A circle of radius 10 cm has an equilateral triangle inscribed in it. The length of the perpendicular drawn from the centre to any side of the triangle is

- 5√3 cm
- 5 cm
- 10√3 cm
- 10 cm

If A, B, C, D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D equal to?

- 0
- 1
- 2
- 4

What is the length of the perpendicular drawn from the centre of circle of radius r on the chord of length √3r?

- r/4
- r/2
- √2r
- r

ABC is an isosceles triangle such that AB = BC = 8 cm and ∠ABC = 90°. What is the length of the perpendicular drawn from B on AC?

- 4√2 cm
- 4 cm
- 2 cm
- 2√2 cm

In the figure given, ∠B = 38°, AC = BC and AD = CD. What is ∠D equal to?

- 26°
- 28°
- 38°
- 52°

How many degrees are there in an angle which equals two-third of its complement?

- 60°
- 48°
- 45°
- 36°

ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. Consider the following statements:

- Triangles ADX and BAY are congruent
- ∠DXA = ∠AYB
- DX is inclined at an angle 60° with AY
- DX is not perpendicular to AY

Which of the above statements are correct?

- 2, 3 and 4 only
- 1, 2 and 4 only
- 1, 3 and 4 only
- 1 and 2 only

In the figure given below, M is the mid-point of AB and ∠DAB = ∠CBA and ∠AMC = ∠BMD. Then the triangle ADM is congruent to the triangle BCM by

- SAS rule
- SSS rule
- ASA rule
- AAA rule

In the figure given below, ABC is a triangle with AB = BC and D is an interior point of the triangle ABC such that ∠DAC = ∠DCA.

Consider the following statements:

- Triangle ADC is an isosceles triangle.
- D is the centroid of the triangle ABC.
- Triangle ABD is congruent to the triangle CBD.

Which of the above statements are correct?

- 1 and 2 only
- 2 and 3 only
- 1 and 3 only
- 1, 2 and 3

In the figure given below, PQ is parallel to RS and PR is parallel to QS, If ∠LPR = 35° and ∠UST = 70°, then what is ∠MPQ equal to?

- 55°
- 70°
- 75°
- 80°

In the figure given below, PQR is a non-isosceles right-angled triangle, right angled at Q. If LM and QT are parallel and QT= PT, then what is ∠RLM equal to?

- ∠PQT
- ∠LRM
- ∠RML
- ∠QPT

In the figure given below, ∠A = 80° and ∠ABC = 60°. BD and CD bisect angles B and C respectively. What are the values of x and y respectively?

- 10 and 130
- 10 and 125
- 20 and 130
- 20 and 125

In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to?

- 60°
- 75°
- 90°
- 100°

ABC is a triangle and D is a point on the side BC. If BC = 12 cm, BD = 9 cm and ∠ADC = ∠BAC, then the length of AC is equal to

- 5 cm
- 6 cm
- 8 cm
- 9 cm

Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then the distance between these chords is

- 5.5 cm
- 5 cm
- 3.5 cm
- 3 cm

Let P, Q, R be the mid-points of sides AB, BC, CA respectively of a triangle ABC. If the area of the triangle ABC is 5 square units, then the area of the triangle PQR is

- 5/3 square units
- 5/2√2 square units
- 5/4 square units
- 1 square unit

Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a

- Square
- Rectangle, but need not be a square
- Rhombus, but need not be a square
- Parallelogram, but need not be a rhombus

A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. The water of this tank will last for

- 3 days
- 2 days
- 4 days
- 5 days

A gardener has 1000 plants. He wants to plant them in such a way that the number of rows and the number of columns remains the same. What is the minimum number of plants that he needs more for this purpose?

- 34
- 24
- 32
- 14

A wall is of the form of a trapezium with height 4 m and parallel sides being 3 m and 5 m. What is the cost of painting the wall, if the rate of painting is Rs.25/- per square metre?

- Rs.800
- Rs.480
- Rs.400
- Rs.240

If three metallic spheres of radii 6 cm, 8 cm, and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be

- 12 cm
- 24 cm
- 30 cm
- 36 cm

10 cylindrical pillars of a building have to be painted. The diameter of each pillar is 70 cm and the height is 4 m. What is the cost of painting at the rate of Rs.5 per square metre?

- Rs.400
- Rs.440
- Rs.480
- Rs.500

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

- 4.5 cm
- 2.25 cm
- 2 cm
- 1.5 cm

If the height of a right circular cone is increased by 200%, and the radius of the base is reduced by 50%, then the volume of the cone

- remains unaltered
- decreases by 25%
- increases by 50%
- increases by 25%

The radius of a sphere is equal to the radius of the base of a right circular cone, and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is

- 3 : 2
- 1 : 2
- 2 : 1
- 2 : 3

The total outer surface area of a right circular cone of height 24 cm with a hemisphere of radius 7 cm upon its base is

- 327 π
- 307 π
- 293 π
- 273 π

The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36 m, then what is its radius equal to?

- 0.001 cm
- 0.01 cm
- 0.1 cm
- 1.0 cm

What is the number of wax balls, each of radius 1 cm, that can be molded out of a sphere of radius 8 cm?

- 1024
- 768
- 512
- 256

In the figure given below, AC is parallel to ED and AB = DE = 5 cm and BC = 7 cm. What is the area ABDE : area BDE : area BCD equal to?

- 10 : 5 : 7
- 8 : 4 : 7
- 2 : 1 : 2
- 8 : 4 : 5

In the figure given below, D is the diameter of each circle. What is the diameter of the shaded circle?

- D(√2 - 1)
- D(√2 + 1)
- D(√2 + 2)
- D(2 - √2)

A field is divided into four regions as shown in the given figure. What is the area of the field in square metres?

- 6 + 3√5/4
- 5 + 3√3/2
- 9 + 3√15/4
- 7 + 2√2

ABCD is a rectangle. The diagonals AC and BD intersect at O. If AB = 32 cm and AD = 24 cm, then what is OD equal to?

- 22 cm
- 20 cm
- 18 cm
- 16 cm

The radius of a circle is increased so that its circumference increases by 15%. The area of the circle will increase by

- 31.25%
- 32.25%
- 33.25%
- 34.25%

Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is

- 950
- 1000
- 1050
- 1100

In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA to OC equal to?

- Ratio of OB to OD
- Ratio of BC to CD
- Ratio of AD to AB
- Ratio of AC to BD

If the surface area of a sphere is reduced to one-ninth of the area, its radius reduces to

- One-fourth
- One-third
- One-fifth
- One-ninth

A copper wire when bent in the form of a square encloses an area of 121 cm^{2}. If the same wire is bent in the form of a circle, it encloses an area equal to

- 121 cm
^{2} - 144 cm
^{2 } - 154 cm
^{2} - 168 cm
^{2}

If the radius of a right circular cone is increased by p% without increasing its height, then what is the percentage increase in the volume of the cone?

- p
^{2 } - 2p
^{2} - p
^{2}/100 - p(2 + p/100)

The area of a regular hexagon of side 'a' is equal to

- √2/3 a
^{2}square units - 3√3/2 a
^{2}square units - 1/3 a
^{2}square units - √3/2 a
^{2}square units

Three circles each of radius 3.5 cm touch one another. The area subtended between them is

- 6(√3π - 2) square units
- 6(2π - √3) square units
- 49/8 (2√3 - π) square units
- 49/8 (√3 - π) square units 8

A ball of radius 1 cm is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is 14 m, what is the surface area of the pipe?

- 2200 square cm
- 4400 square cm
- 8800 square cm
- 17600 square cm

If the perimeter of a rectangle is 10 cm and the area is 4 cm^{2}, then its length is

- 6 cm
- 5 cm
- 4.5 cm
- 4 cm

If 3 sin x + 5 cos x = 5, then what is the value of (3 cos x – 5 sin x)?

- 0
- 2
- 3
- 5

If tan (A + B) = √3 and tan A = 1, then tan (A - B) is equal to

- 0
- 1
- 1/√3
- √2

The angles of elevation of the top of a tower from two points situated at distance 36 m and 64 m from its base and in the same straight line with it are complementary. What is the height of the tower?

- 48 m
- 30 m
- 25 m
- 24 m

If 2 cot θ = 3, then what is the value of (2 cos θ - sin θ) / (2 cos θ + sin θ)?

- 1/3
- 1/2
- 3/4
- 2/3

The value of cosec^{2} 67 + sec^{2} 57 - cot^{2} 33 - tan^{2} 23 is

- 2√2
- 2
- √2
- 0

If tan A + cot A = 4, then tan^{4} A + cot^{4} A is equal to

- 194
- 191
- 110
- 80

The angle of elevation of the tip of a tower from a point on the ground is 45°. Moving 21 m directly towards the base of the tower, the angle of elevation changes to 60°. What is the height of the tower, to the nearest meter?

- 48 m
- 49 m
- 50 m
- 51 m