Math Questions for SSC CHSL and RRB NTPC EXAM

Q1. The length of shadow of a tree is 16 m when the angle of elevation of the Sun is 60°. What is the height of the tree?
(a) 8 m
(b) 16 m
(c) 16√3 m
(d) 16/√3 m


Q2. The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of 100 m from its base is 45°. If the angle of elevation of the top of complete pillar at the same point is to the 60°, then the height of the incomplete pillar is to be increased by..
(a) 50√2 m
(b) 100 m
(c) 100 (√3-1) m
(d) 100 (√3+1) m

Q3. ABCD is a rhombus. A straight line through C cuts AD produced at P and AB produced at Q. If DP = 1/2 AB, then the ratio of the length of BQ and AB is..
(a) 2 : 1
(b) 1 : 2
(c) 1 : 1
(d) 3 : 1

Q4. If tan⁡α,tan⁡β are the roots of x^2+px+q=0 (p ≠ q) then tan⁡〖(α+β)=?〗...
(a) p-1
(b) p/(q-1)
(c) 2q + p
(d) None of these

Q5. If cos⁡θ≥1/2 in the first quadrant, then which one of the following is correct?
(a) θ≤ π/3
(b) θ≥ π/3
(c) θ≤ π/6
(d) θ≥ π/6

Q6. If sin (x + 54°) = cos⁡x, where 0 < x, x + 54° < 90°, then what is the value of x?
(a) 54°
(b) 36°
(c) 27°
(d) 18°

Q7. From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff (take√3=1.732).. 
(a) 10(√30+2) m
(b) 10(√30-1) m
(c) 10√3 m 
(d) 7.32 m 

Q8. If a ≠ b, then which of the following statements is true?
(a) (a+b)/2=√ab
(b) (a+b)/2<√ab
(c) (a+b)/2>√ab
(d) All of the above

Q11. If 2 + x√3=1/(2 + √3), then the simplest value of x is:

(a) 1

(b) -2

(c) 2

(d) -1

Q12. If one angle of a triangle is equal to the sum of the other two, then the triangle is:

(a) Right-angled

(b) Obtuse-angled

(c) Acute-angled

(d) None of these

Q13. ABC is an equilateral triangle and CD is the internal bisector of C. If DC is produced to E such that AC = CE then CAE is equal to:

(a) 45°

(b) 75°

(c) 30°

(d) 15°

Q14. The side AB of a parallelogram ABCD is produced to E in such way that BE = AB, DE intersects BC at Q. The point Q divides BC in the ratio..

(a) 1 : 2

(b) 1 : 1

(c) 2 : 3

(d) 2 : 1

Q15. In triangle ABC, P and Q are the mid points of the sides AB and AC respectively. R is a point on the segment PQ such that PR : RQ = 1 : 2, If PR = 2 cm, then BC = 

(a) 4 cm

(b) 2 cm

(c) 12 cm

(d) 6 cm

 

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