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SSC CGL Exam Quantitative Aptitude Study Material

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Trigonometry

In the given Figure, PAB is a secant and PT is a tangent to the circle from P. If PT=5 cm, PA=4 cm and AB=x cm then x is

a) 4/9cm
b) 9/4cm
c) 5cm
d) 2/3cm

✔Answer

✔Solution

Correct Answer Is : 9/4cm

Solution Is :

If A is an acute angle and cot A+cosec A=3, then the value of sin A is

a) 1
b) `3/5
c) `4/5
d) 0

✔Answer

✔Solution

Correct Answer Is : `3/5

Solution Is :

In a given circle, the chord PQ is of length 18cm, AB is the perpendicular bisector of PQ at M. If MB=3, them the length of AB is

a) 27cm
b) 30cm
c) 28cm
d) 25cm

✔Answer

✔Solution

Correct Answer Is : 30cm

Solution Is :

If sec x+cosx=2 then the value of sec^16x+cos^16x will be

a) √3
b) 2
c) 1
d) 0

✔Answer

✔Solution

Correct Answer Is : √3

Solution Is :

The minimum value of 2sin²θ +3cos²θ is

a) 1
b) 3
c) 2
d) 4

✔Answer

✔Solution

Correct Answer Is : 2

Solution Is : Given that
2sin2θ+ 3cos2θ
= 2(1 - cos2θ) + 3cos2θ
= 2 - 2cos2θ+ 3 cos2θ
= 2 + cos2θ
For minimum value cosθ = 0
Minimum value of 2sin2θ + 3 cos2θ= 2

The value of sin² 22° + sin ²68° + cot² 30° is

a) 3/4
b) 4
c) 5/4
d) 3

✔Answer

✔Solution

Correct Answer Is : 4

Solution Is : Sin²22°+sin²68°+cot²30°
⇒ sin²(90-68)°+sin²68°+cot230 °
⇒ cos²68°+sin²68°+cot²30° =1+(?3)²
1+3 =4

If 5sinθ = 3, the numerical value of (secθ - tanθ)/(secθ+tanθ)

a) 1/3
b) 1/2
c) 1/4
d) 1/5

✔Answer

✔Solution

Correct Answer Is : 1/4

Solution Is :

A kite is flying at the height of 75m from the ground. The string makes an angle θ (where cotθ = 8/15) with the level ground. Assuming that there is no slack in the string the length of the string is equal to :

a) 75m
b) 85m
c) 40m
d) 65m

✔Answer

✔Solution

Correct Answer Is : 85m

Solution Is :

If Secθ + tanθ = p, (p≠ 0) then secθ is equal to

a) (P +1/P), P≠ 0
b) 1/2(P +1/P), P≠ 0
c) 2(P -1/P), P≠ 0
d) (P -1/P), P≠ 0

✔Answer

✔Solution

Correct Answer Is : 1/2(P +1/P), P≠ 0

Solution Is : Secθ+ tanθ = p ...(i)
We know that sec²θ - tan²θ = 1
⇒(secθ - tanθ) (secθ + tanθ) = 1
Now, Put the value of secθ+ tanθ = p
secθ - tanθ = 1/p ...(ii)
Now, solving eqn. (i) and (ii)
secθ =1/2(p+(1/p))

If 1 + cosθ = 3 sinθcosθ, then the integral value of cot?θ (0<θ<π/2)

a) 1
b) 2
c) 0
d) 3

✔Answer

✔Solution

Correct Answer Is : 1

Solution Is :

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SSC CGL Exam Quantitative Aptitude Study Material

Trigonometry

In the given Figure, PAB is a secant and PT is a tangent to the circle from P. If PT=5 cm, PA=4 cm and AB=x cm then x is

Correct Answer Is : 9/4cm

Solution Is :

If A is an acute angle and cot A+cosec A=3, then the value of sin A is

Correct Answer Is : `3/5

Solution Is :

In a given circle, the chord PQ is of length 18cm, AB is the perpendicular bisector of PQ at M. If MB=3, them the length of AB is

Correct Answer Is : 30cm

Solution Is :

If sec x+cosx=2 then the value of sec^16x+cos^16x will be

Correct Answer Is : √3

Solution Is :

The minimum value of 2sin2θ +3cos2θ is

Correct Answer Is : 2

Solution Is : Given that 2sin2θ+ 3cos2θ = 2(1 - cos2θ) + 3cos2θ = 2 - 2cos2θ+ 3 cos2θ = 2 + cos2θ For minimum value cosθ = 0 Minimum value of 2sin2θ + 3 cos2θ= 2

The value of sin2 22° + sin 268° + cot2 30° is

Correct Answer Is : 4

Solution Is : Sin222°+sin268°+cot230° ⇒ sin2(90-68)°+sin268°+cot230 ° ⇒ cos268°+sin268°+cot230° =1+(?3)2 1+3 =4

If 5sinθ = 3, the numerical value of (secθ - tanθ)/(secθ+tanθ)

Correct Answer Is : 1/4

Solution Is :

A kite is flying at the height of 75m from the ground. The string makes an angle θ (where cotθ = 8/15) with the level ground. Assuming that there is no slack in the string the length of the string is equal to :

Correct Answer Is : 85m

Solution Is :

If Secθ + tanθ = p, (p≠ 0) then secθ is equal to

Correct Answer Is : 1/2(P +1/P), P≠ 0

Solution Is : Secθ+ tanθ = p ...(i) We know that sec2θ - tan2θ = 1 ⇒(secθ - tanθ) (secθ + tanθ) = 1 Now, Put the value of secθ+ tanθ = p secθ - tanθ = 1/p ...(ii) Now, solving eqn. (i) and (ii) secθ =1/2(p+(1/p))

If 1 + cosθ = 3 sinθcosθ, then the integral value of cot?θ (0<θ<π/2)

Correct Answer Is : 1

Solution Is :

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The minimum value of 2sin²θ +3cos²θ is

Solution Is : Given that
2sin2θ+ 3cos2θ
= 2(1 - cos2θ) + 3cos2θ
= 2 - 2cos2θ+ 3 cos2θ
= 2 + cos2θ
For minimum value cosθ = 0
Minimum value of 2sin2θ + 3 cos2θ= 2

The value of sin² 22° + sin ²68° + cot² 30° is

Solution Is : Sin²22°+sin²68°+cot²30°
⇒ sin²(90-68)°+sin²68°+cot230 °
⇒ cos²68°+sin²68°+cot²30° =1+(?3)²
1+3 =4

Solution Is : Secθ+ tanθ = p ...(i)
We know that sec²θ - tan²θ = 1
⇒(secθ - tanθ) (secθ + tanθ) = 1
Now, Put the value of secθ+ tanθ = p
secθ - tanθ = 1/p ...(ii)
Now, solving eqn. (i) and (ii)
secθ =1/2(p+(1/p))