Advance Maths Quiz for SSC, Railways

Q1.The angles of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h metre, then, in metre, the height of the building is 

(a) (h cot⁡x)/(cot⁡x+cot⁡y ) 

(b)  (h cot⁡y)/(cot⁡x+cot⁡y )

(c) (h cot⁡x)/(cot⁡x-cot⁡y )

(d) cot⁡x/(cot⁡x+cot⁡y )

Q2.ABC is a triangle in which DE || BC and AD: DB = 5 : 4, Then DE : BC is 

(a) 4 : 9  

(b) 5 : 9 

(c) 4 : 5

(d) 9 : 5

Q3.One of the angles of a right-angled triangle is 15°, and the hypotenuse is 1 m. The area of the triangle (in sq. cm.) is 

(a) 1200 

(b) 1215

(c) 1220

(d)1250 

Q4.G is the centroid of ∆ABC. If AG = BC, then angle BGC is - 

(a) 90°

(b)  30°

(c) 60°

(d) 120°

Q5.Two sides of a triangle are of length 4 cm and 10 cm. If the length of the third side is ‘a’ cm, then

(a) a>5 

(b) 6<a<12

(c) a<6

(d) 6<a<14

Q6.Taking any three of the line segments out of segments of length 2 cm, 3cm, 5 cm and 6 cm, the number of triangles that can be formed is: 

(a) 3 

(b) 2

(c) 1

(d) 4

Q7.Internal bisectors of angles ∠B and ∠C of a triangle ABC meet at O. If ∠BAC=80°, then the value of angle BOC is 

(a) 120° 

(b) 140°

(c) 110°

(d) 130°

Q8.By decreasing 15° of each angle of a triangle, the ratios of their angles are 2 : 3 : 5, the radian measure of greatest angle is 

(a) 11π/24 

(b) π/12

(c) π/24

(d) 5π/24

(a) (3√3)/2 

(b) 9/4

(c) 3/4

(d) 3/2

Q10.If  29tan⁡θ=31, then the value of (1+2 sin⁡θ  cos⁡θ)/(1-2 sin⁡θ  cos⁡θ ) is equal to 

(a) 490 

(b) 810

(c) 900

(d) 540

Answers
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3-

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5-
(d);
The sum of any two sides of a triangle is greater than third side and their difference is less than third side.
∴ a+4>10
⇒a>10-4
⇒a>6
Again, a-4<10
⇒a<14

∴6<a<14
6-
b);
The sum of two sides of a triangle is greater than the third side.
(3, 5, 6) and (2, 5, 6)
7-

8-
(a);
2x+3x+5x=180°-45°=135°
⇒10x=135°
⇒x=135/10=27/2
∴ Largest angle
=5x+15°=(5×27/2)^°+15°
(135+30)/2=(165°)/2
∴180°=π radian

∴(165°)/2=π/180×165/2=11π/24 radian
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10-

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