CDS
Combined
Defence Services Examination
1. If
p(x) is a common multiple of degree 6 of the polynomials f(x) =x³+x²-x-1 and
g(x)= x³+x²-x-1. Then which one of the following is correct?
a) P(x)=(x-1)² (x+1)² (x²+1)
b) P(x)=(x-1) (x+1) (x²+1)
c) P(x)=(x-1)³ (x+1) (x²+1)
d) P(x)=(x-1)² (x4+1)
2.
If the roots of the equation x²-2ax+a²+a-3=0 are real and less than 3, then
which one of the following is correct?
a) a < 2
b) 2<a<3
c) 3<a<4
d) A>4
3.
Two students A and B solve an equation of the form x²+px+q=0. A starts with a wrong
value of p and obtains the roots as 2 and 6. B starts with a wrong value of q
and gets the roots as 2 and -9. What are the correct roots of the equation?
a) 3 and -4
b) –3 and -4
c) -3 and 4
d) 3 and 4
4. Consider
the following
I.
sin²1◦+cos²1◦=1
II.
sec²33◦-cot²57◦=cosec²37◦-tan²53◦
which
of the above statement is/are correct?
a) I only
b) II only
c) Both I and II
d) Neither I nor II
5. If
p=a sin x + b cos and q= a cos x- b sin x, then what is the value of p²+q²?
a) a+1
b) ab
c) a²+b²
d) a²-b²
6. Statement
I Let the side DE of a Δ DEF be divided at S, so that DS/DE=½. If a line
through S parallel to EF meets DF at T, then the area of Δ DEF is twice the
area of the ΔDST.
Statement
II The area of the similar triangles are
proportional to the squares on the corresponding sides. Which one of the
following is correct in respect of the above statements?
a) Both statements I and II are
true and statement II is the correct explanation of statement I.
b) Both statements I and II are true but statement II is not the
correct explanation of statement I
c) Statement I is true but
statement II is false.
d) Statement II is true but
statement II is false.
7.
What is the value of k that (2x-1) may be a factor of 4x4-(k-1)x³+kx²-6x+1?
a) 8
b) 9
c) 12
d) 13
8.
If 196 x4=x6, then x³ is equal to which one of the following?
a) x6/14
b) 14x4
c) x²/14
d) 14x²
9.
The sides of a parallelogram are 12cm and 8cm long and one of the diagonals is
10cm long. If d is the length of other diagonal, then which one of the
following is correct?
a) d< 8cm
b) 8cm<d<10cm
c) 10cm<d<12cm
d) D>12cm
10.The
base of a triangular wall is 7 times its height. If the cost of painting the
wall at Rs 350 per 100sq m is Rs 1225, then what is the base length?
a) 50 m
b) 70 m
c) 75 m
d) 100 m
Direction
(Q. Nos. 11-12) The areas of the ends of a frustum of a pyramid are P and Q where
P<Q and H is its thickness.
11.
What is difference in radii of the ends of the frustum?
a) √Q-√P⁄√
b) √Q-√P⁄
c) √Q-√P
d) None of these
12.
What is the volume of the frustum?
a) 3H(P+Q+√PQ)
b) H(P+Q+√PQ)
c) H(P+Q+√PQ)/3
d) H(P+Q-√PQ)/3
13.What
number should be added to 231228 to make it exactly divisible by 33?
a) 1
b) 2
c) 3
d) 4
14.
Let AB be a line segment such that a point P on the locus satisfies
AB²-AP²-BP²=0. What is the locus?
a) The straight line AB itself
b) The perpendicular bisector
of AB
c) A straight line
parallel to AB
d) A circle
15.
If 2x+3y≤6,x≥0,y≥0, then one of the solution is
a) X=-2 and y=3
b) X=1 and y=2
c) X=1 and y=1
d) X=-1 and y=-1
16.
A number consists of two digits. The sum of the digits is 10. On reversing the
digits of the number , the number decreases by 36. What is the product of the
two digits?
a) 21
b) 24
c) 36
d) 42
17.
Which one among the following is not correct?
a) Two congruent triangles are
necessarily similar.
b) All equiangular triangles
are similar
c) Two isosceles right
triangles are similar
d) All isosceles triangles are
similar
18.
ABCD is a rhombus with diagonals AC and BD. Then, which one among the following
is correct?
a) AC and BD bisect each other
but not necessarily perpendicular to each other.
b) AC and BD are perpendicular
to each other but not necessarily bisect each other.
c) AC and BD bisect each other
and perpendicular to each other.
d) AC and BD neither bisect
each other nor perpendicular to each other.
19.
The sum of a number and its reciprocal is 10/3, then the numbers are
a) 3, 1/3
b) 3, -1/3
c) -3,1/3
d) -3,-1/3
20.
Which one among the following statements is correct?
a) Simple bar diagrams are
those diagrams which show two characteristics of the data.
b) In pie diagrams all the
items are converted into angles.
c) A bar diagrams is one in
which data are shown in terms of bars.
d) Bar diagrams present data
through length and breadth.
21.
The following characteristic relate to the person participating in athletic
events
I.
Height of the person
II.
Colour of the eye of the person
III.
Number of times a person correctly hits a target in ten attempts.
Which
of the following in respect of the above is correct?
a) I is a continuous variable,
II is not a variable and III is a discrete variable
b) I is a continuous variable ,
II and III are discrete variables.
c) I and III are discrete
variables and II is not a variable.
d) I , II and III all are
discrete variable.
22.
Consider the following statements
I.
The data collected by the investigator to be used by himself are called
primary data.
II.
The data obtained from government agencies are called secondary data
Which
of the above statements is/are corrects?
a) Only I
b) Only II
c) Both I and II
d) Neither I nor II
23.
Which one among the following statements is not corrects?
a) For size of readymade
garments, mode is the best suitable measure.
b) For average rate of increase
when the rate of population growth is given, geometric mean is best suitable.
c) For average rate of speed
when different distances are covered by different rates of speed, harmonic mean
is best suitable.
d) For average level of
intelligence of students in a class, arithmetic mean is the best suitable.
24.If
the surface area of a sphere is 616 sq cm, what is its volume?
a) 431/2/3 cu cm
b) 4102/3 cu cm
c) 1257 cu cm
d) 1023 cu cm
25.
What are the dimensions (length, breadth and height, respectively) of a cuboid
with volume 720 cu cm, surface area 484
sq cm and the area of the base 72 sq cm?
a) 9,8 and 10 cm
b) 12,6 and 10 cm
c) 18, 4 and 10cm
d) 30, 2 and 12cm
26.
consider the following statements
I.
Every composite number is a natural number.
II.
Every whole number is a natural number
Which
of the statements given above is/are correct ?
a) Only I
b) Only II
c) Both I and II
d) Neither I nor II
27.
Consider the following statements
I.
Vertically opposite angles are equal
II.
Vertically opposite angles are supplementary
III.
Adjacent angles are complementary
Which
of the statements given above is/are correctly?
a) Only III
b) Only I
c) I and II
d) II and III
28.
A large solid metallic cylinder whose
radius and height are equal to each other is to be melted and 48 identical
solid balls are to be recast from the liquid metal so formed. What is the ratio
of the radius of a ball to the radius of the cylinder?
a) 1 : 16
b) 1 : 12
c) 1 : 8
d) 1 : 14
29.
The geometric mean of vitiates 32, 4, 8, x, 2 or 8. What is the value of
vitiate x?
a) 2
b) 4
c) 8
d) 16
30.
In the Δ ABC the base BC is trisected at D and E. the line through d, parallel
to AB, meets AC at F and the line through E parallel to AC meets AB at G. let
EG and DF intersect at H. what is the ratio of the sum of the area of the
parallelogram AGHF and the area of the Δ DHE to the area of the ΔABC?
a) ½
b) 1/3
c) ¼
d) 1/6
31.
A cardboard sheet in the form of a circular sector of radius 30 cm and central
angle 144◦ is folded to make a cone. What is the radius of the cone?
a) 12 cm
b) 18 cm
c) 21 cm
d) None of these
32.
Two transversals S and T cut a set of distinct parallel lines. S cuts the
parallel lines in points A,B,C,D and T cuts the parallel lines in points E,F,G
and G, respectively. If AB=4, CD=3 and EF=12, then what is length of GH?
a) 4
b) 6
c) 8
d) 9
33.
If the area of a circle is equal to the area of a square with side 2√
units, what is the diameter of the circle?
units, what is the diameter of the circle?
a) 1 unit
b) 2 units
c) 4 units
d) 8 units
34.
If x +1/x=a, then what is the value of x³+x²+1/x³+1/x²?
a) a³+a²
b) a³+a²-5a
c) a³+a²+3a-2
d) a³+a²-4a-2
35.
From the top of a cliff 200 m high, the angles of depression of the top and
bottom of a tower are observed to be 30◦ and 45◦, respectively. What is the
height of the tower?
a) 400 m
b) 400√3 m
c) 400 / √3 m
d) None of these
36.
If x³+5x² +10k leaves remainder -2x when divided by x²+2, then what is the
value of k?
a) -2
b) -1
c) 1
d) 2
37.
If one of the roots of quadratic equation 7x²-50x +k=0 is 7, then what is the
value of k?
a) 7
b) 1
c) 50/7
d) 7/50
38.
If a×=b, by=c and xyz=1, then what is the value of C³?
a) a
b) b
c) ab
d) a/b
39.
Let ABCD be a parallelogram. Let m and n be positive integers such that
n<m<2n. Let AC=2 mn and BD =m²-n². Let AB =(m²+n²)/2.
Statement
I AC>BD
Statement
II ABCD is a rhombus.
Which
one of the following is correct in respect of the above statements?
a) Both statements I and II are
true and statement II is the correct explanation of statement I.
b) Both statements I and II are
true but statement II are true but statement II is not the correct explanation
of statement I.
c) Statement I is true but
statement II is false.
d) Statement II is true but
statement I is false.
40.
A square, a circle and an equilateral triangle have same perimeter.
Consider
the following statement
I.
The area of square is greater than the area of the triangle.
II.
The area of circle is less than the area of triangle.
Which
of the statements is/are correct?
a) Only I
b) Only II
c) Both I and II
d) Neither I nor II
41.
The expression sin² x + cos² x -1 =0 is
satisfied by how many values of x?
a) Only one value of x?
b) Two values of x
c) Infinite values of x
d) No value of x
42.
The area of a rectangle whose length is 5 more than twice its width is 75 sq
units. What is the perimeter of the rectangle ?
a) 40 units
b) 30 units
c) 24 units
d) 20 units
43.
Two numbers are in the ratio 2 : 3. If 9
is added to each number, they will be in the ratio 3 : 4. What is the
product of the two numbers?
a) 360
b) 480
c) 486
d) 512
44.
Consider the following statements in respect of an equilateral ΔABC.
I.
There is a point P inside the
ΔABC such that each of its sides subtends an angle of 120◦at P.
II.
There is a point P inside the ΔABC such that the ΔPBC is obtuse angled
and A is the orthocenter of ΔPBC.
Which
of the above statement is/are correct?
a) Only I
b) Only II
c) Both I or II
d) Neither I nor II
45.
What is the value of
1.001×1.001×1.001+0.999×0.999×0.999
1.001×1.001-1.001×0.999+0.999×0.999
a) 1
b) 2
c) 3
d) 4
46.
The curved surface area of a right circular cone of radius 14 cm is 440 sq cm.
what is the slant height of the cone?
a) 10 cm
b) 11 cm
c) 12 cm
d) 13 cm
47.
If the volume of a cube is 729 cu cm, what is the length of its diagonal?
a) 9√2 cm
b) 9√3 cm
c) 18 cm
d) 18√3 cm
48.
The altitude of an equilateral triangle is √3 cm. what is its perimeter?
a) 3 cm
b) 3√3 cm
c) 6 cm
d) 6√3 cm
49.
The area of an equilateral triangle is √3 cm. what is its perimeter?
a) 2a²
b) 3a²
c) 4a²
d) 5a²
50.
The total surface area of a cube is 150sq cm. what is its volume?
a) 64 cu cm
b) 81 cu cm
c) 125 cu cm
d) 160cu cm
51.
The HCF and LCM of two natural numbers are 12 and 72, respectively. What is the
difference between the two numbers, if one of the numbers is 24?
a) 12
b) 18
c) 21
d) 24
52.
A person sold an article for Rs. 136 and got 15% loss. Had he sold it for Rs x,
he would have got a profit of 15%.
Which
one of the following is correct?
a) 190< x < 200
b) 180 < x < 190
c) 170 < x < 180
d) 160 < x < 170
53.
Consider the following statements
I.
The angular measure in radian of an circular arc of fixed length
subtending at its centre decreases, if the radius of the arc increases.
II.
1800◦is equal to 
dian
dian
Which
of the statement is /are correct?
a) Only I
b) Only II
c) Both I and II
d) Neither I nor II
54.
There are two taps A and B to fill up a water tank. The tank can be filled in
40min, if both taps are on. The same tank can be filled in 60 min, if tap A
alone is on. How much time will tap B alone take, to fill up the same tank?
a) 64 min
b) 80 min
c) 96 min
d) 120 min
55.
The pair of numbers which are relatively prime to each other is
a) (68, 85)
b) (65, 91)
c) (92,85)
d) (102, 153)
56.
How many rational numbers are there between 1 and 1000?
a) 998
b) 999
c) 1000
d) Infinite
57.
The sum of two numbers is 20 and their product is 75. What is the sum of their
reciprocals?
a) 1/15
b) 1/5
c) 4/15
d) 7/15
58.
The ratio of two complementary angle is 1 :5. What is the difference between
the two angles?
a) 60◦
b) 90◦
c) 120◦
d) Cannot be determined with
the given data
59.
What is the logarithm of 0.0001 with respect to base 10?
a) 4
b) 3
c) -4
d) -3
60.
Consider the following statements
I.
There is only one value of x in the first quadrant that satisfies sin x
+ cos x =2.
II.
There is only one value of x in the first quadrant that satisfies sin x
–cos x=0.
Which
of the above is/are correct?
a) Only I
b) Only II
c) Both I and II
d) Neither I nor II
61.
If x-2 is a factor of x³+kx²-2x-24, then what is the value of x?
a) 6
b) 5
c) 1
d) -2
62.
AB is a straight line. C is a point whose distance form AB is 3cm. what is the
number of points which are at a distance of 1cm from AB and 5 cm from c?
a) 1
b) 2
c) 3
d) 4
63.
The angle of elevation of the tip of a tower from a point on the ground is 45◦.
Moving 21 m directly towards the base of the tower, the angle of elevation
changes to 60◦. What is the height of the tower, to the nearest meter?
a) 48 m
b) 49 m
c) 50 m
d) 51 m
64.
A circular ring with centre 0 is kept in
the vertical position by two weightless
thin strings TP and TO attached to the ring at P and Q. the line OT meets the
ring at E whereas a tangential string at E meets TP and TQ at A and B,
respectively. If the radius of the ring is 5 cm and OT=13 cm, then what is the
length of AB?
a) 10/3 cm
b) 20/3 cm
c) 10 cm
d) 40/3 cm
65.
What is one of the square roots of 16x6-24x5-25x4-20x3+10x2-4x+1?
a) 4x3-3x2+2x+1
b) 4x3-3x2-2x-1
c) 4x3-3x2+2x-1
d) 4x3-3x2-2x+1
66.
The cost of two articles are in the ration 3 : 5. If there is 30% loss on the
first article and 20% gain on the second article, what is overall percentage of
loss or gain?
a) 2.25% gain
b) 5.25% loss
c) 2% loss
d) None of these
67.
The number 58129745812974 is divisible by
a) 11
b) 9
c) 4
d) None of these
68.
What is the HCF of
36(3x4+5x3-2x2).9(6x3+4x2-2x),
54(27x4-x)?
a) 9x (x+1)
b) 9x(3x-1)
c) 18x(3x-1)
d) 18x(x+1)
69.
What is the length of the uniform wire of diameter 0.4 cm that can be drawn
from a solid sphere of radius 9 cm?
a) 243 m
b) 240 m
c) 60.75 m
d) 60 m
70.
What will be the cost of plaster the inner surface of a well 14 m deep and 4 m
in diameter at the rate of Rs 25 per sq m?
a) Rs 4000
b) Rs 4200
c) Rs 4400
d) Rs 5400
71.
A Wheel of radius 2.1 m of a vehicle makes 75 revolutions in 1 min. what is the
speed of the vehicle?
a) 78 km/h
b) 59.4 km/4
c) 37.4 km/h
d) 35.4 km/h
72.If
a positive integer leaves remainder 28 when divided by 143, then what is the
remainder obtained on dividing the same number by 13?
a) 0
b) 2
c) 9
d) 10
73.
What is the compound interest on Rs 1600 at 25% per annum for 2yr compounded
annually?
a) Rs 700
b) Rs 750
c) Rs 800
d) Rs 900
74.
The graphs of ax + by = c, dx + ey =f will be
I.
Parallel if the system has no solution
II.
Voincident if the system has finite number of solutions.
III.
Intersecting if the system has only one solution
Which
of the above statements are correct?
a) Only I and II
b) Only II and III
c) Only I and III
d) I, II and III
75.
The medians of ΔABC intersect at G. Which one of the following is correct?
a) Five times the area of Δ AGB
is equal to four times the area of ΔABC.
b) Four times the area of ΔAGB
is equal to three times the area of Δ ABC
c) Three times the area of Δ
AGB is equal to the area of ΔABC.
d) None of above.
76.
If x lies in the first quadrant and cos x = 5/13, what is the value of tan x –
cot x?
a) -139/60
b) 139/60
c) 119/60
d) None of these
77. In the quadrilateral ABCD shown below,
<DAB=<DCX=120◦. If <ABC =105◦,what is the value of <ADC? X
C
D
A B
a) 45◦
b) 60◦
c) 75◦
d) 95◦
78.
In the figure below AO=CD where O is the centre of the circle. What is the
value of <APB?
 |
A B
C D
P
a) 60◦
b) 50◦
c) 45◦
d) 30◦
79.
In the Figure given below < ABC = <AED=90◦.
Consider
the following statements
I.
ABC and ADE are similar triangles.
II.
The four points B,C,E and D may lie on a circle.
Which
of the above statements is/are correct?
A
E
D
C B
a) Only I
b) Only II
c) Both I and II
d) Neither I nor II
80.
If 3x+y=81 and 81x-y=3,
then what is the value of x ?
a) 17/16
b) 17/8
c) 17/4
d) 15/4
81.
Consider the following.
i.
Cot 30◦+1 =2(cos 300◦+1)
cot 30◦-1
II. 2 sin 45◦cos 45◦-tan 45◦cot 45◦=0
Which of the
above identities is/are correct?
a) Only I
b) Only II
c) Both I and II
d) Neither I nor II
82.
If 3 sin x + 5 cos x=5, then what is the value of (3cos x- 5 sin x)?
a) 0
b) 2
c) 3
d) 5
83.
How many numbers between -11 and 11 are multiples of 2 or 3?
a) 11
b) 14
c) 15
d) None of these
84.
If A ={x : x is an even natural number},
B ={x : x is a natural number and
multiple of 5} and
C ={x : x is a natural number and
multiple of 10},
a) {10,20,30,….)
b) {5, 10,15, 20,…)
c) {2,4,6…….}
d) 20,40,60,……}
85.
If a set A contains 60 elements and another set B contains 70 elements and there are 50 elements in common,
then how many elements does A O B contain?
a) 130
b) 100
c) 80
d) 70
86.
What is the mean proportional between (15+√200) and (27-√648)?
a) 4
b) 14√7
c) 3√5
d) 5√3
87.
A stock of food is enough for 240 men for 48 days. How long will the same stock
last for 160 men?
a) 54 days
b) 60days
c) 64days
d) 72 days
88.
If 
and 
then what is the value of 
?
and then what is the value of ?
a) 3/2
b) 5
c) 2/3
d) 1/5
89.
The locus of the mid-points of all equal chords in a circle is
a) The circumference of the
circle concentric with the given circle and having radius equal to the length of the chords
b) The circumference of the
circle concentric with the given circle
and having radius equal to the distance of the chords form the centre
c) The circumference of the
circle concentric with the given circle and having radius equal to half of the
radius of the given circle
d) The circumference of the
circle concentric with the given circle and having radius equal to half of the
distance of the chords from the centre.
90.
If the outer and inner diameters of a stone parapet around a well are 112 cm
and 70 cm respectively , then what is the area of the parapet?
a) 264 sq cm
b) 3003 sq cm
c) 6006 sq cm
d) 24024 sq cm
91.
What is the value of 0.007+17.83+310.0202?
a) 327.86638
b) 327.86638
c) 327.86683
d) 327.8668
92.
A man losses 20% of his money. After spending 25% of the remainder, he has Rs
480 left. What is the amount of money he originally had?
a) Rs 600
b) Rs 720
c) Rs 800
d) Rs 840
93.
Assuming that profit of a shopkeeper in a particular commodity is a linear
expression of transportation charge (t) and the quantity of commodity (q). he
earns a profit of Rs 10000 by selling 20 units at the transport charge of Rs
400. He also earns a profit of Rs 12000 by selling 25 units at the transport
charge of Rs 600. What is the linear expression in t and q?
a) 600q -5t
b) 500q -4t
c) 600q–4t
d) 500q-5t
94.
If x:y=7:5, then what is the value of
a) 5/4
b) 6/5
c) 25/31
d) 31/42
95.
The sum of two numbers is 232 and their HCF is 29. What is the number of such
pairs of numbers satisfying the above condition ?
a) One
b) Two
c) Four
d) None of these
96.
A person bought 8 quintal of rice for certain rupees. After a week, he sold 3
quintal of rice at 10% profit, 3 quintal of rice with neither profit nor loss
and 2 quintal at 5 % loss. In this transaction, what is the profit?
a) 10%
b) 20%
c) 25%
d) None of these
97.
What is the angle of elevation of the sun when the shadow of a pole is √3 times
the length of the pole?
a) 30◦
b) 45◦
c) 60◦
d) None of these
98.
x4+xy3+x3y+xz3+y4+yz3
is divisible by
a) (x-y) only
b) (x3+y3+z3)
only
c) Both (x+y) and (x3+y3+z3)
d) None of these
99.
‘A’ can do a piece of work in ‘x’ days and ’B’ can do the same work 3x days. To
finish the work together they take 12days. What is the value of ‘x’?
a) 8
b) 10
c) 12
d) 16
100.
ABCD is a rectangle. Let E be a point on AB and F a point on CD such that DE is
parallel to BF. If AE=3 c, and if the area of ΔBFC=6 sq cm.
Consider
the following statements.
I.
Area of rectangle ABCD can be of the form pq2 sq cm where p,q are
distinct primes.
II.
Area of the figure EBCD is of the form r2 sq cm , where r is
rational but not an integer.
Which
of the above statements is/are correct?
a) Only I
b) Only II
c) Both I and II
d) Neither I nor II
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