Question 1

The point of intersection of all the angle bisector of a triangle is ______ of the triangle.

Accepted Answer

Incenter

Question 2

ABC is an equilateral triangle and P is the orthocenter of the triangle, then what is the value (in degrees) of ∠BPC?

Accepted Answer

120

Question 3

In a triangle ABC, AD is angle bisector of ∠A and AB : AC = 3 : 4. If the area of triangle ABC is 350 cm2, then what is the area (in cm2) of triangle ABD?

Accepted Answer

150

Question 4

If the radius of the cylinder is decreased by 20%, then by how much percent the height must be increased, so that the volume of the cylinder remains same?

Accepted Answer

56.25

Question 5

ΔPQR has sides PQ and PR measuring 983 and 893 units respectively. How many such triangles are possible with all integral sides?

Accepted Answer

1785

Question 6

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. What i…

Accepted Answer

6√3:1

Question 7

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. What i…

Accepted Answer

6√3:1

Question 8

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. What i…

Accepted Answer

14 : 11

Question 9

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel What is the area of quadrilateral ABCD?

Accepted Answer

Area of quadrilateral ABCD = area of triangle ADC + area of triangle ABC = 126 + ½ * 9 * 40 = 306

Question 10

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel What is the difference between perimeter of triangle ABC and perimeter of triangle ADC?

Accepted Answer

Perimeter of triangle ABC – Perimeter of triangle ADC = (9+40+41) - (15+28+41) = 6 cm

Question 11

An equilateral triangle ABC is inscribed in a circle of radius 20√3. What is the length of the side of the triangle?

Accepted Answer

Radius of circumcircle of an equilateral triangle = side /√3 R = a/√3 a = R√3 = 20√3 *√3 = 60cm

Question 12

An equilateral triangle ABC is inscribed in a circle of radius 20√3. The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?

Accepted Answer

20√3 cm

Question 13

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm. What is the surface area of the cuboid?

Accepted Answer

Let lengths, breadth and height of cuboid be l, b and h respectively According to question l+b+h = 22cm......(i) and √(l^2+b^2+h^2) = 14cm .....(ii) Surface area of cuboid = 2(lb+bh+lh) Squaring eq (i) gives l 2 + b 2 + h 2 + 2(lb+bh+lh) = 484 Substituting l^2+b^2+h^2 from eq (i) 2(lb+bh+lh) = 484 -196 = 288 sq.cm

Question 14

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm. If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?

Accepted Answer

1144 cub.cm

Question 15

The corners of a square of side ‘a’ are cut away so as to form a regular octagon. What is the side of the octagon?

Accepted Answer

a(√2 –1)

Question 16

Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?

Accepted Answer

let n-1, n, n+1 be 3 consecutive integers So (n+1)^2= n^2+ (n-1)^2 (n+1)^2-(n-1)^2= n^2 4n = n^2 So n = 0 or n = 4 n can’t be 0 as n-1 will be negative then So 3,4 and 5 is the only triplet formed.

Question 17

Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles?A. 154 square cmB. 308 square cmC. 462 square cmD. 616 s…

Accepted Answer

462 square cm

Question 18

A rectangular red carpet of size 6 ft ×12 ft has a dark red border 6 inches wide. What is the area of the dark red border?

Accepted Answer

Initially carpet is 6×12 = 72 sq feet Since red border is 6 inches wide from all 4 side So area without border = 5× 11 = 55 sq feet Area of border = total–area without border = 72–55 = 17 sq feet

Question 19

Consider the following statements: 1) An isosceles trapezium is always cyclic. 2) Any cyclic parallelogram is a rectangle. Which of the above statements is/are correct?

Accepted Answer

Since it is an isosceles trapezium So angle C = angle D = x let A = 180 –D = 180 –x (since AB is parallel to CD) B = 180-x A+C = 180 –x + x = 180 degrees (Property of cyclic quadrilateral) ABCD is cyclic parallelogram with AB // CD and AD // BC Considering angles A = C = y (Property of parallelogram) and B=D = x Also since it is cyclic A+C = B+D = 180 degrees So x=y=90 degrees And also opposite sides are equal being a parallelogram Thus ABCD is a rectangle

Question 20

Consider the following statements: 1) The number of circles that can be drawn through three non-collinear points is infinity. 2) Angle formed in minor segment of a circle is acute. Which of the above statements is/are correct?

Accepted Answer

(1) Only one circle can be drawn through 3 non collinear points Angle in the minor segment is always obtuse

Volume and Surface Area Questions