CTET Solved Paper - UPTET October 2017 Paper2
86. In the given figure, ABCD is a cyclic quadrilateral. Then, the ordered pair(x,y) is
- Option : A
- Explanation : (A) Given, ABCD is a cyclic quadrilateral we know that sum of opposite angles of a cyclic quadrilateral is 180o.
4x + 4y + 20 = 180
4x + 4y = 160
⇒ x + y = 40 .......(i)
and (7x + 5) + (3y - 5) = 180o
⇒ 7x + 3y = 180 ....... (ii)
On solving Eqs. (i) and (ii), we get,
x = 15o and y = 25o
- Option : A
- Explanation : (A) 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
- Option : D
- Explanation : (D) Here,
x + y + z = 2 + 1 - 3 = 0
∴ x3 + y3 + z3 - 3xyz
= ( x + y + z)(x3 + y3 + z3 - xy - yz -zx)
=0
- Option : D
- Explanation : (D) 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,
- Option : B
- Explanation : (B)
= 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
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