer & Explanation Answer: C) 1

Explanation: We know that P(S|F) = P(S?F) / P(F). (By formula for conditional probability)
Which is equivalent to P(F|F) = P(F) / P(F) = 1, hence the value of P(F|F) = 1.

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Sub Category: Class 12 Maths Mcqs

370
Q:

Lagrange’s mean value theorem is also called as _____

A) Euclid’s theorem B) Rolle’s theorem
C) a special case of Rolle’s theorem D) the mean value theorem
 
Answer & Explanation Answer: D) the mean value theorem

Explanation: Lagrange’s mean value theorem is also called the mean value theorem and Rolle’s theorem is just a special case of Lagrange’s mean value theorem when f(a) = f(b).

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327
Q:

What is the relation between f(a) and f(h) according to another form of Rolle’s theorem?

A) f(a) < f(a+h) B) f(a) = f(a+h)
C) f(a) = f(a-h) D) f(a) > f(a+h)
 
Answer & Explanation Answer: B) f(a) = f(a+h)

Explanation: According to Rolle’s theorem, if f : [a,a+h] ? R is a function such that
i) f is continuous on [a,a+h]
ii) f is differentiable on (a,a+h)
iii) f(a) = f(a+h) then there exists at least one ? c ? (0,1) such that f’(a+?h) = 0

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228
Q:

Given that E and F are events such that P(E) = 0.5, P(F) = 0.4 and P(E?F) = 0.3, then what will be the value of P(F|E)?

A) 2/5 B) 3/5
C) 3/4 D) 2/4
 
Answer & Explanation Answer: B) 3/5

Explanation: We know that P(F|E) = P(E?F) / P(E). (By formula for conditional probability)
Value of P(E?F) is given to be 0.3 and value of P(E) is given to be 0.5.
P(F|E) = (0.3) / (0.5).
P(F|E) = 3 / 5.

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148
Q:

Let ‘*’ be a binary operation on N defined by a*b=a-b+ab², then find 4*5.

A) 9 B) 88
C) 98 D) 99
 
Answer & Explanation Answer: D) 99

Explanation: The binary operation is defined by a*b=a-b+ab².
?4*5=4-5+4(5²)=-1+100=99.

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142
Q:

What is the relation between f(a) and f(b) according to Rolle’s theorem?

A) Equals to B) Greater than
C) Less than D) Unequal
 
Answer & Explanation Answer: A) Equals to

Explanation: According to Rolle’s theorem, if f : [a,b] ? R is a function such that
i) f is continuous on [a,b]
ii) f is differentiable on (a,b)
iii) f(a) = f(b) then there exists at least one point c ? (a,b) such that f’(c) = 0

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Sub Category: Class 12 Maths Mcqs

134
Q:

Integrate ? log?x² dx

A) log?x² + x+C B) x log?x² – 2x+C
C) x log?x² – 1+C D) x log?x² + x+C
 
Answer & Explanation Answer: B) x log?x² – 2x+C

Explanation: Not available for this question

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