Tag Archives: Mathematics

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Functions & Limits

QUESTION:

If f(x,y) = 3x + 2y and g(x,y) = x2 – y2 for all real numbers of x and y, then f(g(1,2)3) = ?

OPTIONS:

  • -8
  • -3
  • 9
  • 6

CORRECT ANSWER:

-3

EXPLANATION:

F(g(1,2)3) = 3(1-4) + 2(3) = -3

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TRIGONOMETRY

QUESTION:

In a triangle ABC, A = 45o, then the value of (1 + cot B)(1 + cot C) is equal to?

OPTIONS:

  • 0
  • 1
  • -1
  • 2

CORRECT OPTION:

2

EXPLANATION:

Easiest way to solve such questions is to assume angles of triangle.

A = 45o

A + B + C = 180o

B + C = 180 – 45o = 135o

Let’s take, B = 90o & C = 45o

= (1 + cot 90o) (1 + cot 45o)

= (1 + 0) (1 + 1)

= 1 x 2 = 2

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INDUCTION & BINOMIAL THEOREM

QUESTION:

Which member of the binomial expansion of (2x3 + x-1)10 contains x6?

OPTIONS:

  • 6th
  • 7th
  • 8th
  • 9th

CORRECT ANSWER:

7th

EXPLANATION:

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PROBABILITY & PERMUTATIONS

QUESTION:

If five digit numbers are formed from 1, 2, 3, 4, 8. What is the probability of forming a number with 2 and 8 not next to each other?

OPTIONS:

  • 2/5
  • 2/7
  • 5/7
  • 3/5

CORRECT OPTION:

3/5

EXPLANATION:

So probability of 2 and 8 not next to each other is = 72/120 = 3/5

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SEQUENCES & SERIES

QUESTION:

If mth term of an A.P is n and nth term is m, then the (m + n)th term is?

OPTIONS:

  • 0
  • 1
  • -1
  • 2

CORRECT ANSWER:

0

EXPLANATION:

a + (m – 1)d = n and a + (n – 1)d = m;

Subtracting we get (m – n) d = (n – m) or d = -1;

Subtracting the value we get a + (m – 1) – 1 = n or a = n + m – 1;

Tm + n = a + (m + n – 1) d = m + n – 1 + (m + n – 1) (-1) = 0

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QUADRATIC EQUATIONS

QUESTION:

For what value of  m the given equation would have equal root?

(m + 1)X2 + 2(m + 3)X + m + 8 = 0

OPTIONS:

  • 1/2
  • 1/3
  • -1/3
  • 2/3

CORRECT OPTION:

1/3

EXPLANATION:

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MATRICES & DETERMINANTS

QUESTION:

OPTIONS:

  • 0
  • 1
  • 100
  • -100

CORRECT OPTION:

0

EXPLANATION:

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Sets & Functions

QUESTION:

The set of fourth roots of unity are closed with respect to?

OPTIONS:

  • Addition
  • Division
  • Subtraction
  • None of the above

CORRECT OPTION:

Division

EXPLANATION:

Set = {1,-1,i,-i}

Addition: 1 + i is not part of the set;

Subtraction: 1 – i is not part of the set;

Any division operation in the set results in an element which is part of the set. E.g. 1/i = i/i2 = -i. Hence it is closed w.r.t division;

Remember that set of fourth roots of unit are closed w.r.t multiplication and division.

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