COMPLEMENTARY ANGLES
1) sec32/cosec58=?
a) 2/3 b)16/29 c) 16/3 d) 1
2) cos12/sin78 + tan23/cot67=?
a) 0 b) 1 c) 2 d) 3/2
3) tan10 tan15 tan75 tan80=?
a) √3 b) 1 c) 1/√3 d) -1
4) tan5 tan25 tan30 tan65 tan85=?
a) 1 b) √3 c) 1/√3 d) 1/2
5) cos1 cos2 cos3 .....cos180=?
a) 0 b) 1 c) -1 d) 1/2
6) sin43 cos47 + cos43 sin47=?
a) 0 b) 1 c) sin4 d) cos4
7) sec70 sin20+ cos20 cosec70=?
a) 0 b) 1 c) 2 d) -2
8) cosec²57 - tan²33=?
a) 1 b) 0 c) -1 d) 2
9) sec²10 - cot²80=?
a) 0 b) 1 c) 3/4 d) 1/2
10) (2sin²63 +1+ 2 sin²27)/(3 cos²17 - 2+ 3 cos²73)=?
a) 2/3 b) 3/2 c) 2 d) 3
11) sin38- cos52=?
a) 0 b) 1 c) √3/2 d) 2/√3
12) (sin²23+ sin²67)/(cos²13+ sin²77) + sin²59+ cos59sin²21=?
a) 3 b) 2 c) 1 d) 0
13) (2tan²30 sec²52sin²38)/(cosec²70- tan²20)=?
a) 2 b) 1 c) 2/3 d) 3/2
14) (cos38 cosec52)/(tan18 tan35 tan60 tan72 tan55)=?
a) 1/3 b) 1/√3 c) √3 d) 2/√3
15) sin(60+θ) - cos(30-θ)=?
a) 2 sinθ b) 2cosθ c) 0 d) 1
16) If A and B are acute angles such that sinA= cosB then (A+ B)=?
a) 30 b) 45 c) 60 d) 90
17) If cos(x + y)= 0 then sin(x - y)=?
a) sin2x b) cos2y c) sinx cost
18) sin(45+θ) - cos(45- θ)=?
a) 0 b) 1 c) 2 d) -2
19) If sec4A = cosec(A -10) and 4A is acute then A=?
a) 20 b) 25 c) 30 d) 40
20) If sin3A= cos(A -10) and 3A is acute then A= ?
a) 15 b) 20 c) 25 d) 30
21) Fill in the blanks
a) cot34 - tan56= _____
b) cos²67 + cos²23= ____
c) sec²40 - cot²50= _____
d) cosec31 - sec59=____
e) cosec²54 - tan²36= ____
COMPLEMENT ANGLES (A)
1) If sinA + sin²A = 1 then (cos²A + cos⁴)=?
a) 1/2 b) 1 c) 2 d) 3
2) (1+ tan²A)/(1+ cot²A)=?
a) -1 b) sec²A c) tan²A d) cot²A
3) (secA + tanA)(1- sinA)=?
a) sinA b) cosA c) secA d) cosecA
4) (1+ tanθ+ secθ)(1+ cotθ - cosecθ)=?
a) -1 b) 0 c) 1 d) 2
5) If sinθ - cosθ= 0 then the value of (sin⁴θ+ cos⁴θ) is
a) 1/4 b) 1/2 c) 3/4 d) 1
6) If cos9θ = sinθ and 9θ< 90° then the value of tan5θ is
a) 1/√3 b) √3 c) 1 d) 0
7) The value of (tan²θ- sec²θ)/(cot²θ- cosec²θ) is
a) -1 b) 1/2 c) -1/2 d) 1
8) √{(1- sinA)/(1+ sinA)}=?
a) secA - tanA b) secA + tanA c) secA tanA d) none
9) 8) √{(1+ cosA)/(1- cosA)}=?
a) cosecA - corA b) cosecA + tanA c) cosecA cotA d) none
10) (cosecθ - cotθ)²=?
a) (1+ cosθ)/(1- cosθ)
b) (1- cosθ)/(1+ cosθ)
c) (1+ sinθ)/(1- sinθ)
d) (1 - sinθ)/(1 + sinθ)
11) If (tanθ + cotθ)= 5 then the value of (tan²θ+ cot²θ) is
a) 23 b) 24 c) 25 d) 27
12) If tanθ = a/b then (cosθ+ sinθ)/(cosθ - sinθ)=?
a) (a+ b)/(a - b)
b) (a - b)/(a + b)
c) (b+ a)/(b - a)
d) (b- a)/(b + a)
13) If (cosθ + secθ)= 5/2 then the value of (cos²θ+ sec²θ) is
a) 21/4 b) 17/4 c) 29/4 d) 33/4
14) If tanθ= 8/15 then cosecθ= ?
a) 17/8 b) 8/17 c) 15/17 d) 17/15
15) If 5 tanθ= 3 then (5 sinθ - cosθ)/(5 sinθ + cosθ)=?
a) 2/3 b) 1/3 c) 1/2 d) 3/5
16) In a ∆ ABC, angle C=90°. Then, the value of cos(A+ B) is
a) 0 b) 1 c) 1/2 d) 3/5
17) If cosA + cos²A= 1 then sin²A + sin⁴A=?
a) 1 b) 2 c) 3 d) 4
18) If 3 cotθ= 4 then the value of (5 sinθ+ 3 cosθ)/(5 sinθ - 3 cosθ)=?
a) 1/3 b) 3 c) 1/9 d) 9
19) If 2x = secA and 2/x = tanA then 2(x² - 1/x²)=?
a) 1/2 b) 1/4 c) 1/8 d) 1/16.
20) If 3x = cosecx and 3/x = cotx then 3(x²- 1/x²)=?
a) 1/27 b) 1/81 c) 1/3 d) 1/9
21) If tanθ= √3 then secθ=?
a) 2/√3 b) √3/2 c) 1/2 d) 2
COMPLEMENT ANGLES (B)
1) If tanθ= 8/15 then cosecθ=?
a) 15/17 b) 17/15 c) 17/8 d) 8/17
2) If tanθ= √3 then secθ=?
a) 2 b) 1/2 c) √3/2 d) 2/√3
3) If cosecθ√10 then secθ=?
a) 1/√10 b) 2/√10 c) 3/√10 d) √10/3
4) If secθ= 25/7 then sinθ=?
a) 7/25 b) 24/25 c) 7/24 d) 24/7
5) If sinθ= 1/2 then cotθ= ?
a) √3/2 b) 1 c) √3 d) 1/√3
6) If cosθ= 4/5 then tanθ= ?
a) 3/4 b) 4/3 c) 3/5 d) 5/3
7) If tanθ= 4/3 then (sinθ+ cosθ)=?
a) 7/3 b) 7/4 c) 7/5 d) 5/7
8) If (tanθ + cotθ)= 5 then (tan²θ+ cot²θ)=?
a) 27 b) 25 c) 24 d) 23
9) If cosθ+ secθ= 5/2 then cos²θ+ sec²θ=?
a) 17/4 b) 21/4 c) 29/4 d) 33/4
10) If 4 tanθ= 3 then cos²θ - sin²θ=?
a) 4/25 b) 7/25 c) 1 d) 11/25
11) If 4 cotθ= 3 then (sinθ - cosθ)/(sinθ+ cosθ)
12) If 3 cosθ= 2 then (2sec²θ + 2 tan²θ-7)=?
a) 0 b) 1 c) 3 d) 4
13) If secθ+ tanθ+ 1= 0 then (secθ - tanθ)=?
a) 1 b) -1 c) 0 d) 2
14) If cosA + cos²A = 1 then (sin²A + sin⁴A)=?
a) 1/2 b) 2 c) 1 d) 4
15) If sinθ=√3/2 then (cosecθ + cotθ)=?
a) (2+√3) b) 2√3 c) √2 d) √3
16) If √3 tanθ= 3 sinθ then (sin²θ- cos²θ)=?
a) 1/3 b) 1/√3 c) √3 d) 2/√3
DISTANCE FORMULA
1) The distance of the point P(-6,8) from the origin is
a) 8 b) 2√7 c) 6 d) 10
2) The distance of the point (-3,4) from x-axis is
a) 3 b) -3 c) 4 d) 5
3) The point on x-axis which is equidistant from points A(-1,0) and B(5,0) is
a) (0,2) b) (2,0) c) (3,0) d) (0,3)
4) If R(5,6) is the midpoint of the line segment AB joining the points A(6.5) and B(4,y) then y equals
a) 5 b) 7 c) 12 d) 6
5) If the point C(k,4) divides the join of the points A(2,6) and B(5,1) in the ratio 2:3 then the value of k is
a) 16 b) 28/5 c) 16/5 d) 8/5
6) The perimeter of the triangle with vertices (0,4),(0,0) and (3,0) is
a) 7+√5 b) 5 c) 10 d) 12
7) If A(1,3), B(-1,2), C(2,5) and D(x,4) are the vertices of a||gm ABCD then the value of x is
a) 3 b) 4 c) 0 d) 3/2
8) If the points A(x,2), B(-3,-4) and C(7,-5) are collinear then the value of x is
a) -63 b) 63 c) 60 d) -60
9) The area of a triangle with vertices A(5,0), B(8,0) and C(8,4) in square unit is
a) 20 b) 12 c) 6 d) 16
10) The area of ∆ ABC with vertices A(a,0), O(0,0) and B(0,b) in square units is
a) ab b) ab/2 c) a²b²/2 d) b²/2
11) If P(a/2,4) is the midpoint of the line segment joining the points A(-6,5) and B(-2,3) then the value of a is
a) -8 b) 3 c) -4 d) 4
12) ABCD is a rectangle whose three vertices are B(4,0), C(4,3) and D(0,3). The length of one of its diagonals is
a) 5 b) 4 c) 3 d) 25
13) The coordinates of the point P dividing the line segment joining the points A(1,3) and B(4,6) in the 2:1 is
a) (2,4) b) (3,5) c) (4,2) d) (5,3)
14) if the coordinates of one end of a diameter of a circle are (2,3) and the coordinates of its centre are (-2,5) then the coordinates of the other end of the diameter are
a) (-6,7) b) (6,-7) c) (4,2) d) (5,3)
15) In the given figure P(5,-3) and Q(3,y) are the point of trisection of the line segment joining A(7,-2) and B(1,-5). Then, y equals
a) 2 b) 4 c) -4 d) -5/2
16) The mid-point of segment AB is P(0,4). If the coordinates of B are (-2,-3) then the coordinates of A is
a) (2,5) b) (-2,-5) c) (2,9) d) (-2,11)
17) The point P which divides the line segment joining the points A(2,-3) and B(5,2) in the ratio 2:3 lies in the quadrant
a) I b) II c) III d) IV
18) If A(-6,7) and B(-1,-5) are two given points then the distance 2AB is
a) 13 b) 26 c) 169 d) 238
19) Which point on x-axis is equidistant from the points A(7,6) and B(-3,4)?
a) (0,4) b) (-4,0) c) (3,0) d) (0,3)
20) The distance of P(3,4) from the x-axis is
a) 3 units b) 4 units c) 5 units d) 1 units
21) In what ratio does the x-axis divide the join of A(2,-3) and B(5,6)?
a) 2:3 b) 3:5 c) 1:2 d) 2:1
22) In what ratio does the y-axis divide the join of P(-4,2) and Q(8,3)?
a) 3:1 b) 1:3 c) 2:1 d) 1:2
23) If P(-1,1) is the midpoint of the line segment joining A(-3,b) and B(1, b+4) then b=?
a) 1 b) -1 c) 2 d) 0
24)
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