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# Maths (Geometry) Questions for CTET Exam 2017

Q1. If the orthocenter and the centroid of a triangle are the same, then the triangle is:
(a) Obtuse Triangle
(b) Right angled
(c) Equilateral
(d) Scalene Triangle
Q2. The sides of a triangle have lengths 3, 4, and 5. What kind of triangle is it?
(a) acute triangle
(b) right triangle
(c) obtuse triangle
(d) none of these
Q3. G is the centroid of the equilateral ∆ ABC. If AB = 10 cm. Then length of AG is
(a) (2√3)/3 cm
(b) (10√3)/3 cm
(c) 5√2 cm
(d) 8√7 cm
Q4. ABC is an isosceles triangle with AB = AC. A circle through B touching AC at the middle point intersects AB at P. Then AP: AB is
(a) 4: 1
(b) 3: 7
(c) 5: 4
(d) 1: 4
Q5. ABC is an isosceles triangle such that AB = AC and AD is the median to the base BC with ∠ABC = 35°. Then ∠BAD is
(a) 70°
(b) 55°
(c) 115°
(d) 100°
Q6. O and C are respectively the orthocenter and circumcenter of an acute-angled triangle PQR. The points P and O are joined and produced to meet the side QR at S. If ∠PQS = 60° and ∠QCR = 130°, then ∠RPS =
(a) 50°
(b) 35°
(c) 110°
(d) 70°
Q7. If the length of the sides of a triangle are in the ratio 4: 5: 6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is:
(a) 7.5 cm
(b) 7 cm
(c) 6.5 cm
(d) 5.2 cm
Q8. ABC is a triangle. The bisectors of the internal ∠B and external ∠C intersect at D. If ∠BDC = 50°, then ∠A is
(a) 100°
(b) 25°
(c) 110°
(d) 120°
Q9. In ∆ABC, ∠BAC = 90° and AB = 1/2 BC. Then the measure of ∠ACB is:
(a) 60°
(b) 30°
(c) 45°
(d) 15°
Q10. If I is the incentre of ∆ABC and ∠BIC = 135°, then ∆ABC will be –
(a) acute angled
(b) equilateral triangle
(c) right angled
(d) obtuse triangle
Solutions

S2. Ans.(b)
Let a=3, b=4, c=5.
To classify the triangle, compare a^2+b^2 to c^2
a^2+b^2 _ c^2
3^2+4^2 _ 5^2
25 = 25
Since 3^2+4^2=5^2
∴The sides are of right triangle.