Geometry · SSC CGL previous year questions

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2022 48 questions

Q682022 · 13 Dec 2022 · Shift 1
If θ is an acute angle and tan θ + cot θ = 2, then the value of tan200 θ + cot200 θ is:
1. A.1
2. B.2
3. C.-1
4. D.0
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Answer: B
Q692022 · 13 Dec 2022 · Shift 1
In the figure BCDE is a square and ABC is an equilateral triangle then ∠ADC is:
1. A.45°
2. B.30°
3. C.60°
4. D.15°
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Answer: D
Q632022 · 13 Dec 2022 · Shift 4
If A is an acute angle, the simplified form of is :
1. A.Cos2 A
2. B.Sin A
3. C.Sin2 A
4. D.Cos A
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Answer: D
Q732022 · 13 Dec 2022 · Shift 4
ΔPQR is right-angled at Q. The length of PQ is 5 cm and ∠PRQ = 30°. Determine the length of side QR.
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: A
Q672022 · 12 Dec 2022 · Shift 2
ABC is a right-angle triangle at B and tan A = , then sin A + sin B + sin C will be equal to:
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q552022 · 12 Dec 2022 · Shift 3
What is the ASA congruence rule of triangles, where A and S represents angle and side of triangle respectively?
1. A.Two triangles are said to be congruent if all three sides of both the triangles are equal.
2. B.Two triangles are said to be congruent if 2 angles and the included side of one triangle are equal to 2 angles and the included side of the other triangle.
3. C.Two triangles are said to be congruent if 2 sides and the included angle of one triangle are equal to 2 sides and the included angle of the other triangle.
4. D.Two triangles are said to be congruent if any pair of 2 angles and any 1 pair of sides of both the triangles are equal.
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Answer: B
Q582022 · 12 Dec 2022 · Shift 3
If tan3θ⋅tan7θ = 1, where 7θ is an acute angle, then find the value of cot15θ.
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q602022 · 9 Dec 2022 · Shift 1
In triangle ABC, $∠ B = 9 0^{\circ}$ , and $∠ C = 4 5^{\circ}$ , If AC = $22$ cm, then the length of BC is:
1. A.3 cm
2. B.2 cm
3. C.1 cm
4. D.4 cm
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Answer: B
Q692022 · 9 Dec 2022 · Shift 1
ABC is an isosceles triangle such that AB = AC, $∠ A B C = 5 5^{\circ}$ , and AD is the median to the base BC. Find the measure of $∠ B A D$ .
1. A.500
2. B.550
3. C.350
4. D.900
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Answer: C
Q522022 · 9 Dec 2022 · Shift 2
If cos (A – B) = $\frac{3}{2}$ , and cos (A + B) = 0, where A and B are positive acute angles and $A \geq B$ , then the measures of A and B are:
1. A.80o and 10o
2. B.60o and 30o
3. C.70o and 20o
4. D.50o and 40o
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Answer: B
Q692022 · 9 Dec 2022 · Shift 2
Triangle ABC and DEF are similar. If AB = 92 cm, BC = 48 cm, AC =120 cm, and the length of the smallest side of DEF is 200 cm, then find the length of the longest side of triangle DEF?
1. A.400 cm
2. B.225 cm
3. C.350 cm
4. D.500 cm
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Answer: D
Q722022 · 9 Dec 2022 · Shift 2
Two angles of a triangle are equal and the third angle measures 78°. What is the measure of each of the unknown angles?
1. A.50o
2. B.51o
3. C.49o
4. D.52o
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Answer: B
Q532022 · 9 Dec 2022 · Shift 3
If it is given that for two right angled triangles ABC and DFE, ∠A = 25°, ∠E = 25°, ∠B = ∠F = 90° and AC = ED, then which one of the following is TRUE?
1. A.ΔABC ≌ ΔFED
2. B.ΔABC ≌ ΔDFE
3. C.ΔABC ≌ ΔEFD
4. D.ΔABC ≌ ΔDEF
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Answer: C
Q652022 · 9 Dec 2022 · Shift 3
If $sin θ = \frac{8}{17}$ where $θ$ is an acute angle, then what is the value of $tan θ + cot θ$ ?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
Show answer
Answer: C
Q592022 · 9 Dec 2022 · Shift 4
In the given figure, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. The value of tan C - cot B is ________.
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q622022 · 8 Dec 2022 · Shift 1
ABCD is a square and ΔMAB is an equilateral triangle. MC and MD are joined. What is the degree measure of ∠MDC?
1. A.78°
2. B.60°
3. C.65°
4. D.75°
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Answer: D
Q512022 · 8 Dec 2022 · Shift 2
In ∆ABC and ∆PQR, AB = PQ and ∠B = ∠Q. The two triangles are congruent by SAS criteria if:
1. A.BC = QR
2. B.AC = PR
3. C.AC = QR
4. D.BC = PQ
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Answer: A
Q692022 · 8 Dec 2022 · Shift 2
If tan (α + β) = √3, tan (α - β) = 1 where (α + β) and (α - β) are acute angles, then what is tan (6α)?
1. A.-1
2. B.0
3. C.1
4. D.√2 - 1
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Answer: A
Q722022 · 8 Dec 2022 · Shift 3
If the angles of a triangle are (x – 6) degree, (x + 26) degree and 8x degree, then what is the value of 2x?
1. A.12 degrees
2. B.16 degrees
3. C.48 degrees
4. D.32 degrees
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Answer: D
Q602022 · 8 Dec 2022 · Shift 4
If α is an acute angle, tan⁡ (4α − 50°) = cot ⁡(50° − α), then find the value of α (in degrees).
1. A.60°
2. B.45°
3. C.30°
4. D.90°
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Answer: C
Q612022 · 8 Dec 2022 · Shift 4
in the following figure, if l || m, then find the measures of angles marked by a and b.
1. A.a = 90° and b = 90°
2. B.a = 55° and b = 125°
3. C.a = 70° and b = 110°
4. D.a = 60° and b = 120°
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Answer: C
Q522022 · 7 Dec 2022 · Shift 2
In triangle XYZ, P is the incentre of the triangle XYZ. If angle XYZ = 50 degree, then what is the value of angle XPZ?
1. A.100 degree
2. B.115 degree
3. C.140 degree
4. D.130 degree
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Answer: B
Q672022 · 7 Dec 2022 · Shift 4
If in a triangle ABC as drawn in the figure, AB = AC and ∠ACD = 130°, then ∠BAC is equal to:
1. A.60°
2. B.50°
3. C.70°
4. D.80°
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Answer: D
Q712022 · 6 Dec 2022 · Shift 1
AD is the median of triangle ABC. P is the centroid of triangle ABC. If AP = 14 cm, then what is the length of PD?
1. A.14 cm
2. B.28 cm
3. C.21 cm
4. D.7 cm
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Answer: D
Q512022 · 6 Dec 2022 · Shift 4
If , where θ is a positive acute angle, then the value of sec θ is:
1. A.6
2. B.8
3. C.5
4. D.4
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Answer: D