2024 CDS -1 MATH-14454

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2024 CDS -1 MATH (Test Code: 14454)

  1. 1

  2. 2

  3. 3

  4. 6

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?

  1. 8

  2. 6

  3. 5

  4. 2

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

  1. 1 : 1

  2. 1 : 3

  3. 2 : 1

  4. 2 : 3

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 ? 

  1. Rs.175.25 

  2. Rs.152.25 

  3. Rs.76.25 

  4. Rs.24.25 

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 ?

  1. 12

  2. 16

  3. 18

  4. 20

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 ?

  1. 20%

  2. 40%

  3. 75%

  4. 100%

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?

  1. There are infinitely many such equations having different roots.

  2. There is only one such equation which is x2 + 2x - 100 = 0.

  3. There is only one such equation which is x2 - 2x - 100 = 0.

  4. There is no such equation.

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 ?

  1. 10

  2. 17

  3. 21

  4. 37

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

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

  1. 4

  2. 3

  3. 2

  4. 1

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 ?

  1. 24/7 cm

  2. 96/7 cm

  3. 24 cm

  4. 24 cm

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

  1. 1

  2. 2

  3. 3

  4. 4

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. 1 and  2 only
  2. 2 and  3 only

  3. 1 and  3 only

  4. 1, 2 and 3

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

  1. 6

  2. 5

  3. 4

  4. 2

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

  1. 3

  2. 4

  3. 5

  4. 6

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

  1. 3

  2. 4

  3. 6

  4. 7

When the number

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

  1. 15

  2. 12

  3. 4

  4. 3

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 ?

  1. 36/25

  2. 12/5

  3. 4

  4. 2

  1. -2a

  2. a

  3. 2a

  4. 3a

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 ?

  1. 45

  2. 90

  3. 400

  4. 500

  1. a

  2. b

  3. c

  4. d

  1. 5

  2. 7

  3. 9

  4. 11

  1. 91

  2. 90

  3. 13

  4. 12

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. 1 and 2 only

  2. 2 and  3 only

  3. 1 and  3 only

  4. 1, 2 and 3

  1. 1 and 2 only

  2. 2 and  3 only

  3. 1 and  3 only

  4. 1, 2 and 3

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 ?

  1. 12

  2. 18

  3. 24

  4. 28

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 ?

  1. 45 days

  2. 50 days

  3. 55 days

  4. 60 days

  1. a

  2. b

  3. c

  4. d

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 ?

  1. 5 : 1

  2. 6: 1

  3. 10 : 1

  4. 11 : 1

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

  1. -3

  2. -2

  3. 5

  4. 8

  1. 1 only

  2. 2 only

  3. Both 1 and 2

  4. Neither 1 nor 2

  1. 3

  2. 5

  3. 7

  4. 9

  1. 1

  2. 4

  3. 7

  4. 9

  1. 720

  2. 480

  3. 360

  4. 60

  1. 126 square cm

  2. 189 square cm

  3. 252 square cm

  4. 315 square cm

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 ?

  1. 0.35

  2. 0.7

  3. 1.05

  4. 1.4

  1. 1.4

  2. 1.7

  3. 2.2

  4. 2.6

  1. 154 square cm
  2. 144 square cm

  3. 132 square cm

  4. Cannot be determined due to insufficient data

  1. 40 square cm

  2. 42 square cm

  3. 45  square cm

  4. 48 square cm

  1. a

  2. b

  3. c

  4. d

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

  1. 20%

  2. 25%

  3. 30%

  4. 40%

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 ?

  1. 5

  2. 6

  3. 7.5

  4. 9

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 ?

  1. 5

  2. 6

  3. 7

  4. 8

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

  1. 1: 1

  2. 2 : 3

  3. 3 : 1

  4. 4: 3

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 ?

  1. Rs.16

  2. Rs.15

  3. Rs.5

  4. Rs.1

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 ?

  1. 8 < X < 12

     

  2. 12 < x < 16

  3. 16 < X  < 18

  4. 18 < x < 20

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

  1. (√2 +1) : 1

  2. (√3 +1) : 1

  3. 3 : 2

  4. 5 : 4

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 ?

  1. 24  square cm

  2. 30 square cm

  3. 36 square cm

  4. 40 square cm

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

 

  1. 25°

  2. 27°

  3. 28°

  4. 30°

  1. 0

  2. 1

  3. 2

  4. 4

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 ?

  1. 4 m

  2. 5 m

  3. 6 m

  4. 9 m

  1. 1 only

  2. 2 only

  3. Both 1 and 2

  4. Neither 1 nor 2

  1. a

  2. b

  3. c

  4. d

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?

  1. 100%

  2. 99%

  3. 98%

  4. 50%

  1. a

  2. b

  3. c

  4. d

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. 1 and  2 only

  2. 2 and 3 only

  3. 1  and  3 only

  4. 1, 2 and 3

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 ?

  1. 48

  2. 40

  3. 36

  4. Cannot be determined due to insufficient data

  1. 1

  2. 9

  3. 16

  4. 25

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.

  1. a

  2. b

  3. c

  4. d

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

  1. a

  2. b

  3. c

  4. d

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.

  1. a

  2. b

  3. c

  4. d

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

  1. a

  2. b

  3. c

  4. d

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

  1. a

  2. b

  3. c

  4. d

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°.

  1. a

  2. b

  3. c

  4. d

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

  1. a

  2. b

  3. c

  4. d

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.

  1. a

  2. b

  3. c

  4. d

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 .

  1. a

  2. b

  3. c

  4. d

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:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

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

  1. 142 cm

  2. 148 cm

  3. 156 cm

  4. 221 cm

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?

  1. 104 km

  2. 144 km

  3. 156 km

  4. 504 km

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:

At what time will the  two trains meet?

  1. 5:28a.m.

  2. 5:44 a.m.

  3. 4:56 a.m.

  4. 6:24 a.m

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:

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 ?

  1. 21.6 seconds

  2. 18.2 seconds

  3. 17.4 seconds

  4. 15.4 seconds

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

What is the area of the shaded region ? 

  1. 38.5 square cm

  2. 48 square cm

  3. 52.5 square cm

  4. 66.5  square cm

Question:

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

  1. \frac{19}{25}

  2. \frac{18}{25}

  3. \frac{17}{25}

  4. \frac{16}{25}

Question:

What is the length of MN ?

  1. \frac{3}{8} cm

  2. \frac{5}{8} cm

  3. \frac{9}{8} cm

  4. \frac{15}{8} cm

Question:

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

  1. \frac{200}{117}

  2. \frac{212}{117}

  3. \frac{275}{117}

  4. \frac{250}{117}

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 ?

  1. 1.2 lac

  2. 1.25 lac

  3. 1.30 lac

  4. 1.50 lac

Question:

What is the maximum of differences between the number of people coming from different groups P, Q, Rand S?

  1. 1.6 lac

  2. 1.8 lac

  3. 2.4 lac

  4. 2.6 lac

Question:

What is the difference between number of  people coming from R having age group A and those coming from Q having age group D ?

  1. 6,000

  2. 8,000

  3. 12,000

  4. 18,000

Question:

What is the area of the overlapping region ?

  1. \frac{8}{5} square cm

  2. \frac{5}{4} square cm

  3. \frac{4}{5} square cm

  4. \frac{3}{4} square cm

Question:

What   is   the   area  of  the non-overlapping region?

  1. \frac{3}{4} square cm

  2. \frac{11}{4} square cm

  3. \frac{3}{2} square cm

  4. \frac{5}{4} square cm

Question:

What is AB + BC equal to ?

  1. 10 cm

  2. 12 cm

  3. 13 cm

  4. 14 cm

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

What is the area of triangle EOF ?

  1. 12.5 √3 square cm

  2. 6.25 √3 square cm

  3. 12.5 square cm

  4. 6.25 square cm

Question:

What is the area of trapezium AEFB ?

  1. 30 square cm

  2. 25 square cm

  3. 20 square cm 

  4. 18.75 square cm

Question:

What is the area of the shaded region ?

  1. 14.75 square cm

  2. 14.25 square cm

  3. 7.225 square cm

  4. 7.625 square cm

Question:

What is the length of the side of the triangle ABC?

  1. 2√3 unit

  2. 4√3 unit

  3. 6√3 unit

  4. 8√3 unit

Question:

  1. a

  2. b

  3. c

  4. d

Question:

What is the sum of the areas of the two circles?

  1. 17π square unit

  2. 16.75π square unit

  3. 16.5π square unit

  4. 16.25π square unit

Question:

Which one of the following is correct in respect of angle θ?

0 < θ < 30°

  1. 0 < θ < 30°

  2.  30° < θ < 45°

  3. 45° < θ < 60°

  4. 60° < θ < 90°

Question:

  1. a

  2. b

  3. c

  4. d

Question:

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

  1. 2: 7

  2. 2: 5

  3. 3: 5

  4. 5: 8

Question:

What is the perimeter of the shaded region ?

  1. 24π cm

  2. 18π cm

  3. 15π cm

  4. 12π cm

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