CTET Solved Paper MCQ - UPTET December 2016

71 The complement of the supplement of 138⁰ is

Supplement of 138⁰ = (180⁰ - 138⁰)
= 42⁰
Now, complement of 42⁰
= (90⁰ - 42⁰) = 48⁰

72 In the given figure, the line segment XY is parallel to side AC of △ABC and divides the triangle into two parts of equal areas, then ratio of AX and AB is

73 The value of

= {3 - 4}^-1
= (-1)^-1
= -1

74 The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of the longest altitude is

∴ Shortest base have longest altitude.
Side of a triangle are 35 cm, 54 cm, and 61 cm (given)
∴ Altitude corresponding to base 35 cm is the longest.
According to the figure,

In △ADC,
(54)² = h² + (35 - x)² [by Pythagoras theorem]
⇒ h² = (54)² - (35 - x)² .......(i)
In △BDC,
(61)² = h² + x²
⇒ h² = (61)² - x²
⇒ (54)² - (35 - x)² = (61)² - x² [by Eq.(i)]
⇒ 2916 - (1225 + x² - 70x) = 3721 - x²
⇒ 2916 - 1225 - x² + 70x = 3721 - x²
⇒ 70x = 3721 - 2916 + 1225
⇒ x = 29
Now, we know that
(61)² - x² = h² ⇒ (61)² - (29)² = h²
⇒ h² = 2880 ⇒ h = 24√5 cm
∴ Lenght of the longes altitude is 24√5 cm.

75 The sum and multiplication of two numbers are 11 and 18 respectively, then the sum of their reciprocals is

Sum of two numbers is 11.
∴ Let the two numbers be x and (11 - x)
According to the question, x(11 - x) = 18
⇒ -x² + 11x = 18
⇒ x² - 11x + 18 = 0
⇒ x² - 9x - 2x + 18 = 0
⇒ x(x - 9) - 2(x - 9) = 0
⇒ (x - 2)(x - 9) = 0
⇒ x = 2, 9
Thus, the two numbers are 2 and 9