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SSC SI CAPF Exam Quantitative Aptitude Study Material

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Geometry

Internal bisectors of ∠Q and ∠R of ΔPQR intersect at 0. If ∠ROQ = 96° then the value of ∠RPQ is

a) 12°
b) 6°
c) 36°
d) 24°

✔Answer

✔Solution

Correct Answer Is : 12°

Solution Is :

If the sum and difference of two angles are 22/9 radian and 36° respectively, then the value of smaller angle in degree taking the value of π as 22/7 is :

a) 60°
b) 48°
c) 52°
d) 56°

✔Answer

✔Solution

Correct Answer Is : 52°

Solution Is : Let angles are X and Y rad.
X-Y=36° --- (i)
X+Y =22/9
X+Y=(22/9)*(180/π) =440°/π =140°. ----(ii)
Now, on solving (i) and(ii), we get X=68°
and Y=52°. So smaller angle =52°.

If θ be acute angle and tan(4θ -50°) = cot(50°-θ), then the value of θ in degrees is

a) 30
b) 40
c) 20
d) 50

✔Answer

✔Solution

Correct Answer Is : 30

Solution Is : Tan(4θ- 50°) = cot(50°-θ )
⇒tan(4θ- 50°) = tan(90 - (50° -θ))
⇒ 4θ- 50° = 90 -50°+θ
⇒ 3θ= 90°
θ = 30°.

Given that : ΔABC ΔPQR, If area(?PQR)/area(?ABC) = 256/441 and PR=12 cm, then AC is equal to

a) 15.75 cm
b) 16 cm
c) 12 cm
d) 15.5 cm

✔Answer

✔Solution

Correct Answer Is : 15.75 cm

Solution Is : The ratio of the areas of two similar triangles is equal to the ratio of squares of any two corresponding sides.
Therefore, (Area of Δ PQR)/(Area of Δ ABC)=(PR ²)/AC² (PR ²)/AC² = 256/441 (12 ²)/AC² = 256/441
Taking square roots of both sides,
12/AC=16/21
⇒16×AC=12×21
⇒ AC = (12×21)/16=63/4
=15.75 cm

In ΔABC, D and E are two mid points of sides AB and AC respectively. If ∠BAC = 40° and ∠ABC = 65° then ∠CED is :

a) 130°
b) 75°
c) 125°
d) 105°

✔Answer

✔Solution

Correct Answer Is : 105°

Solution Is :

ABCD is a cyclic quadrilateral. Diagonals AC and BD meets at P. If ∠APB = 110° and ∠CBD = 30°, then ∠ADB measures

a) 55°
b) 30°
c) 70°
d) 80°

✔Answer

✔Solution

Correct Answer Is : 80°

Solution Is :

O is the circumcentre of ΔABC. If ∠BAC = 85°, ∠BCA = 75°, then ∠OAC is equal to :

a) 60°
b) 70°
c) 50°
d) 40°

✔Answer

✔Solution

Correct Answer Is : 70°

Solution Is :

O is the in centre of ΔPQR and ΔQPR = 50°, then the measure of ∠QOR is :

a) 125°
b) 100°
c) 130°
d) 115°

✔Answer

✔Solution

Correct Answer Is : 115°

Solution Is :

The internal bisectors of the ∠B and ∠C of the ΔABC, intersect at O. If ∠A =:100°, then the measure of ∠BOC is :

a) 140°
b) 120°
c) 110°
d) 130°

✔Answer

✔Solution

Correct Answer Is : 140°

Solution Is :

If PQRS is a rhombus and ∠SPQ = 50°, then ∠RSQ is

a) 55°
b) 65°
c) 75°
d) 45°

✔Answer

✔Solution

Correct Answer Is : 65°

Solution Is :

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SSC SI CAPF Exam Quantitative Aptitude Study Material

Geometry

Internal bisectors of ∠Q and ∠R of ΔPQR intersect at 0. If ∠ROQ = 96° then the value of ∠RPQ is

Correct Answer Is : 12°

Solution Is :

If the sum and difference of two angles are 22/9 radian and 36° respectively, then the value of smaller angle in degree taking the value of π as 22/7 is :

Correct Answer Is : 52°

Solution Is : Let angles are X and Y rad. X-Y=36° --- (i) X+Y =22/9 X+Y=(22/9)*(180/π) =440°/π =140°. ----(ii) Now, on solving (i) and(ii), we get X=68° and Y=52°. So smaller angle =52°.

If θ be acute angle and tan(4θ -50°) = cot(50°-θ), then the value of θ in degrees is

Correct Answer Is : 30

Solution Is : Tan(4θ- 50°) = cot(50°-θ ) ⇒tan(4θ- 50°) = tan(90 - (50° -θ)) ⇒ 4θ- 50° = 90 -50°+θ ⇒ 3θ= 90° θ = 30°.

Given that : ΔABC ΔPQR, If area(?PQR)/area(?ABC) = 256/441 and PR=12 cm, then AC is equal to

Correct Answer Is : 15.75 cm

In ΔABC, D and E are two mid points of sides AB and AC respectively. If ∠BAC = 40° and ∠ABC = 65° then ∠CED is :

Correct Answer Is : 105°

Solution Is :

ABCD is a cyclic quadrilateral. Diagonals AC and BD meets at P. If ∠APB = 110° and ∠CBD = 30°, then ∠ADB measures

Correct Answer Is : 80°

Solution Is :

O is the circumcentre of ΔABC. If ∠BAC = 85°, ∠BCA = 75°, then ∠OAC is equal to :

Correct Answer Is : 70°

Solution Is :

O is the in centre of ΔPQR and ΔQPR = 50°, then the measure of ∠QOR is :

Correct Answer Is : 115°

Solution Is :

The internal bisectors of the ∠B and ∠C of the ΔABC, intersect at O. If ∠A =:100°, then the measure of ∠BOC is :

Correct Answer Is : 140°

Solution Is :

If PQRS is a rhombus and ∠SPQ = 50°, then ∠RSQ is

Correct Answer Is : 65°

Solution Is :

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Solution Is : Let angles are X and Y rad.
X-Y=36° --- (i)
X+Y =22/9
X+Y=(22/9)*(180/π) =440°/π =140°. ----(ii)
Now, on solving (i) and(ii), we get X=68°
and Y=52°. So smaller angle =52°.

Solution Is : Tan(4θ- 50°) = cot(50°-θ )
⇒tan(4θ- 50°) = tan(90 - (50° -θ))
⇒ 4θ- 50° = 90 -50°+θ
⇒ 3θ= 90°
θ = 30°.