# SSC CGL Tier 1 :: Quantitative Aptitude QA Test 61

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## Home SSC CGL Tier 1 / Quantitative Aptitude QA Test 61 Questions and Answers

1 .
If sec 4A = cosec (A + $20^o$), where 4A is an acute angle, find the value of A
$9^o$
$28^o$
$14^o$
$7^o$
2 .
A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is $60^o$. When he moves 30 metres away from the bank, he finds the angle of elevation to be $30^o$. Find the height of the tree
20$\sqrt 3$m
15$\sqrt 3$m
30$\sqrt 3$m
None of the above
3 .
AB and CD are two parallel chords of a circle whose centre is O and radius is 13 cm. If AB = 24 cm and CD = 10 cm, find the distance between AB and CD, if they lie on the same side of the centre O
12 cm
5 cm
7 cm
13 cm
4 .
An exterior angle of a triangle is $105^o$and one of the interior angles is $45^o$, find the other two angles of the triangle
$65^o$, $75^o$
$45^o$, $75^o$
$105^o$, $60^o$
$60^o$, $75^o$
5 .
Point M divides the line segment joining the points A (-1, 3) and B (9, 8) such that $AM \over BM$ = $k \over1$ . If M lies on the line x - y + 2 = 0, find the value of K
$3 \over 2$
$1 \over 2$
$4 \over 3$
$2 \over 3$
6 .
If P (5, -1), Q (-3, -2) and R (-1, 8) are vertices of triangle PQR, find the length of the median through P and the co-ordinates of the centroid
$\sqrt {65} unit$, ($1 \over 3$,$5 \over 3$)
$\sqrt {75} unit$, ($5 \over 3$,$4 \over 3$)
$\sqrt {55} unit$, ($2 \over 3$,$5 \over 3$)
$\sqrt {45} unit$, ($1 \over 3$,$4 \over 3$)
7 .
Given that sin (A + B) = sinA.cosB+cosA.sinB, find the value of sin $105^o$
$\sqrt 3 - 1 \over 2 \sqrt 2$
$\sqrt 3 + 1 \over 2 \sqrt 2$
2$\sqrt 3 + 1 \over 2 \sqrt 2$
$\sqrt 3 + 1 \over \sqrt 3 - 1$
8 .
Find the value of
$6 \over 7$
$7 \over 6$
$2 - \sqrt 3$
$4\over 5$
9 .
If each interior angle of a regular polygon is 8 times its exterior angle then the number of sides of the polygon is
22
18
16
36
10 .
In the following figure, MP = 8 cm, PD = 4 cm and CD = 3 cm. Find the length of MN

3 cm
4 cm
4.5 cm
3.5 cm