CDS 2013 Maths Question Paper -2

The HCF of two numbers is 98 and their LCM is 2352. The sum of the numbers may be
- 1372
- 1398
- 1426
- 1484

Consider the following statements :
To obtain prime numbers less than 121, we are to reject all the multiples of 2f 3, 5 and 7.
Every composite number less than 121 is divisible by a prime number less than 11.

Which of the above statements is/are correct?

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

Which one is one of the factors of

x+1/x+1
x+1/x+3
x+1/x+6
x+1/x+7

What is the HCF of a²b⁴+2a²b² and (ab)⁷ -4a²b⁹ ?

ab
a²b³
a²b²
a³b²

What is the LCM of x²+2x-8, x³-4x² +4x and x² +4x?

x(x + 4) (x – 2)²
x(x +4)(x -2)
x(x + 4) (x + 2)²
x(x + 4)2 (x-2)

A can do a piece of work in 4 days and B can complete the same work in 12 days, What is the number of days required to do the same work together?

Consider the following statements :
x + 3 is the factor of x³ +2x²+ 3x+ 8
x – 2 is the factor of x³ +2x² + 3x + 8.

Which of the statements given above is/are correct?

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

A person sold an article for Rs.3,600 and got a profit of 20%. Had he sold the article for Rs.3,150, how much profit would he have got?
- 4%
- 5%
- 6%
- 10%
What is (x² + y²)(x- y)-(x- y)³ /x²y-xy² equal to?
- 1
- 2
- 4
- -2
If x + y- 7=0 and 3x + y-13 = 0, then what is 4x² + y² +4xy equal to?
- 75
- 85
- 91
- 100
If the expression x³+3x²+4x + k has a factor x + 5, then what is the value of k?
- -70
- 70
- 48
- -48
In a class of 110 students, x students take both Mathematics and Statistics, 2x+20 students take Mathematics and 2x + 30 students take Statistics. There are no students who take neither Mathematics nor Statistics. What is x equal to?

If x² =6 , then what-is one of the values of x equal to?
- 6
- 5
- 4
- 3
The quantity which must be added to (l-x)(l+x²) to obtain x³ is
- 2x ³ + 3x² + x + 1
- 2x³ +x² + x-1
- 2x³ -x² + x-1
- -x²+ x – 1
Consider the following statements :
7710312401 is divisible by 11.
173 is a prime number.

Which of the statements given above is /are correct?

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

19⁵ +21⁵ is divisible by

10 only
20 only
both 10 and 20
neither 10 nor 20

If (49)² – (25)²= 37x, then what is x equal to?

For what values of k will 4x⁵ + 9x⁴ -7x³ – 5x² -4kx + 3k² contain x – 1 as a factor?
- 3, -1/2
- 3, -1
- 0,1/3
- 1,1/3
x(y² -z²) + y(z² -x²) + z(x² – y⁷) is divisible by
- (y-z) only
- (z – x) only
- both (y-z) and (z-x)
- neither (y-z) nor (z-x)
If x/2+y/3=4 and 2/x+3/y=1 then what is x + y equal to?
- 11
- 10
- 9
- 8
A person’s salary has increased from Rs.7,200 to Rs.8,100. What is the percentage increase in his salary?

25%
18%
16 2/3%
12 1/2%

X can do a work in 16 days. In how many days will the work be completed by V if the efficiency of Y is 60% more than that of X ?

10 days
12 days
25 days
30 days

Two lots of onions with equal quantity, one costing Rs.10 per kg and the other costing Rs.15 per kg, are mixed together and whole lot is sold at Rs.15 per kg. What is the profit or loss?

10% loss
10% profit
20% profit
20% loss

For integers a, b and c, if HCF(a, b) = 1 and HCF(a, c) = 1, then which one of the following is correct?
- HCF(a, be) = 1
- HCF(a, be) = a
- HCF(a, be) = b
- None of the above
If b is the largest square divisor of c and a²divides c, then which one of the following is correct? (a, b, c are integers)

b divides a
a does not divide b
a divides b
a and b are co-prime

If k is a positive integer, then every square integer is of the form
- 4/c only
- 4k or 4fc + 3
- 4k + 1 or 4fc + 3
- 4k or 4k + 1
Every prime number of the form 3fc +1 can be represented in the form 6m + 1 (k, m are integers) when
- k is odd
- k is even
- k can be both odd and even
- No such form is possible
How many 200 mm lengths cut from 10 m of ribbon?

What is 26² + 97²equal to?

27² +93²
34² +93²
82² +41²
79²+62²

2 men and 1 woman can complete a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a man gets Rs.90 per day, what should be the wages per day of a woman?
- 48
- 60
- 72
- 135
Which is the smallest number among the following?
- [5^-2)^-2]^-2
- [(5^-2)²]^-2
- [(2^-5)^-2]^-2
- [(2^-5)²]^-2
What is the last digit in 7⁴⁰² + 3⁴⁰² ?
- 0
- 4
- 8
- None of the above
A train running at the speed of 72 kmph goes past a pole in 15 seconds. What is the length of the train?
- 150 m
- 200 m
- 300 m
- 350 m
18 men can earn Rs.360 in 5 days. How much money will 15 men earn in 9 days?
- 600
- 540
- 480
- 360
The pair of rational numbers that between ¼ and ¾ is

262/1000,752/ 1000
24/100,74/100
9/40,31/40
252/1000,748/ 1000

A bus starts with some passengers. At the first stop, one-fifth of the passengers gets down and 40 passengers get in. At the second stop, half of the passengers gets down and 30 get in. The number of passengers now is 70. The number of passengers with which the bus started was.
- 40
- 50
- 60
- 70
A can finish a work in 15 days, B in 20 days and C in 25 days. All these three worked together and earned Rs.4,700. The share of C is
- 1,200
- 1,500
- 1,800
- 2,000
If x is positive even integer and y is negative odd integer, then x^y is
- odd integer
- even integer
- rational number
- None of the above
Two cars A and B start simultaneously from a certain place at the speed of 30 km/hr and 45 km/hr respectively, The car B reaches the destination 2 hours earlier than A. What is the distance between the starting point and destination?
- 90 km
- 180 km
- 270 km
- 360 km
4 goats or 6 sheep can graze a field in 50 days. 2 goats and 9 sheep can graze the field in

100 days
75 days
50 days
25 days

A man cycles with a speed of 10 kmph and reaches his office at 1 p.m. However, when he cycles with a speed of 15 kmph, he reaches his office at 11 a.m. At what speed should he cycle so that he reaches his office at 12 noon?
- 5 kmph
- 12 kmph
- 13 kmph
- 5 kmph
20 workers working for 5 hours a day complete a work in 10 days. If 25 workers are employed to work 10 hours a day, what is the time required to complete the work?
- 4 days
- 5 days
- 6 days
- 8 days
If m and n are natural numbers, then m√n is

always irrational
irrational unless n is the mth power of an integer
irrational unless m is the nth power of an integer
irrational unless m and n are co-prime

Consider the following statements in respect of the quadratic equation ax² + bx + b = 0, where a ≠ 0 :
The product of the roots is equal to the sum of the roots.
The roots of the equation are always unequal and real.

Which of the above statements is/are correct?

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

If α and β are the roots of the equation x²-x -1= 0, then what is α²+ β ²/( α²+ β ²)(α – β) equal to?

2/5
3/5
4/5
None of the above

The perimeter of a rectangle having area equal to 144 cm² and sides in the ratio 4 : 9 is

52 cm
56 cm
60 cm
64 cm

Let A be a pyramid on a square base and B be a cube. Let a, b, c denote the number of edges, number of faces and number of corners respectively. Then the result a = b + c is true for
- A only
- B only
- both A and B
- neither A nor B
What is the area between a square of side 10 cm and two inverted semicircular cross-sections each of radius 5 cm inscribed in the square?

5 cm²
5 cm²
5 cm²
5 cm²

One side of a parallelogram is 8.06 cm and its perpendicular distance from opposite side is 2.08 cm. What is the approximate area of the parallelogram?

56 cm²
56 cm²
76 cm²
56 cm²

What is the volume of a cone having a base of radius 10 cm and height 21 cm?

2200 cm³
3000 cm³
5600 cm³
6600 cm³

What is the area of a circle whose area is equal to that of a triangle with sides 7 cm, 24 cm and 25 cm?
- 80 cm²
- 84 cm²
- 88 cm²
- 90 cm²
If the area of an equilateral triangle is x and its perimeter is y, then which one of the following is correct?
- y⁴ = 432x²
- y⁴ = 216x²
- y² = 432x²
- None of the above
A rectangular field is 22 m long and 10 m wide. Two hemispherical pitholes of radius 2 m are dug from two places and the mud is spread over the remaining part of the field. The rise in the level of the field is
- 8/93 m
- 13/93 m
- 16/93 m
- 23/93 m
The diameter of a circle with centre at C is 50 cm. CP is a radial segment of the circle. AS is a chord perpendicular to CP and passes through P. CP produced intersects the circle at D. If DP =18 cm, then what is the length of AS?

24 cm
32 cm
40 cm
48 cm

A regular hexagon is inscribed in a circle of radius 5 cm. If x is the area inside the circle but outside the regular hexagon, then which one of the following is correct?
- 13 cm² < x < 15 cm²
- 15 cm ² < x < 17 cm²
- 17 cm² < x < 19 cm²
- 19 cm² < x < 21 cm²
If x is the curved surface area and y is the volume of a right circular cylinder, then which one of the following is correct?

The ratio of height to radius of the cylinder is independent of x only
The ratio of height to radius of the cylinder is independent of y only
Either (a) or (b)
Neither (a) nor (b)

A triangle DBF is formed by joining the midpoints of the sides of triangle ABC. Similarly a triangle PQR is formed by joining the mid- points of the sides of the triangle DBF. If the sides of the triangle PQR are of lengths 1, 2 and 3 units, what is the perimeter of the triangle ABC?
- 18 units
- 24 units
- 48 units
- Cannot be determined due to insufficient data
A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m, while the vertex of the cone is 16 m above the ground. What is the area of the curved surface for conical portion?
- 3434/9 square metre
- 3431/8 square metre
- 3432/7 square metre
- 3234/7 square metre
What is the whole surface area of a cone of base radius 7 cm and height 24 cm?

654 square cm
704 square cm
724 square cm
964 square cm

A conical cap has the base diameter 24 cm and height 16 cm. What is the cost of painting the surface of the cap at the rate of 70 paisa per square cm?

The area of an isosceles triangle ABC with AB = AC and altitude AD = 3 cm is 12 square cm. What is its perimeter?

18 cm
16 cm
14 cm
12 cm

If the total surface area of a cube is 6 square unit, then what is the volume of the cube?
- 1 cubic unit
- 2 cubic unit
- 4 cubic unit
- 6 cubic unit
The diameter of the moon is approximately one-fourth of the diameter of the earth. What is the ratio (approximate) of their volumes?

1: 16
1:64
1:4
1:128

A hospital room is to accommodate 56 patients. It should be done in such a way that every patient gets 2.2 m² of floor and 8.8 m³ of space. If the length of the room is 14 m, the breadth and the height of the room are respectively

8 m, 4 m
4 m, 4.2 m
8 m, 4 m
8 m, 4.2 m

If the diagonals of a rhombus are 4.8 cm and 1.4 cm, then what is the perimeter of the rhombus?
- 5 cm
- 10 cm
- 12 cm
- 20 cm

Consider the following statements in respect of two chords XY and ZT of a circle intersecting at P :
PY =PZ.PT
PXZ and PTY are similar triangles.

Which of the above statements is/are correct?

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

ABCD is a quadrilateral such that BC = BA and CD > AD. Which one of the following is correct?
- ∠BAD = ∠BCD
- ∠BAD < ∠BCD
- ∠BAD > ∠BCD
- 2 ∠BAD = ∠BCD
ABC and XYZ are two similar triangles with ∠C= ∠Z, whose areas are respectively 32 cm² and 60.5 cm². If XY = 7.7 cm, then what is AB equal to?

6 cm
8 cm
0 cm
2 cm

A quadrilateral ABCD is inscribed in a circle. If AB is parallel to CD and AC = BD, then the quadrilateral must be a
- parallelogram
- rhombus
- trapezium
- None of the above
ABC is a triangle right angled at A and a perpendicular AD is drawn on the hypotenuse BC. What is BC.AD equal to?
- AC
- AD
- CD
- DB
In a triangle ABC, ∠B = 90° and ∠C = 2 ∠A, then what is AB² equal to?
- 2 BC²
- 3BC²
- ABC²
- 5 BC²
The heights of two trees are x and y, where x > y. The tops of the trees are at a distance z apart. If s is the shortest distance between the trees, then what is s² equal to?

x² + y²-z² – 2xy
x² + y²-z²
x² + y²+ z² – 2xy
z²-x²– y² +2xy

The side AC of a triangle ABC is produced to D such that BC = CD. If ∠ACB is 70 °, then what is ∠ADB equal to?

35°
45°
70°
110°

Consider the following statements :
If the diagonals of a parallelogram ABCD are perpendicular, then ABCD may be a rhombus.
If the diagonals of a quadrilateral ABCD are equal and perpendicular, then ABCD is a square.

Which of the statements given above is/are correct?

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

Consider the following statements :
The perpendicular bisector of a chord of a circle does not pass through the centre of the circle.
The angle in a semicircle is a right angle.

Which of the statements given above is/are correct?

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

E is the midpoint of the median AD of a triangle ABC. If BE produced meets the side AC at F, then CF is equal to
- AC / 3
- 2AC/3
- AC/ 2
- None of the above
PQR is an equilateral triangle. O is the point of intersection of altitudes PL, QM and RN. If OP = 8 cm, then what is the perimeter of the triangle PQR?
- 8√3 cm
- 12√3 cm
- 16√3 cm
- 24√3 cm
ABC is an equilateral triangle inscribed in a circle. D is any point on the arc BC. What is ∠ADB equal to?
- 90°
- 60°
- 45°
- None of the above
Consider the following statements :
If G is the centroid of triangle ABC, then GA = GB = GC.
If H is the orthocentre of triangle ABC, then HA = HB – HC.

Which of the statements given above is/are correct?

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

If the bisectors BI and C7 of the angles B and C of a triangle ABC meet at the point I, then what is ∠B1C equal to?

2A
90°+A/2
90°-A/2
90° + A

If sinθ +cosθ = √3, then what is tan θ + cotθ equal to?

1
√2
2
√3

What is the angle of elevation of the sun when the shadow of a pole of height x m is x/√3 m?
- 30°
- 45°
- 60°
- 75°
What is cos² (45° +θ ) +cos²(45°-θ ) /tan(60°+ θ) tan (30°- θ) equal to?
- -1
- 0
- 1
- 2
If tanθ + sec θ = m, then what is sec θ equal to?

m² -1/2m
m² + 1/2m
m + 1/m
m² +1/m

If 5sinθ + 12cosθ = 13, then what is 5cosθ -12sinθ equal to?
- -2
- -1
- 0
- 1
If 4 tanθ = 3, then what is 4sinθ -cosθ 4sinθ + 9cosθ equal to?

If ,sinθ -cosθ = 0, then what is sin⁴ θ+cos⁴ θ equal to?

What is cosec(75° +θ ) -sec(15°- θ) equal to?

0
1
2 sinθ
2 cosθ

If triangle ABC is right angled at C, then what is cos (A + B) + sin (A + B) equal to?

If α,β,γ are acute angles such that sinα =√3/2 , cosβ = √3/2 , tanγ = 1 then what is α+β+γ equal to?
- 105°
- 120°
- 135°
- 150°
What is sin⁶ θ+ cos⁶ θ+ 3sin² θcos² θ equal to?
- 0
- 1
- 2
- 4
Consider the following statements :
tanθ increases faster than sinθ asθ increases
The value of sinθ +cosθ is always greater than 1.

Which of the above statements is/are correct?

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

What is (sinθ +cos θ) (tanθ +cot θ) /sec θ + cosecθ

1
2
sinθ
cosθ

What is (1 + secθ – tanθ ) cos (1 + secθ + tan θ) (1 – sinθ ) equal to?
- 1
- 2
- tanθ
- cotθ
A spherical balloon of radius r subtends angle 60° at the eye of an observer. If the angle of elevation of its centre is 60° and h is the height of the centre of the balloon, then which one of the following is correct?
- h-r
- h = √2 r
- h = √3 r
- h = 2r
Methods of presentation of data are
- tables only
- graphs only
- diagrams only
- All of the above
The average of u, v, w, x, y, z is 10. What is the average of u + 10, v + 20, w + 30, x + 40, y + 50, z + 60 ?
- 30
- 35
- 40
- 45
If m is the mean of p, q, r, s, t, u, v, then What is (p-m) + (q-m) + (r-m) + (s-m) + (t – m) + (u – m) + (u- m) equal to?
- 0
- s
- (p + v) /2
- None of the above

For the next two (2) items that follow :

The median of the following distribution is 14.4 and the total frequency is 20 :

What is x equal to?
- 4
- 5
- 6
- 7
What is the relation between x and y?
- 2x = 3y
- 3x = 2y
- x = y
- 2x = y