CTET Solved Paper - UPTET December 2016
71. The complement of the supplement of 1380 is
- Option : B
- Explanation : (B) Supplement of 1380 = (1800 - 1380)
= 420
Now, complement of 420
= (900 - 420) = 480
- Option : C
- Explanation : (C)
∴ 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.
- Option : D
- Explanation : (D) 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
