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CTET Solved Paper MCQ - UPTET December 2016 Paper2

136 The graphs of lines x + 2y -3 = 0 and 2x + 4y + 11 = 0

Slope (m) of a line ax + by + c = 0 is m = -(a/b)
∴ Slope (m₁) of line x + 2y -3 = 0,
⇒ m₁ =-(1/2)
and Slope (m₂) of line 2x + 4y + 11 = 0
⇒ m₂ = -(2/4) = -(1/2)
∵ m₁ = m₂ = -(1/2)
Slope of both the lines are equal
∴ Lines are parallel to each other

137 In a pair of adjacent angles (i) Vertex is always common, (ii) one arm is always common and (iii) uncommon arms are always opposite rays. Then

(i) Vertex is always common. (false)
It is not necessary that vertex is always common as in case of parallel lines, vertex is not common of lines which forms pair of adjacent angles ∠1 and ∠2 are adjacent angles. But vertex is not common.

(ii) One arm is always common. (True)
In both figure (a) and (b), l is the common arm.

(iii) Uncommon arms are always opposite rays (True)
In both figure, X and Y are uncommon arms. And, they are always opposite rays.

138 If area of an equilateral triangle is 'a' having height 'b', then

is

139 There are 10 persons in a party. If each one of them shakes hand with others exactly once. The total number of handshakes is

140 A horse is tethered to a stake by a rope of 30 m long. If the horse moves along the circumference of a circle keeping rope tight, find that how far the horse have gone from initial point if the rope has traced an angle of 105⁰ at the center?

Radius = m, θ = 105⁰
Length of the arc (̅AB) = (πrθ)/180⁰

= 55 m
∴ Horse covered a distance of 55 m from initial point A to B.

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Question:

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 320, ∠AOB = 700, Then ∠DBC is equal to

A. 24⁰
B. 86⁰
C. 38⁰
D. 32⁰

Correct answer: C

Explanation:

∠DAC = 320 and ∠AOB = 700 (given) ∠BOC + ∠AOB = 1800 [∵ Liner pair] ⇒ ∠BOC + 700 = 1800 ⇒ ∠BOC = 1800 - 700…

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