CDS 2016 Maths Question Paper -2

What is the solution of

x = 100
x = 10
x = 1
x = 0

If λ is an integer and α,β are the roots of 4x² – I6x + λ/4 = 0 such that 1 <α < 2 and 2 < β < 3, then how many values can λ take ?

What is equal to

If x²=y + z, y²=z+x and z²=x+y, then what is the value of

-1
1
2
4

What would be the maximum value of Q in the equation 5P9 + 3R7 + 2Q8 = 1114?

A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves” the remainder 1,2, 3,4 and 5 respectively. How many integers between and 100 belong to the set A ?

No integer
One
Two
Three

In an examination, a student was asked to divide a certain number by 8. By mistake he multiplied it by 8 and got the answer 2016 more than the correct answer. What was the number?

In the quadratic equation x²+ax + b = 0, a and b can take any value from the set {1, 2, 3, 4}. How many pairs of values of a and b are possible in order that the quadratic equation has real roots ?

The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, then what is the difference of the larger and smaller numbers ?’

Let A = {7, 8, 9, 10, 11, 12} and B = {7, 10, 14, 15}. What is the number of elements in (A-B) and (B~A)
respectively ?

2 and 4
4 and 2
2 and 2
4 and 4

A boy saves Rs. 4.65 daily. What is the least number of days in which he will be able to save an exact number of rupees ?

Two men, A and B run a 4 km race on a course 0.25 km round. If their speeds are in the ratio 5 : 4, how often does the winner pass the other ?

Once
Twice
Thrice
Four times

Which one of the following rational numbers has non-terminating and repeating decimal expansion ?

15/1600
23/8
35/50
17/6

If α and β are the two zeros of the polynomial 25x² – 15x + 2, then what is a quadratic polynomial whose zeros are (2 α)^-1 and (2 β)^-1?

x² + 30x + 2
8x²-30x + 25
8x²-30x
x²+ 30x

What is the remainder when 2100 is divided by 101 ?

In an office, one-third of the workers are women, half of the women are married and one-third of the married women have children. If three-fourth of the men are married and one-third of the married men have children, then what is the ratio of married women to married men ?

A can do 50% more work than B in the same time. B alone can do a piece of work in 30 hours. B starts working and had already worked for 12 hours when A joins him. How many hours should
B and A work together to complete the remaining work ?

6 hours
12 hours
8 hours
2 hours

When the speed of a train is increased by 20%, it takes 20 minutes less to cover the same distance. What is the time taken to cover the same distance with the original speed ?

140 minutes
120 minutes
100 minutes
80 minutes

A candidate scoring x% marks in an examination fails by a marks, while another candidate who scores y% marks gets b marks more than the minimum required pass marks. What is the maximum marks for the examination ?

100(a+b)/x-y
100 (a-b)/x+y
100(a+b)/y-x
100(a-b)/x-y

If p and q are the roots of x²+px + q = 0, then which one of the following is correct ?

P= 0 or 1
P = 1 only
P =-2 or 0
P= -2 only

The cost of 2.5 kg rice is Rs. 125. The cost of 9 kg rice is equal to that of 4 kg pulses. The cost of 14 kg pulses is equal to that of 1.5 kg tea. The cost of 2 kg tea is equal to that of 5 kg nuts. What is the
cost of 11 kg nuts ?

2310
3190
4070
4620

Which one of the following is correct in respect of the number 1729 ?

It cannot be written as the sum of the cubes of two positive integers
It can be written as the sum of the cubes of two positive integers in one way only
It can be written as the sum of the cubes of two positive integers in two ways only
It can be written as the sum of the cubes of two positive integers in three ways only

A shopkeeper increases the cost price of an item by 20% and offers a discount of 10% on this marked price. What is his percentage gain ?

There are two numbers p and q such that their HCF is 1. Which of the following statements are correct ?
Both p and q may be prime.
One number may be prime and the other composite.
Both the numbers may be composite.

Select the correct answer using the code given below:

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

What is

2008-1/2008
2007-1/2007
2007-1/2008
2008-1/1009

A person can row downstream 20 km in hours and upstream 4 km in 2 hours. What is the speed of the current ?

2 km/hour
5 km/hour
3 km/hour
4 km/hour

Consider the following statements in respect of positive odd integers x and y :
x²+ y² is even integer.
x²+y²is divisible by 4.

Which of the above statements is/are correct ?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

What are the roots of the equation

There are twelve friends A, B, C, D, E, F, G, H, I, J, K and L who invested money in some business in the ratio of : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 10 : 11 : 12 and the duration for which they invested the money is in the ratio of : 11 : 10 : 9 : 8 : 7 : 6 : 5 : 4 : 3 : 2 : 1 respectively. Who will get the maximum profit at the end of the year ?

F only
G only
Both F and G
Neither F nor G

2¹²² + 4⁶²+ 8⁴² + 4⁶⁴ + 2¹³⁰ is divisible by which one of the following integers ?

If 2p + 3q = 12 and 4p²+ 4pq -3q² = 126, then what is the value of p + 2q ?

5
21/4
25/4
99/16

The number of digits in 3³⁰ is n and it is given that log₁₀ 3 =0.4771. What is the value of n ?

What is the unit digit of 7¹³⁹ ?

If 4x + 3a = 0, then what is the value of

-4/7a
7/a
-32/7a
24/7a

Incomes of Mahesh and Kamal are in the ratio 1 : 2 and their expenses are in the ratio 1:3. Which one of the following statements is correct?

Mahesh saves more than what Kamal saves
Savings of both of them are equal
Kamal saves more than what Mahesh saves
It is not possible to determine who saves more

X and Y entered into partnership with Rs. 700 and Rs. 600 respectively. After months X withdrew 2/7 of his stock but after 3 months, he puts back 3/5 of what he had withdrawn. The profit at the end of the year is Rs. 726. How much of this should X receive ?

A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10 a.m. pipe X was opened. At what time will the tank be filled if pipe Y is opened at 11 a.m. ?

12:45 hours
5:00 p.m.
11:45 a.m.
11:50 a.m.

A train is travelling at 48 km/hour completely crosses another train having half its length and travelling in opposite direction at 42 km/hour in 12 s. It also passes a railway platform in 45 s. What
is the length of the platform ?

600 m
400 m
300 m
200 m

The speeds of three cars are in the ratio 2:3:4. What is the ratio between the times taken by these cars to travel the same distance ?

4:3:2
2:3:4
4:3:6
6:4:3

If the mean age of combined group of boys and girls is 18 years and the mean of age of boys is 20 and that of girls is then what is the percentage of boys in the group ?

The area of four walls of a room is 120 m² . The length of the room is twice its breadth. If the height of the room is 4m, what is area of the floor ?

40 m²
50 m²
60 m²
80 m²

If a square of side x and an equilateral triangle of side y are inscribed in a circle, then what is the ratio of x to y ?

The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. If the total surface area is 616 cm², what is the volume of the cylinder ?

539 cm³
616 cm³
1078 cm³
1232 cm³

A cubic metre of copper weighing 9000 kg is rolled into a square bar 9 m long. An exact cube is cut off from the bar. How much does the cube weigh ?

1000 kg
1000/3 kg
300 kg
500/3 kg

Into a conical tent of radius 8.4 m and vertical height 3.5 m, how many full bags of wheat can be emptied, if space required for the wheat in each bag is 1.96 m3 ?

Let ABC be a right angled triangle with BC — 5 cm and AC = 12 cm. Let D be a point on the hypotenuse AB such that ∠BCD – 30°. What is length of CD ?

60/13 cm
17/2 cm

Two circles touch externally and sum of their areas is 130π cm² and the distance between their centres is 14 cm. What is the difference in the radii of the circles ?

5 cm
6 cm
7 cm
8 cm

In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP>BP, then what is the ratio of AP to BP ?

What is the number of rounds that a wheel of diameter 5/11m will make in traversing 7 km ?

3300
3500
4400
4900

A building is in the form of a cylinder surmounted by a hemispherical dome on the diameter of the cylinder. The height of the building is three times the radius of the base of the cylinder. The building contains 67 1/21 m³of air. What is the height of the building ?

The radius of the base and the height of a solid right circular cylinder are in the ratio 2 : 3 and its volume is 1617 cm³. What is the total surface area of the cylinder ?

462 cm²
616 cm²
770 cm²
786 cm²

The cost of painting a spherical vessel of diameter 14 cm is Rs. 8008. What is the cost of painting per square centimetre ?

If a quadrilateral has an inscribed circle, then the sum of a pair of opposite sides equals

Half the sum of the diagonals
Sum of the other pair of opposite sides
Sum of two adjacent sides
None of the above

A circle and a square have the same perimeter. Which one of the following is correct ?

Their areas are equal
The area of the circle is larger
The area of the square is π/2 times area of circle
The area of the square is π times area of circle

A drinking glass of height 24 cm is in the shape of frustum of a cone and diameters of its bottom and top circular ends are 4 cm and 18 cm respectively. If we take capacity of the glass as x cm³, then what is the value of x ?

824
1236
1628
2472

In an equilateral triangle another equilateral triangle is drawn inside joining the mid-points of the sides of given equilateral triangle and the process is continued up to 7 times. What is the ratio of area of fourth triangle to that of seventh triangle ?

256 : 1
128 : 1
64 : 1
16 : 1

Rain water from a roof 22 m x 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the vessel is just full, what is the rainfall ?

5cm
3 cm
5cm
2 cm

The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base and its volume is 1/64 the volume of original cone. What is the height from the base at which the section is made ?

15 cm
20 cm
30 cm
45 cm

If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then what is the length of each tangent ?

3√3 cm
√3 cm
6 cm
2√2 cm

What is the volume of a sphere of radius 3 cm ?

36π cm3
19π cm3
9π cm3
6π cm3

The sides of a triangle are given by and (b + c) where b, c are positive. What is the area of the triangle equal to ?

What is area of largest triangle inscribed in a semi-circle of radius ϒ units ?

ϒ2 square units
2ϒ2 square units
3ϒ2 square units
4ϒ2 square units

The diameter of the front wheel of an engine is 2x cm and that of rear wheel is 2y cm. To cover the same distance, what is the number of times the rear wheel revolves when the front wheel revolves n times ?

n/xy
ny/x
nx/y
xy/n

For the next three (03) items that follow :

A tent of a circus is made of canvas and is in the form of right circular cylinder and right circular cone above it. The height and diameter of the cylindrical part of the tent are m and 126 m respectively, The total height of the tent is 21m.

What is the slant height of the cone ?

60 m
65 m
68 m
70 m

What is the curved surface area of the cylinder ?

1980 m²
2010 m²
2100 m²
2240 m²

How many square metres of canvas are used ?

14450
14480
14580
14850

The wheels of a car are of diameter 80 cm each. The car is travelling at a speed of 66 km/hour. What is the number of complete revolutions each wheel makes in 10 minutes ?

4275
4350
4375
4450

What is the area of a triangle with sides of length 12 cm, 13 cm and 5 cm ?

30 cm²
35 cm²
40 cm²
42 cm²

If the perimeter of a circle is equal to that of a square, then what is the ratio of area of circle to that of square ?

22:7
14:11
7:22
11:14

ABCDA is a con-cyclic quadrilateral of a circle ABCD with radius r and centre at O. If AB is the diameter and CD is parallel and half of AB and if the circle completes one rotation about the centre O, then the locus of the middle point of CD is a circle of radius

If sinθ + sinθ =√7/2 , then what is the value of sinθ-cosθ equal to ?

0
1/2
1
√2

If sin x +sin² x =1,than what is the value of cos⁸x +2 cos⁶ x + cos⁴x?

A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression 30°. After some time, the angle of depression becomes 60°. What is the distance
travelled by the car during this time ?

100√3 m
200√3/3 m
100√3/3 m
200√3 m

Two men on either side of a tower 75 m high observe the angle of elevation of the top of the tower to be 30° and 60°. What is the distance between the two men ?

100√3 m
75√3 m
100√3/3 m
60√3 m

What is the value of cosec²68° + sec²56° – cot²34° – tan²22° ?

If 2y cosθ = x sinθ and 2x secθ – y cosecθ = 3, then what is x² + 4y²equal to ?

If sinθ + cosθ =1+√3/2 where 0<θ<π/2 ,then what is tanθ + cotθ equal to ?

√3/4
1/√3
√3
4/√3

If A= sin² θ+ cos⁴ θ where 0≤θ<π/2 ,then which one of the following is correct ?

Consider the following :
sin 1° > sin l^c
cos 1° < cos l^c
tan 1° > tan l^c

Which of the above are not correct ?

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

If tan² x+ 1/tan²x= 2 and 0°<x<90°, then what is the value of x ?

15°
30°
45°
60°

If the length of the shadow of a tower is equal to its height, then what is the Sun’s altitude at that time ?

15°
30°
45°
60°

Consider the following :

Which of the above are correct ?

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

A pole stands vertically inside a triangular park ABC. If the angle of elevation of the top of the pole from each comer of the park is same, then in the triangle ABC, the foot of the pole is at the

Centroid
Circumference
Incentre
Orthocentre

What is the value of tanl°tan20tan30tan4° . .. tan89° ?

0
1
2
√3

The average score of class X is 83.
The average score of class Y is 76.
The average score of class Z is 85.
The average score of class X and Y is 79
and average score of class Y and Z is 81.
What is the average score of X, Y and Z ?

For x>0, if a variable takes discrete values x + 4, X- 3.5, x -2.5, x -3, x – 2, x + 0.5, x -0.5, x + 5, then what is the median ?

x-1.25
x-0.5
x + 0.5
x+ 1.25

The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

is increased by 2
is decreased by 2
is two times the original median
remains the same as that of original set

A cricketer has a certain average of 10 innings. In the eleventh inning he scored 108 runs, thereby increasing his average by 6 runs. What is his new average ?

The mean of 20 observations is 17. On checking it was found that the two observations were wrongly copied as and 6. If wrong observations are replaced by correct values 8 and 9, then what is the correct mean ?

Number of credit cards held by an individual can be treated as

Qualitative data
Discrete data
Categorical data
None of the above

In a class of 100 students, there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls ?

A pie chart depicts the classification of total funds of an organization according to different sources of funds. A particular sector of pie chart for corporate tax has 108° angle at’ the centre. What is the percentage of income from corporate tax to total funds ?

Consider the following statements
The classes of type 15-19, 20-24, 25-29 etc. are exclusive classes.
The classes of type 15-20, 20-25, 25-30 etc. are inclusive classes.

Which of the above statements is/are correct ?

1 only
2 only
Both I and 2
Neither 1 nor 2

Suppose the class interval 10-15 has frequency 30, then what is the frequency density of this class interval ?

Let S be a set of first ten natural numbers. What is the possible number of pairs (a, b) where a, b ∈ S and a ≠ b such that the product ab (>12) leaves remainder 4 when divided by 12 ?

What is the remainder when 13⁵+14⁵+15⁵+16⁵is divided by 29 ?

What is the difference between the sum of the cubes and that of squares of first ten natural numbers ?

2280
2640
3820
4130

A motorist travels to a place 150 km away at an average speed of 50 km/hour and returns at 30 km/hour. What is the average speed for the whole journey ?

35 km/hour
37 km/hour
5 km/hour
40 km/hour

equal to?

7/10
13/10
11/10
17/10