2024 CDS -1 MATH-14454

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2024 CDS -1 MATH (Test Code: 14454)

The speeds of four cars are 2u, 3u, 4u and xu and the time taken by them to cover the same distance is xt, 4t, 3t and 2t respectively, where.

x, u, t are real numbers. What is the value of x?

Qs: 3

If m : n = 1 : 2 and p : q = 3 : 4, then what is (2m + 4p) : (n + 3q) equal to ??

1 : 1
1 : 3
2 : 1
2 : 3

Qs: 4

If the rate of interest is 5%, then what would be the difference between compound interest and simple interest received on Rs.10,000

(each) after 3 years from now ?

Rs.175.25
Rs.152.25
Rs.76.25
Rs.24.25

Qs: 5

If the difference between the interior and exterior angles of a regular polygon is 1440, then what is the number of sides of the polygon ?

Qs: 6

A person bought a book at 314th of its listed price and sold it at 50% more than its listed price. What is the percentage of gain in the transaction ?

20%
40%
75%
100%

Qs: 7

If the sum and product of the roots of a quadratic equation are 2 and - 100 respectively, then which one of the following is correct?

There are infinitely many such equations having different roots.
There is only one such equation which is x² + 2x - 100 = 0.
There is only one such equation which is x² - 2x - 100 = 0.
There is no such equation.

Qs: 8

If 2 is a zero of the polynomial

p(x) = x³ + 3x² - 6x - a, then what is the sum of the squares of the other zeros of the polynomial ?

What is• the difference between the greatest value and the least value of cos² 0 + 3 sin² 0 + 2?

Qs: 13

ABC is a right-angled triangle, right-angled at B such that AB = 6 cm and BC = 8 cm. What is the perimeter of the square inscribed in the

triangle ABC with maximum area ?

24/7 cm
96/7 cm
24 cm
24 cm

Qs: 14

What is the greatest value of k for which 2x² - 4x + k = 0 has real roots ?

Qs: 15

Consider the following data :

110, 41,43, 95, 127, 99, 61, 92, 71, 93, 110, 36

If 93 is replaced by 94, then consider the following statements :

1. The difference between new median and old median is 1.

2. The difference between new mean and old mean is less than 0.1

3. The difference between new mode and old mode is zero.

Which of the statements given above are correct?

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

Qs: 16

What is the digit at the 100th place of number (225)⁴⁰ ?

Qs: 17

If a, b, c, d are natural numbers, then how many possible remainders are there when 1^a + 2^b + 3^c + 4^d is divided by 10?

Qs: 18

If n is a natural number, then what is the of all distinct remainders of 4ⁿ + 6ⁿ + 9ⁿ + 11ⁿwhen divided by 10 for various values of n ?

Qs: 19

When the number

(123456789 10111213 ... 99100) is divided by 16, what will be the remainder?

Qs: 20

A, B, C, D can complete a work in 3, 6, 9, 12 hours respectively. Further, only one person can work at a time in each hour and nobody can work for two consecutive hours. It is not necessary to engage all. What is the minimum number of hours that they will take to finish the work ?

36/25
12/5
4
2

Qs: 21

Qs: 22

A plank of wood 4.25 m long and 3.4 m wide is to be cut into square pieces of equal size. How many square pieces of largest size can be cut from the plank, if no wastage is allowed ?

The expression 555⁷⁷⁷ + 777⁵⁵⁵ is divisible by which of the following?

1. 2

2. 3

3. 37

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

Qs: 27

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

Qs: 28

The sum of two positive numbers is 40. If the GM of these two numbers is lower than their AM by 20%, then what is the difference between the two numbers ?

Qs: 29

50 men can complete a work in 40 days. They begin the work together but a batch of 5 men left after each period of 10 days. What is the time to complete the work ?

45 days
50 days
55 days
60 days

Qs: 30

Qs: 31

A bottle contains spirit and water in the ratio 1 : 4 and another identical bottle contains spirit and water in the ratio 4 : 1. In what ratio should the mixtures in the two bottles be mixed to get a new mixture in which the ratio of spirit to water is 1 : 3 ?

5 : 1
6: 1
10 : 1
11 : 1

Qs: 32

If 3 sin θ + 5 cos θ = 5, then what is the value of 5 sin θ -3 cos θ ?

-3
-2
5
8

Qs: 33

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

126 square cm
189 square cm
252 square cm
315 square cm

Qs: 38

From a sircular metal plate of radius 7 cm and thickness 0•16 mm, a sector is cut off containing an angle 150°. The remaining piece is moulded into a spherical bead of radius r. What is the value of r in cm ?

0.35
0.7
1.05
1.4

Qs: 39

Qs: 40

154 square cm
144 square cm
132 square cm
Cannot be determined due to insufficient data

Qs: 41

40 square cm
42 square cm
45 square cm
48 square cm

Qs: 42

Qs: 43

The cost price of y articles is equal to selling price of z articles. If y : z = 5 : 4, what is the profit percentage ?

Qs: 44

A sum of money invested at simple interest triples itself in 8 years and becomes n times in 20 years. What is the value of n ?

Qs: 45

If the work done by x men in (x + 1) days is equal to the work done by (x + 5) men in (x - 2) days, then what is the value of x ?

Qs: 46

If (a + b) : (b + c) : (c + a) = 5 : 7 : 6, then what is the value of (a - b + c) : ( a + b - c) ?

1: 1
2 : 3
3 : 1
4: 3

Qs: 47

Let x be the compound interest at the end of 3 years on a sum of 1000 at the rate of 10% compounded annually and y be the simple interest at the end of 3 years on a sum of 1000 at the annual rate of 11 %. What is the

difference between x and y ?

Rs.16
Rs.15
Rs.5
Rs.1

Qs: 48

In a quadrilateral ABCD, AB = 6 cm, BC = 18 cm, CD = 6 cm and DA = 10 cm. If the diagonal BD = x, then which one of the following is correct ?

8 < X < 12
12 < x < 16
16 < X < 18
18 < x < 20

Qs: 49

In a quarter circle of radius R, a circle of radius r is inscribed. What is the ratio of R tor?

(√2 +1) : 1
(√3 +1) : 1
3 : 2
5 : 4

Qs: 50

In a quadrilateral ABCD, AB = BC and CD = DA; AC and BD are diagonals such that AC = 6 cm and BD = 12 cm. What is the area

of the quadrilateral ?

24 square cm
30 square cm
36 square cm
40 square cm

Qs: 51

If tan (3A) = cot (A - 22°), where 3A is an acute angle, then what is the value of A ?

25°
27°
28°
30°

Qs: 52

Qs: 53

The angles of elevation of the top of a tower from two points A and B at a distance of x m and (x + 5) m from the base of the tower of height 6 m and in the same straight line with it are complementary. What is the value of x ?

Qs: 54

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

Qs: 55

Qs: 56

The length, breadth and height of a cuboid are increased by 10%, 20% and 50 % respectively.

What is the percentage increase in volume of the cuboid?

100%
99%
98%
50%

Qs: 57

Qs: 58

If P² varies as R and Q² varies as R, (P≠ Q), then which of the following are correct?

1. P² + Q² varies as R.

2. PQ varies as R.

3. P² - Q² varies as R.

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

Qs: 59

p number of men can finish a piece of work in q days. If there are 50% more men, then the work will be finished 12 days earlier. What is the value of q ?

48
40
36
Cannot be determined due to insufficient data

Qs: 60

Qs: 61

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

Let a, b, c and d be positive integers.

Question: Which one of a, b, c, d is closest to the product abed?

Statement-I: a> b > c

Statement-II: c is not the smallest.

Qs: 62

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

Let mn = k, where m and n are prime numbers and k is an even number.

Question: What is the value of mn-n+1?

Statement-I: m > n

Statement-II: One of the numbers is 2

Qs: 63

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

Question : If p is a positive integer, then

what is the remainder when pⁿ is divided by p + 1 ?

Statement-I: n is even.

Statement-II: p is even.

Qs: 64

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

Question : Is xy positive ?

Statement-I: x = 3√-0.19683

Statement-II: y = 3√x

Qs: 65

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

Let a, b and c be the sides of a triangle ABC.

Question: Is the triangle equilateral ?

Statement-I: a² + b² + c² = (ab + be + ca)

Statement-II: 3a² + 3b² + 4c² = 2ab + 4bc + 4ca

Qs: 66

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

Area of a rectangle with length x and breadth y is P and area of a parallelogram (which is strictly not a rectangle) with adjacent sides of length x and y is Q

Question: Is P > Q?

Statement-I: x: y = 2: 1

Statement-II: The angle between the two adjacent sides parallelogram is 60°.

Qs: 67

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

A circle touches all the four sides AB, BC, CD, DA of a quadrilateral ABCD.

Question: What is the perimeter of the quadrilateral?

Statement-I: AB + DC = 10 cm

Statement-II: AD+ BC= 10 cm

Qs: 68

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

Question : What is the ratio of the lengths of diagonals of a rhombus ?

Statement -I : One diagonal of the rhombus is equal to its side.

Statement -II : The longer diagonal of the rhombus is equal to √3 times its side.

Qs: 69

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

The chord of a circle of radius R touches at a point on the circumference of a concentric circle of radius r. The length of the chord is 24 units.

Question : What are the values of r and R?

Statement-I : r is an integer .

Statement-II : R is an integer .

Qs: 70

Consider the following for the next ten (10) items that follow :

Each item contains a Question followed by two Statements. Answer each item using the following instructions :

Choose option

(a) If the Question can be answered by one of the Statements alone, but not by the other.

(b) If the Question can be answered by either Statement alone.

(c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

(d) If the Question cannot be answered even by using both Statements together

Question:

Qs: 71

Question:

Qs: 72

Question:

If p is the perimeter of the smallest sector, then what is the value of 9p ?

142 cm
148 cm
156 cm
221 cm

Qs: 73

Consider the following for the next three (03) items that follow :
Two trains A and B started from stations P and Q respectively towards each other . Train A started at 7 p.m. at a speed of 60 km/hr and train B started at
4 a.m. (next day) at a speed of 90 km/hr. The area of the quadrilateral distance between the two stations P and Q is 800 km.

Question:

How far from station Q will the two trains meet?

104 km
144 km
156 km
504 km

Qs: 74

Question:

At what time will the two trains meet?

5:28a.m.
5:44 a.m.
4:56 a.m.
6:24 a.m

Qs: 75

Question:

If the lengths of the two trains A and B are 400 m and 500 m respectively, then what is the time taken by them to cross each other ?

21.6 seconds
18.2 seconds
17.4 seconds
15.4 seconds

Question:

Question:

Question:

Question:

What is the area of the shaded region ?

38.5 square cm
48 square cm
52.5 square cm
66.5 square cm

Qs: 80

Question:

What is the ratio of the area of the shaded region to the area of the non-shaded region ?

$\frac{19}{25}$
$\frac{18}{25}$
$\frac{17}{25}$
$\frac{16}{25}$

Qs: 81

Question:

What is the length of MN ?

$\frac{3}{8} cm$
$\frac{5}{8} cm$
$\frac{9}{8} cm$
$\frac{15}{8} cm$

Qs: 82

Question:

What is the ratio of the area of the quadrilateral PQNM to the area of the quadrilateral RSNM?

$\frac{200}{117}$
$\frac{212}{117}$
$\frac{275}{117}$
$\frac{250}{117}$

Qs: 83

Question:

If the people coming from a particular State belonging to S are 15% and 24,000 in number , then what is the total number of migrating people belonging to the age group B ?