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# Maths Quiz (Geometry) for KVS/NVS and CTET Exams

Q1. If each interior angle of a regular polygon is 108° then find its number of sides.
(a) 5
(b) 6
(c) 8
(d) 7

Q2. If ∠AOB = 75°, ∠BOC = 105° then choose the correct answer:
(a) OC ⊥ AB
(b) OC ∥ OA
(c) O, C & A are collinear
(d) None of these

Q3. If base and height of a ∆ be reduced to half then find the ratio of areas of previous & new triangles
(a) 4 : 1
(b) 2 : 1
(c) 1 : 4
(d) None of these

Q4. The ratio of areas of two isosceles triangle is 9 : 16. If the corresponding angles are equal them find the ratio of altitudes.
(a) 4 : 3
(b) 3 : 4
(c) 81 : 256
(d) None of these

Q5. AB is a diameter of a circle point P is on the circle. If ∠PAB = 40° then find ∠PBA.
(a) 40°
(b) 60°
(c) 50°
(d) None of these

Q6. If PAB is an intersecting line which intersects the circle at points A & B. PT is a tangent then PA × PB will be
(a) PT2
(b) PT × PB
(c) AT × BT
(d) None of these

Q7. x, x + 1 and x – 1 are the sides of a right angled ∆, then its hypotenuse will be:
(a) 5
(b) 4
(c) 1
(d) 0

Q8. ABCD is a rectangle & ∆ABP is a right angled ∆, ∠PAB = 60° then find ∠PDC.
(a) 15°
(b) 20°
(c) 30°
(d) 10°

Solutions

S1. Ans.(a)
Sol. Each interior angle =((2n-4)/n)×90°
⇒ 108°n=180°n-360°
⇒ 72°n=360°
⇒ n=(360°)/(72°)=5
∴ Number of sides = 5

S3. Ans.(a)
Sol.
∆1=1/2 bh
∆2=1/2×(b/2)(h/2)
∴(∆1/∆2) ×(1/2 b.h)/(1/2.bh/4)=4/1
=4∶1

S4. Ans.(b)
Sol. The ratio of the areas of similar triangles is equal to the ratio of the squares of the corresponding sides.
∴ Ratio of the areas of similar triangle =a^2 ∶b^2
∴ Ratio of altitudes =√(9/16)=3/4=3∶4

S10. Ans.(c)
Sol. From the given figure,
⇒ (5x + 3x + x) = 180°
⇒ 9x = 180°
⇒ x = 20°