1 .
If sec 4A = cosec (A + $20^o$), where 4A is an acute angle, find the value of A
A.  $9^o$
B.  $28^o$
C.  $14^o$
D.  $7^o$
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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
A.  20$\sqrt 3$m
B.  15$\sqrt 3$m
C.  30$\sqrt 3$m
D.  None of the above
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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
A.  12 cm
B.  5 cm
C.  7 cm
D.  13 cm
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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
A.  $ 65^o$, $75^o$
B.  $45^o$, $75^o$
C.  $105^o$, $60^o$
D.  $60^o$, $75^o$
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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
A.  $3 \over 2$
B.  $1 \over 2$
C.  $4 \over 3$
D.  $2 \over 3$
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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
A.  $\sqrt {65} unit$, ($1 \over 3$,$5 \over 3$)
B.  $\sqrt {75} unit$, ($5 \over 3$,$4 \over 3$)
C.  $\sqrt {55} unit$, ($2 \over 3$,$5 \over 3$)
D.  $\sqrt {45} unit$, ($1 \over 3$,$4 \over 3$)
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7 .
Given that sin (A + B) = sinA.cosB+cosA.sinB, find the value of sin $105^o$
A.  $\sqrt 3 - 1 \over 2 \sqrt 2$
B.  $\sqrt 3 + 1 \over 2 \sqrt 2$
C.  2$\sqrt 3 + 1 \over 2 \sqrt 2$
D.  $\sqrt 3 + 1 \over \sqrt 3 - 1$
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8 .
Find the value of image
A.  $6 \over 7$
B.  $7 \over 6$
C.  $2 - \sqrt 3$
D.  $4\over 5$
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9 .
If each interior angle of a regular polygon is 8 times its exterior angle then the number of sides of the polygon is
A.  22
B.  18
C.  16
D.  36
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10 .
In the following figure, MP = 8 cm, PD = 4 cm and CD = 3 cm. Find the length of MN

image
A.  3 cm
B.  4 cm
C.  4.5 cm
D.  3.5 cm
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