CDS 2012 Maths Question Paper -2

A cloth store is offering “Buy 3, get 1free”. What is the net percentage discount being offered by the store ?

20%
25%
30%
33 1/3%

X can do a piece of work in 25 days. Y is 25% more efficient than X. The number of days taken by Y is :

15 days
20 days
21 days
30 days

A train takes 10 s to cross a pole and 20 s to cross a platform of length 200 m. What is the length of the train ?

400 m
300 m
200 m
100 m

A sum of money becomes 3 times in 5 years. In how many years will the same sum become 6 times at the same rate of simple interest ?

15 years
5 years
10 years
5 years

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

500
700
800
1000

45 people take 18 days to dig a pond. If the pond would have to be dug in 15 days, then the number of people to be employed will be :

A merchant earns a profit of 20% by selling a basket containing 80 apples which cost Rs. 240. But he gives one-fourth of it to his friend at cost price and sells the remaining apples. In order to earn the same profit, at what price must he sell each apple ?

3.00
3.60
3.80
4.80

The least number of four digits which is a perfect square is :

1204
1024
1402
1420

Consider the following statements :
Every integer is a rational number.
Every rational number is a real number.

Which of the above statements is/are correct ?

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

The product of HCF and LCM of 18 and 15 is :
- 120
- 150
- 175
- 270
What is 3 x 0.3 x 0.03 x 0 .003 x 0.0003 x 30 equal to ?
- (0.09)³
- (0. 009)³
- (0.0009)³
- None of the above
What is 0.242424 equal to ?
- 23/99
- 8/33
- 7/33
- 47/198
A and B can do a piece of work in 10 hours. B and C can do it in 15 hours, while A and C take 12 hours to complete the work. B independently can complete the work in :
- 12 hours
- 16 hours
- 20 hours
- 24 hours
The sum of the squares of two numbers is 97 and the square of their difference is 25. The product of the two numbers is :
- 45
- 36
- 54
- 63
Age of X is six times that of Y. After 4 years, X is four times elder to Y. What is the present age of Y ?
- 4 years
- 5 years
- 6 years
- 7 years
A milkman bought 15 kg of milk and mixed 3 kg of water in it. If the price per kg of the mixture becomes Rs. 22, what is cost price of the milk per kg ?

28.00
26.40
24.00
22.60

What is 5% of 50% of 500 ?
- 5
- 25
- 25
- 25
Which one of the following has least number of divisors ?
- 88
- 91
- 96
- 99
A man buys a television set which lists for Rs. 5,000 at 10% discount. He gets an additional 2% discount (after the first discount) for paying cash. What does he actually pay for the set ?
- 4,410
- 4,400
- 4,000
- 4,500
Sex ratio is defined as the number of females per 1000 males. In a place the total inhabitants are 19,35,000 out of which 9,35,000 are females. What is the sex ratio for the place ?
- 935
- 1000
- 1935
- 9350
A car is traveling at a constant rate of 45 km per hour. The distance travelled by car from 10.40 am to 1.00 pm is :
- 165 km
- 150 km
- 120 km
- 105 km
A number consists of two digits whose sum is 8. If 18 is added to the number, the digits are reversed. The number is equal to :
- 26
- 35
- 53
- 62
If log₁₀ a = p and log₁₀ b = q, then what is log₁₀ (a^p b^q) equal to ?
- p² + q²
- p² – q²
- p²q²
- P²/q²

If two factors of a⁴ – 2a³ – 9a² + 2a + 8 are (a + 1) and (a – 1), then what are the other two factors ?

(a – 2) and (a+4)
(a + 2) and (a+4)
(a + 2) and (a-4)
(a – 2) and (a-4)

The price of an article is Rs. 25. After two successive cuts by the same percentage, the price becomes Rs. 20.25. If each time the cut was x%, then :
- x = 9
- x = 10
- x = 11
- x = 11.5
If 0.764 y = 1.236 x, then what is the value of y-x/y+x ?

What is the value of
- 730
- 4
- 5
- 247
Three planets revolve round the sun once in 200, 250, 300 days respectively in their own orbits. When do they all come relatively to the same position as at a certain point of time in their orbits ?
- After 3000 days
- After 2000 days
- After 1500 days
- After 1200 days
What is the greatest number that divides 13850 and 17030 and leaves a remainder 17 ?
- 477
- 159
- 107
- 87
If the sum of an integer and its reciprocal is 10/3, then the integer is equal to :
- 3
- 6
- 12
- 13
Let x ∈{2, 3, 4} and y ∈ {4, 6, 9, 10}. Let A be the set of all order pairs (x, y) such that x is a factor of y. How many elements does the set A contain ?
- 12
- 10
- 7
- 6
Which one of the following is a null set ?

A = { x is a real number : x > 1 and x < 1 }
B={x:x+3=3}
C = {Φ }
D = { x is a real number : x ≥ 1 and x ≤1 }

If (x – 6) is the HCF of x² – 2x – 24 and x² – kx – 6, then what is the value of k ?
- 3
- 5
- 6
- 8
If the expression x³ + 4x² + 4x + k has (x + 4) as a factor, then what is the value of k ?
- -16
- 16
- 32
- -32
If 4, then what is x equal to ?
- 150
- 216
- 316
- 450
Which one of the following is neither prime number nor composite number ?
- 1
- 2
- 3
- None of the above
Consider the following table :

How are x and y related ?

y = 100 – l0x
y = 100 – 5x²
y = 20 – x – x²
y = 100 – 5x – 5x²

If a/b-b/a=x/y and a/b+ b/a = x-y , then what is x equal to ?

a + b/a
a+b/b
a-b/a
None of the above

The quadratic equation whose roots are 3 and -1 is :
- x² – 4x + 3 = 0
- x² – 2x -3 = 0
- x² + 2x – 3 = 0
- x² + 4x + 3 = 0
Consider the following statements :
If n is a prime number greater than 5, then n⁴ – 1 is divisible by 2400.
Every square number is of the form 5n or (5n – 1) or (5n + 1) where n is a whole number.

Which of the above statements is/are correct ?

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

What is the value of k which will make the expression 4k² + 12k + k a perfect square ?
- 5
- 7
- 8
- 9
If one root of the equation x²/a+x/b+1/c= 0 is reciprocal of the other, then which one of the following is correct ?
- a = b
- b = c
- ac = 1
- a = c
If f(x) is a polynomial with constant term 10 having a factor (x – k) where k is an integer, then what is the possible value of k ?
- -20
- 20
- 8
- 5
If a = 2 +√3 , then what is the value of (a² + a^-2) ?
- 12
- 14
- 16
- 18

If x + y = 9 and xy = 8, then what is one of the values of (x⁴ – y⁴) ?
- 4025
- 4065
- 4095
- 4905

There are some benches in a class room having the number of rows 4 more than the number of columns. If each bench is seated with 5 students, there are two seats vacant in a class of 158 students. The number of rows is :
- 4
- 8
- 6
- 10
If tan θ- 3/4 and θ is acute, then what is sinθ equal to ?
- -3/5
- 3/5
- 4/5
- -4/5
What is the value of sec(90° – θ). sinθ sec 45° ?
- 1
- √3/2
- √2
- √3
On walking 120 m towards a chimney in a horizontal line through its base the angle of elevation of tip of the chimney changes from 30° to 45°. The height of the chimney is :
- 120 m
- 60( √3-l)m
- 60( √3+l)m
- None of the above
If an angle measures p degrees and q radians, then which one of the following is correct ?
- πp = 90q
- πp = 360q
- πp = 180q
- πq = 180p
If the angle θ is in the first quadrant and tan θ= 3, then what is the value of (sin θ + cosθ ) ?
- 1/√10
- 2/√10
- 3/√10
- 4/√10

A wheel makes 12 revolutions per minute. The angle in radian described by a spoke of the wheel in 1 second is :
- 5π /2
- 2 π/5
- 3π /5
- 4π /5
A ladder 20 m long is placed against a wall so that the foot of the ladder is 10 m from the wall. The angle of inclination of the ladder to the horizontal will be :
- 30°
- 45°
- 60°
- 75°
If 0 <θ < 90°, then all the trigonometric ratios can be obtained when :
- only sinθ is given
- only cos θ is given
- only tan θ is given
- any one of the six ratios is given
What is sin A cos A tan A + cos A sin A cot A equal to ?
- sin²A + cosA
- sin²A + tan²A
- sin²A + cot²A
- cosec²A – cot²A
What is sinθ /1+cosθ +1+cosθ /sinθ equal to ?
- 2 cosecθ
- 2 secθ
- secθ
- cosecθ
The angles of elevation of the top of a tower from two points which are at distances of 10 m and 5 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is :
- 5 m
- 15m
- √50 m
- √75 m
The angles of elevation of the top of an inaccessible tower from two points on the same straight line from the base of the tower are 30° and 60° respectively. If the points are separated at a distance of 100 m, then the height of the tower is close to :
- 6 m
- 6 m
- 6 m
- 6 m
If sinθ cos θ= √3 /4, then the value of sin⁴ θ + cos⁴ θ is :
- 7/8
- 5/8
- 3/8
- 1/8
The locus of a point in rhombus ABCD which is equidistant from A and C is :
- a fixed point on diagonal BD
- diagonal BD
- diagonal AC
- None of the above
In a triangle ABC, ½ ∠A+1/3 ∠C+ ½ ∠B = 80°; then what is ∠C equal to ?
- 35°
- 40°
- 60°
- 70°
In a triangle ABC, ∠BCA = 60° and AB² = BC² + CA²+ X. What is X equal to ?
- (BC)(CA)
- – (BC)(CA)
- (AB)(BC)
- Zero
Consider the following statements :
The locus of points which are equidistant from two parallel lines is a line parallel to both of them and drawn midway between them.
The perpendicular distances of any point on this locus line from two original parallel lines are equal. Further, no point outside this locus line has this property.

Which of the above statements is/are correct ?

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

If the diagonals of a quadrilateral are equal and bisect each other at right angles, then the quadrilateral is a :

rectangle
square
rhombus
trapezium

If two parallel lines are cut by two distinct transversals, then the quadrilateral formed by the four lines is always a :

square
parallelogram
rhombus
trapezium

ABCD is a parallelogram. If the bisectors of the angle A and angle C meet the diagonal BD at points P and Q respectively, then which one of the following is correct ?

PCQA is a straight line
Triangle APQ is similar to triangle PCQ
AP = CP
AP = AQ

Let X be any point within a square ABCD. On AX a square AXYZ is described such that D is within it. Which one of the following is correct ?

AX = DZ
∠ADZ = ∠BAX
AD = DZ
BX = DZ

In a triangle ABC, XY is drawn parallel to BC, cutting sides at X and Y where AB = 4.8 cm, BC = 7.2 cm, BX = 2 cm. What is the length of XY ?

4 cm
1 cm
2 cm
3 cm

Let ABC be a triangle with AB = 3 cm, AC = 5 cm. If AD is a median drawn from the vertex A to the side BC, then which one of the following is correct ?

AD is always greater than 4 cm but less than 5 cm
AD is always greater than 5 cm
AD is always less than 4 cm
None of the above

Consider the following statements :
Area of a segment of a circle is less than area of its corresponding sector.
Distance traveled by a circular wheel of diameter 2d cm in one revolution is greater than 6d cm.

Which of the above statements is/are correct ?

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

The angles x°, a°, c° and (π – b)° are indicated in the figure given above. Which one of the following is correct ?
- x = a + c – b
- x = b – a – c
- x = a + b + c
- x = a – b + c
In the figure given above YZ is parallel to MN, XY is parallel to LM and XZ is parallel to LN. Then MY is :
- the median of triangle LMN
- the angular bisector of ∠LMN
- perpendicular to LN
- perpendicular bisector of LN
In the figure given above, AB is parallel to CD. ∠ABC = 65°, ∠CDE = 15° and AB = AE. What is ∠AEF equal to ?
- 30°
- 35°
- 40°
- 45°
In the figure given above AEC is a triangle. BC is parallel to AE. If BC = AC, then what is ∠CAE equal to ?

20°
30°
40°
50°

In the figure given above EC is parallel to AB, ∠ECD – 70° and ∠BDO = 20°. What is ∠OBD equal to ?
- 20°
- 30°
- 40°
- 50°
In the figure given above, LOM is a straight line. What is x equal to?
- 45
- 60
- 70
- 80
What is the volume of the largest sphere that can be carved out of a cube of edge 3 cm ?
- 9π cubic cm
- 6π cubic cm
- 4.5π cubic cm
- 37π cubic cm
If the ratio of the diameters of two spheres is 3 : 5, then what is the ratio of their surface areas ?
- 9 : 25
- 9 : 10
- 3:5
- 27
What is the height of a solid cylinder of radius 5 cm and total surface area is 660 cm²?

10 cm
12 cm
15 cm
16 cm

The diameter of base of a right circular cone is 7 cm and slant height is 10 cm, then what is its lateral surface area ?

110 square cm
100 square cm
70 square cm
49 square cm

The perimeter of a rectangle is 82 m and its area is 400 m². What is the breadth of the rectangle ?

18m
16 m
14 m
12 m

The area enclosed between the circumferences of two concentric circles is 16 cm² and their radii are in the ratio 5:3. What is the area of the outer circle ?

9π cm²
16π cm²
25π cm²
36π cm²

The volume of a cube is numerically equal to sum of its edges. What is the total surface area in square units ?

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops ?

13m
17 m
18m
23 m

A right circular metal cone (solid) is 8 cm high and the radius is 2 cm. It is melted and recast into a sphere. What is the radius of the sphere ?

2 cm
3 cm
4 cm
5 cm

The sum of the perpendiculars drawn from an interior point of an equilateral triangle is 20 cm. What is the length of side of the triangle ?

40/√3 cm
40√3 cm
20√3 cm
20/√3 cm

Let the largest possible right circular cone and largest possible sphere be fitted into two cubes of same length. Let C and S denote the volume of cone and volume of sphere respectively, then which one of the following is correct ?
- C = 2S
- S = 2C
- C = S
- C = 3S
The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by :
- 30%
- 31%
- 25%
- 75%
If the circumference of a circle is equal to the perimeter of square, then which one of the following is correct ?
- Area of circle = Area of square
- Area of circle ≥ Area of square
- Area of circle > Area of square
- Area of circle < Area of square
10 circular plates each of thickness 3 cm each are placed one above the other and a hemisphere of radius 6 cm is placed on the top just to cover the cylindrical solid. What is the volume of the solid so formed ?
- 264π cubic cm
- 252π cubic cm
- 236π cubic cm
- None of the above
The circumferences of two circles are in the ratio 2:3. What is the ratio of their areas ?
- 2:3
- 4:9
- 1:3
- 8 : 27
The area of a circle inscribed in an equilateral triangle is 154 cm2. What is the perimeter of the triangle ?
- 21 cm
- 42√3 cm
- 21√3 cm
- 42 cm
The lengths of three line segments in cm are given in each of the four cases. Which one of the following cases is not suitable to be the three sides of a triangle ?
- 2,3,4
- 2, 3, 5
- 2,4,5
- 3, 4, 5
In histogram the width of the bars is proportional to :
- frequency
- number of classes
- class interval
- None of the above
Which one of the following relations for the numbers 10, 7, 8, 5, 6, 8, 5, 8, 6 is correct ?

Mean = Median
Mean = Mode
Mean > Median
Mean > Mode

What is the harmonic mean of 10, 20, 25, 40 and 50 ?

The mean weight of 150 students in a class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What is the number of boys in the class ?

The mean of 100 values is 45. If 15 is added to each of the first forty values and 5 is subtracted from each of the remaining sixty values, the new mean becomes :

Which of the following is/are correctly matched ?
Weight of a person : Continuous variable
Educational qualification of the person : Attribute

Select the correct answer using the code given below :

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

Consider the following distribution :

For what value of f, is the arithmetic mean of the above distribution 3.1 ?