If each of the dimensions of a rectangle is increased by 200%, the area is increased by

- 300%
- 400%
- 600%
- 800%

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

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

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

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)

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}

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

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

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

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

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%

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

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

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)

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, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to?

- 60°
- 75°
- 90°
- 100°

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, 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, 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, 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, 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

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

From an aeroplane vertically above a straight horizontal road, the angle of depression of two consecutive kilometer stones on the opposite sides of the aeroplane are found to be α and β. The height of the aeroplane above the road is

- (tan α + tan β) / (tan α tan β)
- (tan α tan β) / (tan α + tan β)
- (cot α cot β) / (cot α + cot β)
- (cot α + cot β) / (cot α cot β)

AB, CD and EF are three parallel lines, in that order. Let d_{1} and d_{2} be the distances from CD to AB and EF respectively. d_{1} and d_{2} are integers, where d_{1} : d_{2} = 2 : 1. P is a point on AB, Q and S are points on CD and R is a point on EF. If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?

- slightly less than 10 units
- 10 units
- slightly greater than 10 units
- slightly less than 20 units
- slightly greater than 20 units

If N = (11^{p + 7})(7^{q – 2})(5^{r + 1})(3^{s}) is a perfect cube, where p, q, r and s are positive integers, then the smallest value of p + q + r + s is:

- 5
- 6
- 7
- 8
- 9

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

- 30
- 25
- 20
- 15
- None of the above

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

- 5 years
- 6 years
- 7 years
- 8 years
- 9 years

Arup and Swarup leave point A at 8 AM to point B. To reach B, they have to walk the first 2 km, then travel 4 km by boat and complete the final 20 km by car. Arup and Swarup walk at a constant speed of 4 km/hr and 5 km/hr respectively. Each rows his boat for 30 minutes. Arup drives his car at a constant speed of 50 km/hr while Swarup drives at 40 km/hr. If no time is wasted in transit, when will they meet again?

- At 9.15 AM
- At 9.18 AM
- At 9.21 AM
- At 9.24 AM
- At 9.30 AM

A dice is rolled twice. What is the probability that the number in the second roll will be higher than that in the first?

- 5/36
- 8/36
- 15/36
- 21/36
- None of the above

A shop, which sold same marked price shirts, announced an offer - if one buys three shirts then the fourth shirt is sold at a discounted price of ₹100 only. Patel took the offer. He left the shop with 20 shirts after paying ₹20,000. What is the marked price of a shirt?

- ₹1260
- ₹1300
- ₹1350
- ₹1400
- ₹1500

Four two-way pipes A, B, C and D can either fill an empty tank or drain the full tank in 4, 10, 12 and 20 minutes respectively. All four pipes were opened simultaneously when the tank is empty. Under which of the following conditions the tank would be half filled after 30 minutes?

- Pipe A filled and pipes B, C and D drained
- Pipe A drained and pipes B, C and D filled
- Pipes A and D drained and pipes B and C filled
- Pipes A and D filled and pipes B and C drained
- None of the above

AB is a chord of a circle. The length of AB is 24 cm. P is the midpoint of AB. Perpendiculars from P on either side of the chord meets the circle at M and N respectively. If PM < PN and PM = 8 cm. then what will be the length of PN?

- 17 cm
- 18 cm
- 19 cm
- 20 cm
- 21 cm

The sum of series, (–100) + (–95) + (–90) + …………+ 110 + 115 + 120, is:

- 0
- 220
- 340
- 450
- None of the above

The sum of two positive integers is 52 and their LCM is 168. What is the ratio between the numbers?

- 2 : 3
- 5 : 4
- 7 : 6
- 7 : 8

What is the number of all possible positive integer values of n for which n^{2} + 96 is a perfect square?

- 2
- 4
- 5
- Infinite

The rabbit population in community A increases at 25% per year while that in community B increases at 50% per year. If the present populations of A and B are equal, what will he the ratio of the number of rabbits in community B to that in community A after 2 years?

- 1.44
- 1.72
- 1.90
- 1.26

The sum of two numbers is 143. If the greater number is divided by the difference of the numbers, the quotient is 7. What is the difference of the two numbers?

- 9
- 11
- 14
- 15

In a certain year, a school had 60% boys and 40% girls as students. In the next five years the number of boys decreased by 10% and the number of girls increased by 10%. What is the change in total roll strength of the school in the five years?

- 3% increase
- 2% decrease
- No change
- 5% decrease

X paid Rs. 47 for certain cups of tea and coffee. If tea costs Rs. 5 per cup and coffee costs Rs. 8 per cup, which one of the following statements is correct?

- He drank 8 cups of tea and coffee.
- He drank the same number of cups of tea and coffee.
- He drank more tea than coffee.
- He drank more coffee than tea.

How many times will the digit 5 come in counting from 1 to 99 excluding those which are divisible by 3?

- 16
- 15
- 14
- 13