CTET Solved Paper MCQ - UPTET October 2017 Paper2

86 In the given figure, ABCD is a cyclic quadrilateral. Then, the ordered pair(x,y) is

Given, ABCD is a cyclic quadrilateral we know that sum of opposite angles of a cyclic quadrilateral is 180^o.
4x + 4y + 20 = 180
4x + 4y = 160
⇒ x + y = 40 .......(i)
and (7x + 5) + (3y - 5) = 180^o
⇒ 7x + 3y = 180 ....... (ii)
On solving Eqs. (i) and (ii), we get,
x = 15^o and y = 25^o

87 For what value of x, the mode of the following data is 27?
25, 26, 27, 23, 27, 26, 24, x, 27, 26, 25, 25

We know that mode is the value of the observation which occurs most frequently from question, occurrence of 25= 3
occurrence of 26 = 3 and occurrence of 27 = 3
Since mode of following data is 27.
So, value of x is 27.

88 If x=2, y=1, z=-3, then x³ + y³ = z³ - 3xyz equals

Here,
x + y + z = 2 + 1 - 3 = 0
∴ x³ + y³ + z³ - 3xyz
= ( x + y + z)(x³ + y³ + z³ - xy - yz -zx)
=0

89 In a religious gathering, the ratio of number of ladies to that of gents was 3 : 2. When 20 more gents joined, the ratio was reversed. The number of ladies was

Let number of ladies = 3x and number of gents = 2x
According to the question,

⇒ 5x=40 ⇒ x=8
So, number of ladies = 3x = 3 × 8 = 24

90 For three non-zero real numbers a, b, c if

, then the value of k is,

= λ (Let)
∴ a = 2λ, b = 3λ, c = 4λ .....(i)
and 2a - 3b + 5c = λk .....(ii)
From Eqs. (i) and (ii), we get
2(2λ) - 3(3λ) + 5(4λ) = λk
⇒ λ(4 - 9 + 20) = λk ⇒ k = 15