CDS 2008 Maths Question Paper -1

ORDERING OF SENTENCES

In an examination 70% candidates passed in English and 65% in Mathematics. If 27% candidate fail in both the subject and 248 passed the examination. The total number of candidates was :
- 400
- 348
- 420
- 484
A car runs x km at an average speed ₁km/ hr and y km at an average speeds of ₂ km/ hr. What is the average speed of the car for the entire journey ?

Average age of A and B is 20 years. If C were to replace A. The average would be 19 and if C were to replace B , the average would be 21. What are the ages of A, B and C (in years)?
- 22, 18, 20
- 18, 22, 20
- 22, 20, 18
- 18, 20, 22

One year ago the ratio between Samer’s and Ashok’s age was 4 : 3. One year hence the ratio of their ages will be 5 : 4. The sum of their present ages :
- 20
- 16
- 18
- 15
Subhash purchase a tape recorder at 9/10^th of its selling price and sold it at 8% more than its selling price. His gain is
- 9%
- 10%
- 18%
- 20%

Tarun bought a TV with 20% discount on the labelled price. Had he bought it with 25% discount, he would have saved Rs. 500. At what price did he buy the T.V?

1500
10000
12000
8000

A reduction of 20% in the price of mangoes enables a person to purchase 12 more for Rs. 15. The price of 16 mangoes before reduction was :

Annual payment will discharge a debt of Rs. 770 due in 5 years, the rate of interest being 5% per annum is :

Divide Rs. 3903 between A and B, so that A ‘s share at end of 7 years, may equal to B ‘s share at end of 9 years, compound interest being at 4 percent

2028, Rs. 1875
2018, Rs. 1885
2008, Rs. 1895
2038, Rs. 1865

Vijay obtains a loan of Rs. 64000 against his fix deposit. If the rate of interest be 2.5 paise per rupee per annum, calculate the compound interest payable after 3 years :

4921
5020
4821
4920

A television is marked at Rs. 3575 cash of Rs. 1500 as cash down payment and Rs. 420 a month for 5 months. The rate of interest for this instalment plan :

A pocket transistor is sold for Rs. 125 cash or for Rs. 26 as cash down load payment followed by 4 equal monthly instalments. If the rate of interest charged is 25% per annum the monthly instalment will be :

A sum of Rs. 7500 is to be paid back in 3 annual instalment. How much is each instalment, if the interest is compound annually on the balance at 4% and is to be included in each instalment ?

2800, Rs. 2700, Rs. 2600
2600, Rs. 2700, Rs. 2800
2800, Rs. 2600, Rs. 2700
2700, Rs. 2800, Rs. 2600

In what proportion must rice at Rs. 3.10 per kg be mixed with rice at Rs. 3.60 per kg so that the mixture be worth Rs. 3.25 a kg ?

3 : 7
7 : 3
5 : 3
3 : 5

In what proportion must water be mixed with milk to gain 16 2/3%by selling it at cost price ?

1: 6
6: 1
1: 5
5: 1

In a zoo, there are rabbits and pigeons. If heads are counted these are 200 and if legs are counted there are 580. How many pigeons are there ?

A and B can do a piece of work in 10 days and B and C can do in 15 days and C and A in 20 days, they all work it for 6 days and then A leaves and B and C go on together for 4 days more. If B then leaves, how long will C takes to complete the work ?

20 days
25 days
10 days
15 days

To do a certain work B would take three times as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. Then how long would each take separately? (in days)

24, 40, 30
30, 40, 24
4,0, 30, 24
24, 30, 40

A piece of work was to be completed in 40 days, a number of men employed on it did only half the work in 24 days, 16 more men were then set on and the work completed in the specified time. How many men were employed at first ?

Wages for 45 women amount to Rs. 15525 in 48 days. How many men must work 16 days to receive Rs. 5750, the daily wages of a man being double those of a woman ?

A, B and C together earn Rs. 1350 in 9 days. A and C together earn Rs. 470 in 5 days. B and C together earn Rs. 760 in 10 days. Daily earning of C is :

Two pipes P and Q would fill a cistern in 24 hours and 32 hours respectively. If both pipes are opened together, find when the first pipe must be turned off so that the cistern may be just filled in 16 hours

12 hours
10 hours
13 hours
11 hours

A man is walking at a speed of 12 km/hour after every km he takes rest for 12 minutes. How much time will be take to cover a distance of 36 km ?

8 hours
10 hours
7 hours
6 hours

A boy goes to school at a speed of 3 km/hour and returns to village at a speed of 2 km/ hour. If he takes 5 hours in all, the distance between the village and the school is:

3 km
4 km
5 km
6 km

The distance between two station Delhi and Amritsar, is 1450 km. A train starts at 3.10 pm from Delhi and moves towards Amritsar at an average speed of 20 km/hour. Another train starts from Amritsar at 4 pm and moves towards Delhi at an average speed of 60 km/ hour. How far will the two trains meet ?

115 km
120 km
125 km
200 km

Two guns fire from the same place at an interval of 13 minutes but a person in a train approaching the place hears the speed report 12 minutes 30 seconds after the first. The speed of train, supposing after that sound travel at 330 m/sec, is

47 13/25 km/hr
13/25 km/hr
47 km/hr
13 25 km/hr

A train with 90 km/hour crosses a bridge in 36 seconds. Another train 100 m shorther crosses the same bridges at 45 km/hour. Find the time taken by the second train to cross the bridge

64 sec.
60 sec.
72 sec.
1 hour

A man can row 30 km upstream and 44 km downstream in 10 hours. Also, he can row 40 km upstream and 55 km downstream in 13 hour. The rate of the current is

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

If the area and perimeter of a rectangle are 240 cm2 and 68 cm respectively. Then its breadth is :

24 cm
10 cm
8 cm
9 cm

There is a rectangular field of area 60 square cm. Sum of its diagonal and length is 5 times of its breadth. The breadth of rectangular field is :

3 cm
4 cm
5 cm
15 cm

If the three sides of a right angled triangle are produced on either side then which of the following statement relating to the figure so obtained is correct ?
Of the twelve angle formed at the three vertices by adjoining lines, four are acute, four obtuse and four right angles.
The mean measure of the above twelve angles 90°
The measure and of the above twelve angles will generally have three or five distinct values.

Select the correct answer using the codes given below codes

1, 2, 3 and 4
1 and 2
1 and 3
2 and 3

From a point P in the base BC of an isosceles triangle ABC, a straight line is drawn perpendicular to the base cutting AB in Q and CA produced in R, then :

ΔAQR is equilateral

ΔAQR is isosceles

Q is the midpoint of AB

A is the midpoint of CR

Which of the following statements relating to triangles ABC and DEF are not correct ?
- If AB = DE, BC = EF and the areas of the two triangles are equal, then they are congruent.
- If ∠ACD = ∠DEF = 90°, AB = DE, AC = DF then the triangles are congurent.
- If ∠ABC = ∠DEF, ∠ACB = ∠DFE and the areas of the triangles are equal then they are congruent.
- If ∠ABC = ∠DEF, ∠ACB = ∠DEF and ∠BAC = ∠EDF, then the triangles are congruent.
If PL,QM and RN are altitudes of ΔPQR whose ortho centre O, then Q is the orthocentre of :

ΔPRO
ΔPRN
ΔPRL
ΔQRO

ABCD is a parallelogram. If E and F are any two points lying on the sides DC and AD respectively, then relation between the areas. Δ1 and Δ2 of AEB and BFC respectively, then :
- Δ1= Δ2
- Δ1= 2 Δ2
- 2 Δ 1 = Δ2
- 2 Δ 1 = 3 Δ2
ABCD is a cyclic quadrelateral. The tangents to the circle drawn at A and C meet at P. If ABC =110°, then APC is equal to :

20°
40°
60°
70°

If in a circle a chord of length 16 cm is at a distance 15 cm from the centre of the circle, then the radius of the circle is

16 cm
15 cm
8 cm
17 cm

The area of shaded region on the given below figure is :
- 150 m²
- 156 m²
- 160 m²
- 180 m²
While calculating the area of a field the surver recorded the following observation in this field book.

Area of the field is :

567 sq. m
569 sq. m
592 sq. m
6055 sq. m

Edge of cube is decreased by 20% the percentage of decrease in the surface area is:

A hemispherical basin 150 cm in diameter holds water one hundred and twenty times as much as a cylindrical tub. If the height of the tub is 15 cm, then diameter of the tub (in cm) is :

23 cm
24 cm
25 cm
26 cm

If the volume of a right circular cylinder with its height equal to twice of the radius is 169 5/7 cm 7 , then its diameter is equal to

6 cm
3 cm
2 cm
4 cm

If p sin A = q and A is acute angle, then the value of √p2-q2 tan A is :
- p
- q
- pq
- p/q
If 2 sin² θ+ cos² 45 = tan 45° and 0 ≤ θ ≤ 90° then sin q is :

1
√3
1/
√3
½

Which of the following is not correctly matched ?

If Then

θ= 75° sin θ< cosθ
θ= 35° cosec θ< secθ
θ= 42° tan θ< cotθ
θ=18° tan θ< secθ

Eliminating t from the equations x = cos t, y = 2 sin t .cost, we get

y² = 4x² + 4x⁴
y² = 4x² – 4x⁴
y² = 2x² + 4x⁴
y² = 2x² – 4x⁴

The value of cos²θ(1 +tan² θ) +sin² θ(1 + cot² θ) is :

If a person standing on the bank of river finds that the angle of elevation of the top of a tower on the other bank directly opposite to him is 45°, then :
- the height of the tower is half the breadth of the river
- the height of the tower is twice the breadth of the river.
- the height of the tower is the same as the breadth of the river.
- the height of the tower is thrice the breadth of the river.
AB is a vertical pole the end A is on the ground, C is the middle point AB, P is a point on the level ground the position BC substends an angle a at P. If AP = n. AB, then tan a is :
- n/2n²+1
- n/n² -1
- n/n² +1
- n2-1/n²+1

The following table shows the distribution of weekly salary (in Rs.) of 1000 workers.

Weekly salary (in Rs.) Frequency

less than 50 40

50-75 120

75-100 200

100-125 300

125-150 150

150-175 100

175-200 55

200 and above 35
The percentage of workers with weekly salary less than Rs. 125 and weekly salary more than Rs. 150 are respectively :

(81, 19)
(66, 34)
(66, 19)
(81, 34)

The last class-interval in a frequency distribution has an open end. Which one of the following in the most suitable diagram for graphical representations ?

absolute frequency curve
relative frequency curve
percentage frequency curve
cumulative frequency curve

10³ =1000 is same as :

log₃1000 = 10
log₁₀ 1000 = 3
log₁₀₀₀3 = 10
log₃ 10 = 1000

Which of the following is correct ?
factors of x³ + 1 are (x + 1), (x² + x + 1)
factors of x³ + 1 are (x + 1), (x² – x + 1)
factors of x³ – 1 are (x – 1), (x² – x – 1)
factors of x³ – 1 are (x – 1), (x² + x + 1)

Codes:

1 and 3 are correct
1 and 4 are correct
2 and 4 are correct
2, 3 and 4 are correct

If x – 5 and x – k are distinct factors of x² – 3x-10, then value of k is :
- -1
- -2
- -3
- 5
The sum of the digit of a two digit is 8. The number obtained by reversing the digit is 18 less than the original number. The original number :

What is the value of sin²° sin⁴° sin⁶°…sin88°/cos88° cos86° cos84° …cos2°?
- 0
- 1
- 2
- 4
A man borrowed Rs. 40,0000 at 8% simple interest per year. At the end of second year he paid back certain amount and at the end of fifth year he paid back Rs. 35,960 and cleared the debt. What is the amount did he pay back after the second year?

16,200
17,400
18,600
None of these

Value of
- x
- 1
- x^–1
- x^–1
If x^a × x^b × x^c = 1 then a³ + b³ + c³ is equal to :
- a
- abc
- a + b + c
- 3abc
A dishonest dealer professes to sell his goods at cost price by using a false weight and thus gains 11 1/9% For weighing a kilogram he uses a weight of:

960 gm
940 gm
920 gm
900 gm

The length of a pendulumi is 60 cm. The angle through which its swing when its tip describes an arc of length 16.5 cm is :

15°30’
15° 45’
16° 15’
none of these

If A and B are subsets of X then :
- A ∪ B = X A’ = B
- A ∪B = X B’ = A
- A ∪ B = X A ∩ B =Φ
- A ∪B = X and A’ = B A ∪ B =Φ
Let A be the set of square of natural numbers and let x € A, y € A, then :

x + y €A
x – y €A
x/y €A
xy €A

The polynomial x² – x + 1 has :
- one proper linear factors
- two proper linear factors
- no proper linear factor
- none of the above
Which of the following quadratic polynomial can be factorised into a product of real linear factors ?

2x² – 5x + 9
2x² + 4x – 5
2x² + 4x + 9
5x² – 3x + 2

If log₁₀2 = 0.3010, then the value of 1og₁₀25 is :

462
398
268
none of these

1og₂7 is :
- an integer
- a prime number
- a rational number
- an irrational number
The points A (2a, 4a), B (2a, 6a) and C ({ 2 + √3) √a, are vertices of :

a scalene triangle
an isosceles triangle
an equilateral triangle
none of these

The vertices of ΔABC are (2, 1), (5, 2) and (3, 4) respectively. The circumcentre is :
- (8/3,3)
- (13/4,9/4)
- (10/3,7/3)
- none of these
The distance between the parallel lines y = mx + c and y = mx + d is :

|c – d|
½ |c-d |
none of these

The point of intersection of the diagonals of a rectangle whose sides are x = a, x = a’, y = b, y = b’
- none of these
How are the points (3, 4) and (2,-6) situated with respect to line 3x – 4y – 8 = 0 ?

both lie on the line
they lie on same side of the line
they lie on opposite sides of the line
none of the above

The radius of the circle 16 (x² + y²) + 24x + 32y + 9 = 0 is :
- 3
- 1/3
- 2
- 1
Pie diagrams used to represent statistical data are

one dimensional
three dimensional
two-dimensional
none of these

If log₇ log₅ ( √x+ 5 +√x ) = 0 the value of x is:

1
0
2
none of these

The value of (55)³+ (45)³/(55)²– 55 x 45+ (45)²:
- 100
- 105
- 125
- none of these
Which of the following values of x do not satisfy the inequality (x² – 3x + 2 > 0) at all :

1 ≤ x ≤ 2
–1 ≥ x ≥– 2
0 ≤ x ≤ 2
0 ≥ x ≥– 2

Let x, y be two positive such that x + y=1, then the minimum value of (x+1/x)2 +(y+1/y)2is:
- 12
- 20
- 5
- 15
Let p and q be the roots of quadratic equation x² – (a – 2) x – a – 1 = 0 the minimum possible value of p² + q² ?

y = the value of y is :
- none of these

Directions: These questions consist of two statements each printed as ‘Assertion (A)’ and ‘Reason (R)’. While answering these questions you are required to choose any one of the following four responses.

both A and R are true and R is the correct explanation of A
both A and R are true but R is not the correct explanation of A
A is true but R is false
A is false but R is true

Assertion (A) : The number 63215988 is divisible by 11.

Reason (R) : The number formed by the last two digits is divisible by 11.

Assertion (A) : Period of cos (3x + 4) is

Reason (R) : If the period of f (x) is l then the period of f (ax + b) is l.

Assertion (A) : Median is not useful in those cases where large weights are to be given to the extreme items.

Reason (R) : Median ignores the importance of extreme items.

Assertion (A) : The area of a quadrilateral whose one diagonal is 10 m and lengths of the perpendicular drawn from the other vertices to this diagonal are 4 m and 6 m is 50 m²

Reason (R) : The quadrilateral can be split into two triangles whose altitudes are equal to the lengths of the given perpendiculars.

Assertion (A) : No polynomial of degree one or higher has a multiplicative inverse which is a polynomial.

Reason (R) : The coefficients of the terms in a polynomial are all real numbers.

Assertion (A) : A bar chart is a two dimensional figure.

Reason (R) : In a bar chart, the height of each bar is of significance and not its width.

Assertion (A) : Mode is not a good measure of central tendency.

Reason (R) : Mode lays too much emphasis only on the modal group and does not consider other variates at all.

Assertion (A) : If p is a prime number and it divides ab, where a,b are positive integers, then p must divide either a or b.

Reason (R) : This true if p is any positive integer.

Assertion (A) : The sum

Reason (R) : The sum of two irrational numbers is always irrational.

Assertion (A) : If O is the ortho center of the triangle ABC, then ∠BOC and ∠BAC are supplementary.

Reason (R) : Both the triangles BOC and BAC have a common base.

The number in the unit place in (623)³⁸ is:

The product of two numbers is 192 and the sum of these two numbers is 28. The smaller number of these two numbers is :

Sum of two numbers is 1215 and their HCF is 81. How many pair of such number can be formed ?

Sum and difference of the LCM and HCF of two numbers are 592 and 518 respectively. If the sum of two numbers be 296. Then numbers are :

111, 105
37, 259
36, 332
none of these

A can do a piece of work in 12 days. B is 60% more efficient than A. Then number of days it takes B to do the same work is
- 7
- 7 ½
- 7 3/2
- 6
A bag contains 1 rupee, fifty paise, twenty five paise and ten paise coins in the ratio 1 : 3 : 5 : 7. If the total amount is Rs. 22.25, then number of twenty five paise coins is

A bag contains 1 rupee, 50 paise and 25 paise coins in the ratio 5 : 6 : 7. If the total amount is Rs. 390, then number of 25 paise coin is

A, B and C go into business as partners and collect a profit of Rs. 1000. If A’s capital : B ‘s capital = 2 : 3 and B ‘s capital : C’s capital = 2 : 5, the share of profit which goes to C is

Ram’s monthly income is 15% more than that of Shyam. Shyam’s monthly income is 10% less than that of Sohan. If the difference between the monthly income of Ram and Sohan is Rs. 350, the monthly income of Shyam is

7000
8000
9000
6000

If base of the triangle is increased by 10% and the area is unchanged then the corresponding altitude must be decreased by:
- 11 1/9 %
- 9 1/11%
- 11%
- 10%