CTET Solved Paper MCQ - CTET September 2016 Paper2

36 Abhi is twice as old as his daughter. Five years ago, his age was four times his daughter's age. If the present age of the daughter is x yr, then

Let the present age of his daughtcr be x yr and present age of Abhi be y yr.
Then, y = 2x ..... (i)
Five years ago, y - 5 = 4 (x - 5)
Putting the value of Eq.(i) in this
equation, we get
4(x - 5) = 2x - 5

37 When x=1/9 and y =-3/4, then the value of 94 the expression 81x² + 16y² - 72xy is

x = 1/9; and y = -1/4 (given)
81x² + 16y² - 72xy = (9x - 4y)²
= (9x(1/9) - 4x(-3/4))²
(on outputting value of x and y in the equation)
=(1 + 3)² = 4² = 16

38 A person marks his goods 40% above the cost price and allows 40% discount on the marked price. His loss/gain percent is

Let the cost price be Rs 100/-.
Then, marked price is Rs 140/-.
Selling price = 40% discount on MRP
= 140 -140 x 40⁄100
=140-56
SP = Rs. 84/-
since SP < CP
∴ There is a loss.
Loss percentage = CP - SP⁄CP x 100
= 100 - 84⁄100 x100
= 16% Loss

39 Two sides of a right triangle measure 15 cm and 17 cm. Which of the following statements can be true of the length of the third side of the triangle? A. It is between 4 cm and 7 cm. E. It is between 20 cm and 23 cm. C. It is less than 10 cm.

In a right triangle, measure of two sides are 15 cm and 17 cm.
Let the 3rd side of the triangle be 'x' cm
Now, there are two cases,
(i) (15)² + x² = (17)² (as according to the pythagoras theorem)
⇒ 225 + x² = 289
⇒ x² = 289 - 225
⇒ x² = 64
⇒ x = 8cm
(ii) (15)² + (17)² = x²
⇒ 225 + 289 =x² ⇒ x = 514
⇒ x = 2267cm
So, statement B and C are true.

40 The angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. The sum of the supplement of the largest angle and the complement of the smallest angle is

Let 2x, 3x, 5x and 8x be the angles of the quadrilateral.
Sum of angles of a quadrilateral = 360 °
⇒ 2x+3x+5x+8x=360^o
⇒ 18x=360° ⇒ x=20° Now, smallest angle = 2x = 2 x 20° = 40^o
Complement of the smallest angle = 90^o- 40° = 50°...(i)
Largest angle=8x =8 x20^o =160°
Supplement of the largest angle= 180° -160° = 20° ... (ii)
Now, sum of the supplement of largest
angle and complement of smallest angle= 20^o +50°= 70^o

CTET Solved Paper MCQ - CTET September 2016 Paper2

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