Q1. If ABC is an equilateral triangle and D is a point on BC such that AD ⏊ BC, then:
(a) AB : BD = 1 : 1
(b) AB : BD = 1 : 2
(c) AB : BD = 2 : 1
(d) AB : BD = 3 : 2
Q2. All sides of a quadrilateral ABCD touch a circle. If AB = 6 cm, BC = 7.5 cm, CD = 3 cm, then DA is:
(a) 3.5 cm
(b) 4.5 cm
(c) 2.5 cm
(d) 1.5 cm
Q3. Inside a square ABCD, ∆BEC is an equilateral triangle. If CE and BD intersect at O, then ∠BOC is equal to:
(a) 60°
(b) 75°
(c) 90°
(d) 120°
Q4. Angle ‘A’ of a quadrilateral ABCD is 26° less than angle B. Angle B is twice angle C and angle C is 10° more than angle D. What would be the measure of angle A?
(a) 104°
(b) 126°
(c) 106°
(d) 132°
Q5. D and E are two points on the sides AC and BC, respectively of ∆ABC such that DE = 18 cm, CE = 5 cm and ∠DEC = 90°. If tan (∠ABC) = 3.6, then ∠A = ?
(a) 2∠C
(b) 2∠B
(c) 2∠D
(d) None of these
Q6. If the internal bisectors of ∠ABC = ∠ACB of ∆ABC meet at O and also ∠BAC = 80°, then ∠BOC is equal to:
(a) 50°
(b) 160°
(c) 40°
(d) 130°
Q7. Suppose ∆ABC be a right-angled triangle where ∠A = 90° and AD ⏊ BC. If area (∆ABC) = 40 cm2, area (∆ACD) = 10 cm2 and AC = 9 cm, then the length of BC is:
(a) 12 cm
(b) 18 cm
(c) 4 cm
(d) 6 cm
Q8. Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact and ∠PAB = 35°. Then ∠ABP is:
(a) 35°
(b) 55°
(c) 65°
(d) 75°
Q9. In ∆ABC, D and E are point on AB and AC respectively such that DE ∥ BC and DE is divides the ∆ABC into two parts of equal areas. Then ratio of AD: BD is:
(a) 1: 1
(b) 1: √2-1
(c) 1:√2
(d) 1:√2+1
Q10. I is the incentre of a triangle ABC. If ∠ABC = 65° and ∠ACB = 55°, then the value of ∠BIC is:
(a) 130°
(b) 120°
(c) 140°
(d) 110°
Q11. The angles of a triangle are in Arithmetic progression. The ratio of the least angle in degrees to the number of radians in the greatest angle is 60: 𝜋. The angles in degrees are:
(a) 30°, 60°, 90°
(b) 35°, 55°, 90°
(c) 40°, 50°, 90°
(d) 40°, 55°, 85°
Q12. One of the angles of a triangle is two-thirds of the sum of the adjacent angles of parallelogram. Remaining angles of the triangle are in the ratio 5: 7. What is the value of the second largest angle of the triangle?
(a) 25°
(b) 40°
(c) 35°
(d) Cannot be determined
Q13. If the length of a chord of a circle at a distance of 12 cm from the centre is 10 cm. then the diameter of the circle is:
(a) 13 cm
(b) 15 cm
(c) 26 cm
(d) 30 cm
Q14. In ∆ABC, P and Q are the middle points of the sides AB and AC respectively. R is a point on the segment PQ such that PR: PQ = 1 : 2. If PR = 2 cm, then BC = ?
(a) 4 cm
(b) 2 cm
(c) 12 cm
(d) 6 cm
Q15. What is the length of the radius of the circum-circle of the equilateral triangle, the length of whose side is 6√3 cm?
(a) 6√3 cm
(b) 6 cm
(c) 5.4 cm
(d) 3√6 cm
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