Q: Consider the following inequalities in respect of any triangle ABC: 1) AC –AB < BC 2) BC –AC < AB 3) AB –BC < AC Which of the above are correct?

AC-AB AC BC-AC BC AB-BC AB Sum of 2 sides of triangle is always greater than the third side So all three statements are true

Question 1

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 2

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 3

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 4

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 5

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 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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

Question 16

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

Question 17

Consider the following inequalities in respect of any triangle ABC: 1) AC –AB < BC 2) BC –AC < AB 3) AB –BC < AC Which of the above are correct?

Accepted Answer

AC-ABAC BC-ACBC AB-BCAB Sum of 2 sides of triangle is always greater than the third side So all three statements are true

Question 18

ABC is a right angled triangle in which ∠A = 90°, AB = 5 cm and AC = 12 cm. What is the approximate volume (in cm3) of the double cone formed by rotating the triangle about its hypotenuse?

Accepted Answer

290

Question 19

PQ is a diameter of a circle with centre O. RS is a chord parallel to PQ subtends an angle of 40° at the centre of the circle. If PR and QS are produced to meet at T, then what will be the measure (in degrees) of ∠PTQ?

Accepted Answer

70

Question 20

The diagonal of a square is 10 cm. What is the length (in cm) of its side?

Accepted Answer

5√2

Volume and Surface Area Questions