CDS Questions
A copper wire when bent in the form of a square encloses an area of 121 cm^2
A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent in the form of a circle, it encloses an area equal to
- 121 cm2
- 144 cm2
- 154 cm2
- 168 cm2
If the surface area of a sphere is reduced to one-ninth of the area
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
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
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 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
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. What is the area of the field
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
D is the diameter of each circle. What is the diameter of the shaded circle
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)
AC is parallel to ED and AB = DE = 5 cm and BC = 7 cm
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
What is the number of wax balls, each of radius 1 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
The diameter of a metallic sphere is 6 cm
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
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
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%
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 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
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
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
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
A gardener has 1000 plants. He wants to plant them in such a way
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 village having a population of 4000 requires 150 litres of water
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
What is the LCM of x^3 + 8, x^2 + 5x + 6 and x^3 + 4x^2 + 4x
What is the LCM of x3 + 8, x2 + 5x + 6 and x3 + 4x2 + 4x?
- x (x + 2)2 (x + 3) (x2 - 2x + 4)
- x (x - 2)2 (x - 3) (x2 + 2x + 4)
- (x + 2)2 (x + 3) (x2 - 2x + 4)
- (x - 2)2 (x - 3) (x2 - 2x + 4)
The HCF of two expressions p and q is 1. What is the reciprocal of their LCM
The HCF of two expressions p and q is 1. What is the reciprocal of their LCM?
- p + q
- p - q
- pq
- (pq)-1
The sum of two positive integers is 52 and their LCM is 168
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
The product of two numbers is 6912 and their GCD is 24
The product of two numbers is 6912 and their GCD is 24. What is their LCM
- 296
- 288
- 286
- 280
What is the HCF of 8(x^5 - x^3 + x) and 28(x^6 + 1)
What is the HCF of 8(x5 - x3 + x) and 28(x6 + 1)?
- (x4 + 1 - x2)
- 4(x4 + 1 - x2)
- 2(x4 + 1 - x2)
- None
If for integer a, b and c if HCF(a,b) = 1 and HCF(a,c) = 1
If for integer a, b and c if HCF(a,b) = 1 and HCF(a,c) = 1, then which one of the following is correct?
- HCF(a,bc) = a
- HCF(a,bc) = b
- HCF(a,bc) = 1
- None
What is the number of integral solutions of the equations
What is the number of integral solutions of the equations HCF(a,b) = 5 and a + b = 65?
- Exactly one
- Infinitely many
- Less than 65
- None
In a fire range, four shooters are firing at their respective targets
In a fire range, four shooters are firing at their respective targets. The first, the second, the third and the fourth shooter hit the target once in every 5, 6, 7 and 8 seconds respectively. If all of them hit the target at 9:00 am, when will they hit their target together again.
- 9:04 am
- 9:08 am
- 9:10 am
- 9:14 am
Three persons start walking together and their steps measure
Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
- 75 m 60 cm
- 50 m 40 cm
- 25 m 20 cm
- 75 m 60 cm
There are five hobby clubs in a college viz., photography, yachting, chess, electronics and gardening
There are five hobby clubs in a college viz., photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days?
- 5
- 3
- 18
- 10
The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0
The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 intersect each other, if
- k = 6
- k ≠ 6
- k = 0
- k ≠ 0
Leela got married 6 years ago. Today her age is 1¼ times her age at the time of her marriage
Leela got married 6 years ago. Today her age is 1¼ times her age at the time of her marriage. Her son’s age is 1/10 times her age. What is the present age of her son?
- 1 year
- 2 years
- 3 years
- 4 years
Sunil wants to spend Rs.200 on two types of sweets, costing Rs.7 and Rs.10 respectively
Sunil wants to spend Rs.200 on two types of sweets, costing Rs.7 and Rs.10 respectively. What is the maximum number of sweets he can get so that no money is left over?
- 25
- 26
- 27
- 28
The system of equations 2x + 4y = 6 and 4x + 8y = 8 is
The system of equations 2x + 4y = 6 and 4x + 8y = 8 is
- Consistent with a unique solution
- Consistent with infinitely many solutions
- Inconsistent
- None of the above
X paid Rs. 47 for certain cups of tea and coffee. If tea costs Rs. 5 per cup
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.
A person has only Rs. 1 and Rs. 2 coins with her
A person has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then the number of Rs. 1 and Rs. 2 coins are, respectively.
- 30 and 20
- 35 and 15
- 25 and 25
- 15 and 35
The cost of a diamond varies directly as the square of its weight
The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?
- ₹ 1,00,000
- ₹ 1,40,000
- ₹ 1,50,000
- ₹ 1,75,000
In a class of 49 students, the ratio of girls to boys is 4:3
In a class of 49 students, the ratio of girls to boys is 4:3. If 4 girls leave the class, the ratio of girls to boys would be
- 11:7
- 8:7
- 6:5
- 9:8
The ratio of two numbers is 1:5 and their product is 320
The ratio of two numbers is 1:5 and their product is 320. What is the difference between the squares of these two numbers?
- 1024
- 1256
- 1536
- 1640
The angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is
The angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is
- 20°
- 40°
- 50°
- 60°
The areas of two circular fields are in the ratio 16 : 49
The areas of two circular fields are in the ratio 16 : 49. If the radius of the bigger field is 14 m, then what is the radius of the smaller field?
- 4 m
- 8 m
- 9 m
- 10 m
In a certain school, the ratio of boys and girls is 7 : 5
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
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
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
The costs of two articles are in the ratio 3:5
The costs of two articles are in the ratio 3:5. If there is 30% loss on the first article and 20% gain on the second article, what is the overall percentage of loss or gain?
- 2% loss
- 2.25% gain
- 5.25% loss
- 1.25% gain
In a rare coin collection, there is one gold coin
In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1:2. Based on the information; the total number of corns in the collection now becomes
- 90
- 80
- 60
- 50
Two glasses of equal volume are respectively half and three-fourths filled
Two glasses of equal volume are respectively half and three-fourths filled with milk. They are then filled to the brim by adding water. Their contents are then poured into another vessel. What will be the ratio of milk to water in this vessel?
- 5:3
- 1:3
- 3:2
- 2:3
If a% of a + b% of b = 2% of ab, then what percent of a is b
If a% of a + b% of b = 2% of ab, then what percent of a is b?
- 50%
- 75%
- 100%
- Cannot be determined
5/9 th part of the population in a village are males. If 30% of the males are married
5/9 th part of the population in a village are males. If 30% of the males are married, the percentage of unmarried females in the total population is
- 20 2/9
- 27 2/9
- 27 7/9
- 29 2/9
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