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SSC CGL Mains Geometry Questions : 23rd August

Dear aspirants,

As you all know, the upcoming months are lined up with various important exams like SSC CGL Mains 2018, so we are here to help you with the subject that is common to all of the given exams. We are providing daily quantitative aptitude quizzes, practice which will help you to score good marks in this section. We aim to provide the best study material to our readers with exam level questions to help them get used to the recent pattern. Attempt this quiz and check your preparation.

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Q1. If ABCDEF is a regular hexagon, then what is the value (in degrees) of ∠ADB?
यदि ABCDEF एक नियमित षट्भुज है, तो ∠ADB का मान (डिग्री में) क्या होगा?
(a) 15
(b) 30
(c) 45
(d) 60

S1. Ans.(B)
Sol. ABCDEF is a regular hexagon


Q2. If ∠A = 44°, BP = BR and CN =RC then ∠PRN = ?
यदि ∠A = 44°, BP = BR और CN =RC तो∠PRN = ?

(a) 58°
(b) 78°
(c) 68°
(d) 66°

S2. Ans.(c)
Sol.

Q3. In the given figure, AC ⊥ CE and ∠A : ∠B : ∠C = 3 : 2 : 1, find the value of ∠ECD :
दी गयी आकृति में, AC ⊥ CE और ∠A : ∠B : ∠C = 3 : 2 : 1, तो ∠ECD का मान ज्ञात करें

(a) 50°
(b) 45°
(c) 55°
(d) 60°

S3. Ans.(d)
Sol. ATQ
∠A : ∠B : ∠C = 3 : 2 : 1
∴ ∠A = 3x, ∠B = 2x, ∠C = x
In ∆ABC
⇒ ∠A + ∠B + ∠C = 180°
⇒ 3x + 2x + x = 180°
⇒ x = 30°
∴ ∠C = 30°
∠ECD = 180 – ∠C – ∠ACE
= 180° – 30° – 90°
= 60°

Q4. In triangle ABC, DE || BC where D is a point on AB and E is point on AC. DE divides the area of ∆ABC into two equal parts. Then DB : AB is equal to
त्रिभुज ABC में, DE || BC जहां D, AB पर एक बिंदु है और E, AC पर बिंदु है। DE, ∆ABC के क्षेत्रफल को दो समान भागों में विभाजित करता है। तो DB : AB किसके बराबर होगा?


Q5. G is the centroid of ∆ABC. The medians AD and BE intersect at right angles. If the lengths of AD and BE are 9 cm and 12 cm respectively; then the length of AB (in cm) is ?
G त्रिभुज ABC का केन्द्रक है। माध्यिका AD और BE समकोण पर प्रतिच्छेद करते हैं। यदि AD और BE की लंबाई क्रमशः 9 सेमी और 12 सेमी है; फिर AB की लंबाई (सेमी में) क्या है?
(a) 11
(b) 10
(c) 10.5
(d) 85

S5. Ans.(b)
Sol.


Q6. If O is the circumcentre of a triangle ABC lying inside the triangle, the ∠OBC + ∠BAC is equal to
यदि O एक त्रिभुज ABC की परिकेन्द्र है जो त्रिभुज के अंदर स्थित है, ∠OBC + ∠BAC किस के बराबर है?
(a) 120°
(b) 110°
(c) 90°
(d) 60°

S6. Ans.(c)
Sol.

Q7. D and E are mid-points of sides AB and AC respectively of the ∆ ABC. A line drawn from A meets BC at H and DE at K. AK : KH = ?
D और E, त्रिभुज ABC की भुजा AB और AC के मध्य बिंदु हैं। A से खींची गई एक रेखा BC को H और DE को K पर मिलती है. AK: KH =?
(a) 2 : 1
(b) 1 : 1
(c) 1 : 3
(d) 1 : 2

S7. Ans.(b)
Sol.

∵ Point D & E are mid points of sides AB and AC
∴ DE will be parallel to BC
(By Thales theorem)
⇒ DE will cut AH into equal parts
∴ AK : KH = 1 : 1

∵ Point D & E are mid points of sides AB and AC
∴ DE will be parallel to BC
(By Thales theorem)
⇒ DE will cut AH into equal parts
∴ AK : KH = 1 : 1

S8. Ans.(c)
Sol.

Q9. ABCD is square and CDE is an equilateral triangle outside the square. What is the value (in degrees) of ∠BEC?
ABCD एक वर्ग है और CDE वर्ग के बाहर एक समबाहु त्रिभुज है. ∠BEC का मान (डिग्री में) क्या है?
(a) 15
(b) 30
(c) 25
(d) 10

S9. Ans.(A)
Sol.

Q10. There is a circular garden of radius 21 metres. A path of width 3.5 metres is constructed just outside the garden. What is the area (in metres²) of the path?
21 मीटर त्रिज्या का एक वृत्ताकार बगीचा है। बगीचे के ठीक बाहर 3.5 मीटर चौड़ाई का रास्ता बनाया गया है। पथ का क्षेत्रफल (मीटर²में) क्या है?
(a)500.5
(b) 575.6
(c) 521.2
(d) 560.7

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