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

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

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

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 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

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%

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

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

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

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

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

- 60°
- 48°
- 45°
- 36°

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

- 26°
- 28°
- 38°
- 52°

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

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

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

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

In the figure given, LM is parallel to QR. If LM divides the triangle PQR such that area of trapezium LMRQ is two times the area of triangle PLM, then what is PL/PQ equal to?

- 1/3
- 1/√2
- 1/√3
- 1/2

In histogram the width of the bars is proportional to

- number of classes
- class interval
- cumulative frequency
- frequency

What is the angle of elevation of the sun when the shadow of a pole is √3 times the length of the pole?

- 30°
- 45°
- 60°
- 75°

If sin x + cos x = c, then sin^{6} x + cos^{6} x is equal to

- (1 + 6c
^{2}- 3c^{4})/16 - (1 + 6c
^{2}- 3c^{4})/4 - (1 + 6c
^{2}+ 3c^{4})/16 - (1 + 6c
^{2}+ 3c^{4})/4

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

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

- 194
- 191
- 110
- 80

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

- 2√2
- 2
- √2
- 0

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 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

In a certain school, the ratio of boys and girls is 7 : 5. If there are 2400 students in the school, then how many girls are there?

- 500
- 700
- 800
- 1000

Age of X is 6 times that of Y. After 4 years, X is 4 times elder to Y. What is the present age of Y?

- 4 yr
- 5 yr
- 6 yr
- 7 yr

Two numbers are in the ratio 3:5. If 9 is subtracted from each number, then they are in the ratio of 12:23. What is the second number?

- 44
- 55
- 66
- 77

A fruit-seller buys lemons at 2 for a rupee and sells them at 5 three rupees. What is his gain percent?

- 10%
- 15%
- 20%
- 25%