If a2 + 1 = a,  then the value of a12 + a6 + 1 is from Quan

Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

101.

Three sides of a triangular field are of length 15 m, 20 m and 25 m long, respectively.

  • 750

  • 150

  • 300

  • 600

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102.

The value of (tan 1°  tan 2°  tan 3°.... tan 89°) is

  • undefined

  • 0

  • 1

  • 89

31 Views

103.

A, B, C and D purchase a gift worth ₹ 60. A pays 1/2 of what others are paying, B pays 1/3rd of what others are paying and C pays 1/4 of what others are paying. What is the amount paid by D?

  • 14

  • 15

  • 16

  • 13

36 Views

104.

Mohan gets 3 marks for each correct sum and loses 2 marks for each wrong sum. He attempts 30 sums and obtains 40 marks. The number of sums solved correctly is

  • 25

  • 10

  • 15

  • 20

33 Views

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105.

The greatest common divisor of
  3 to the power of 3 to the power of 333 end exponent space plus space 1 and 3 to the power of 3 to the power of 334 end exponent space plus space 1 is

  • 3 to the power of 3 to the power of 333 end exponent space plus space 1

  • 20

  • 2

  • 1

39 Views

106.

If the length of the sides of a triangle are in the ratio 4 : 5 : 6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is

  • 10 cm

  • 8 cm

  • 7.5 cm

  • 6 cm

44 Views

107.

The cost of manufacture of an article was ₹ 900. The trader wants to gain 25% after giving a discount of 10%. The marked price should be

  • ₹ 1000

  • ₹ 1500

  • ₹ 1250

  • ₹ 1200

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108.

If a2 + 1 = a,  then the value of a12 + a6 + 1 is

  • 2

  • 3

  • -3

  • 1


B.

3

a2 + 1 = a
  rightwards double arrow space space space space straight a space plus space 1 over straight a space equals space 1
On Squaring both sides, we get,
           straight a squared space plus space 1 over straight a squared space plus space 2 space equals space 1
rightwards double arrow space space space straight a squared space plus space 1 over straight a squared space equals space minus 1
On Cubing both sides, we get,
        space space space open parentheses straight a squared space plus space 1 over straight a squared close parentheses cubed space equals space left parenthesis negative 1 right parenthesis cubed
rightwards double arrow space space straight a to the power of 6 space plus space 1 over straight a to the power of 6 space plus space 3 straight a squared space cross times space 1 over straight a squared open parentheses straight a squared space plus space 1 over straight a squared close parentheses space equals space minus 1 space space rightwards double arrow space space straight a to the power of 6 space plus space 1 over straight a to the power of 6 space plus space 3 space cross times space minus 1 space equals space minus 1
rightwards double arrow space space space space straight a to the power of 6 space plus space 1 over straight a to the power of 6 space plus space 1 space equals space 3 space space space space space space space space space space space space space... left parenthesis straight i right parenthesis
If we put a = 1  in equation (i), it satisfies the equation. i.e. a = 1.
Now,  put a = 1. in  a12 + a6 + 1 i.e (1)12 + (1)6 + 1 = 3

             

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109.

If straight x space equals space straight a space sec space straight theta space cos space straight ϕ comma space space straight y space equals space straight b space sec space straight theta space sin space straight ϕ and straight z space equals space straight c space tan space straight theta. then the value of straight x squared over straight a squared space plus space straight y squared over straight b squared space equals space straight z squared over straight c squared

  • 9

  • 0

  • 1

  • 4

28 Views

110.

A person distributes his pens among four friends A, B, C and D in the ratio 1 third space colon space 1 fourth space colon space 1 fifth space colon space 1 over 6. What is the minimum number of pens that the person should have?

  • 75

  • 45

  • 57

  • 65

39 Views

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