CDS (I) 2024, Elementary Mathematics question paper

1. A.
   1
2. B.
   2
3. C.
   3
4. D.
   6

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1. A.
   8
2. B.
   6
3. C.
   5
4. D.
   2

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1. A.
   $1 : 1$
2. B.
   $1 : 3$
3. C.
   $2 : 1$
4. D.
   $2 : 3$

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1. A.
   Rs. 175.25
2. B.
   Rs. 152.25
3. C.
   Rs. 76.25
4. D.
   Rs. 24.25

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1. A.
   20%
2. B.
   40%
3. C.
   75%
4. D.
   100%

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1. A.
   12
2. B.
   16
3. C.
   18
4. D.
   20

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1. A.
   There are infinitely many such equations having different roots.
2. B.
   There is only one such equation which is $x^2 + 2x - 100 = 0$.
3. C.
   There is only one such equation which is $x^2 - 2x - 100 = 0$.
4. D.
   There is no such equation.

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1. A.
   10
2. B.
   17
3. C.
   21
4. D.
   37

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1. A.
   $\sqrt{\frac{1 + t}{1 - t}}$
2. B.
   $\frac{t}{\sqrt{1 - t^2}}$
3. C.
   $\frac{\sqrt{1 - t^2}}{t}$
4. D.
   $\sqrt{\frac{1 - t}{1 + t}}$

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1. A.
   $-\lambda + \delta$
2. B.
   $\lambda - \delta$
3. C.
   $\lambda + \delta$
4. D.
   $-\lambda - \delta$

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1. A.
   $p = 1/8$
2. B.
   $p \le 1/8$
3. C.
   $p \ge 1/8$
4. D.
   $p \le 1/4$

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1. A.
   4
2. B.
   3
3. C.
   2
4. D.
   1

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1. A.
   24/7 cm
2. B.
   96/7 cm
3. C.
   24 cm
4. D.
   32 cm

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1. A.
   1
2. B.
   2
3. C.
   3
4. D.
   4

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1. A.
   1 and 2 only
2. B.
   2 and 3 only
3. C.
   1 and 3 only
4. D.
   1, 2 and 3

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1. A.
   6
2. B.
   5
3. C.
   4
4. D.
   2

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1. A.
   3
2. B.
   4
3. C.
   5
4. D.
   6

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1. A.
   3
2. B.
   4
3. C.
   6
4. D.
   7

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1. A.
   15
2. B.
   12
3. C.
   4
4. D.
   3

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1. A.
   36/25
2. B.
   12/5
3. C.
   4
4. D.
   2

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1. A.
   $-2a$
2. B.
   a
3. C.
   2a
4. D.
   3a

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1. A.
   45
2. B.
   90
3. C.
   400
4. D.
   500

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1. A.
   $x - 5y$
2. B.
   $x + 5y$
3. C.
   $x^2 + 5xy + 25y^2$
4. D.
   1

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1. A.
   5
2. B.
   7
3. C.
   9
4. D.
   11

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1. A.
   91
2. B.
   90
3. C.
   13
4. D.
   12

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1. A.
   1 and 2 only
2. B.
   2 and 3 only
3. C.
   1 and 3 only
4. D.
   1, 2 and 3

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1. A.
   1 only
2. B.
   2 only
3. C.
   Both 1 and 2
4. D.
   Neither 1 nor 2

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1. A.
   12
2. B.
   18
3. C.
   24
4. D.
   28

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1. A.
   45 days
2. B.
   50 days
3. C.
   55 days
4. D.
   60 days

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1. A.
   $0 < x < 0.5$
2. B.
   $x = 0.5$
3. C.
   $0.5 < x < 1.0$
4. D.
   $x > 1.0$

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1. A.
   $5 : 1$
2. B.
   $6 : 1$
3. C.
   $10 : 1$
4. D.
   $11 : 1$

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1. A.
   $-3$
2. B.
   $-2$
3. C.
   5
4. D.
   8

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1. A.
   1 only
2. B.
   2 only
3. C.
   Both 1 and 2
4. D.
   Neither 1 nor 2

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1. A.
   3
2. B.
   5
3. C.
   7
4. D.
   9

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1. A.
   1
2. B.
   4
3. C.
   7
4. D.
   9

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1. A.
   720
2. B.
   480
3. C.
   360
4. D.
   60

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1. A.
   126 square cm
2. B.
   189 square cm
3. C.
   252 square cm
4. D.
   315 square cm

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1. A.
   0.35
2. B.
   0.7
3. C.
   1.05
4. D.
   1.4

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1. A.
   1.4
2. B.
   1.7
3. C.
   2.2
4. D.
   2.6

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1. A.
   154 square cm
2. B.
   144 square cm
3. C.
   132 square cm
4. D.
   Cannot be determined due to insufficient data

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1. A.
   40 square cm
2. B.
   42 square cm
3. C.
   45 square cm
4. D.
   48 square cm

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1. A.
   $P^2 Q$
2. B.
   $PQ^2$
3. C.
   $\sqrt{PQ}$
4. D.
   $P^{1/3} Q^{2/3}$

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1. A.
   20%
2. B.
   25%
3. C.
   30%
4. D.
   40%

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1. A.
   5
2. B.
   6
3. C.
   7.5
4. D.
   9

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1. A.
   5
2. B.
   6
3. C.
   7
4. D.
   8

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1. A.
   1 : 1
2. B.
   2 : 3
3. C.
   3 : 1
4. D.
   4 : 3

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1. A.
   Rs. 16
2. B.
   Rs. 15
3. C.
   Rs. 5
4. D.
   Rs. 1

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1. A.
   $8 < x < 12$
2. B.
   $12 < x < 16$
3. C.
   $16 < x < 18$
4. D.
   $18 < x < 20$

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1. A.
   $(\sqrt{2} + 1) : 1$
2. B.
   $(\sqrt{3} + 1) : 1$
3. C.
   3 : 2
4. D.
   5 : 4

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1. A.
   24 square cm
2. B.
   30 square cm
3. C.
   36 square cm
4. D.
   40 square cm

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1. A.
   $25^\circ$
2. B.
   $27^\circ$
3. C.
   $28^\circ$
4. D.
   $30^\circ$

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1. A.
   0
2. B.
   1
3. C.
   2
4. D.
   4

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1. A.
   4 m
2. B.
   5 m
3. C.
   6 m
4. D.
   9 m

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1. A.
   1 only
2. B.
   2 only
3. C.
   Both 1 and 2
4. D.
   Neither 1 nor 2

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1. A.
   $\frac{200}{3}$ km
2. B.
   100 km
3. C.
   $\frac{400}{3}$ km
4. D.
   $\frac{1000}{3}$ km

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1. A.
   100%
2. B.
   99%
3. C.
   98%
4. D.
   50%

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1. A.
   Rs. 2307
2. B.
   Rs. 2376
3. C.
   Rs. 2508
4. D.
   Rs. 2896

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1. A.
   1 and 2 only
2. B.
   2 and 3 only
3. C.
   1 and 3 only
4. D.
   1, 2 and 3

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1. A.
   48
2. B.
   40
3. C.
   36
4. D.
   Cannot be determined due to insufficient data

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1. A.
   1
2. B.
   9
3. C.
   16
4. D.
   25

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   If the Question can be answered by one of the Statements alone, but not by the other.
2. B.
   If the Question can be answered by either Statement alone.
3. C.
   If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
4. D.
   If the Question cannot be answered even by using both Statements together.

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1. A.
   $\frac{88}{3}$ square cm
2. B.
   $\frac{77}{3}$ square cm
3. C.
   $\frac{149}{6}$ square cm
4. D.
   $\frac{616}{9}$ square cm

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1. A.
   142 cm
2. B.
   148 cm
3. C.
   156 cm
4. D.
   221 cm

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1. A.
   104 km
2. B.
   144 km
3. C.
   156 km
4. D.
   504 km

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1. A.
   5:28 a.m.
2. B.
   5:44 a.m.
3. C.
   4:56 a.m.
4. D.
   6:24 a.m.

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1. A.
   21.6 seconds
2. B.
   18.2 seconds
3. C.
   17.4 seconds
4. D.
   15.4 seconds

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1. A.
   $\frac{512}{17}$ square cm
2. B.
   $\frac{625}{13}$ square cm
3. C.
   $\frac{1024}{17}$ square cm
4. D.
   $\frac{1296}{13}$ square cm

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1. A.
   $\frac{13}{16}$
2. B.
   $\frac{15}{16}$
3. C.
   $\frac{17}{16}$
4. D.
   $\frac{17}{4}$

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1. A.
   $\frac{416}{17}$ square cm
2. B.
   $\frac{312}{13}$ square cm
3. C.
   $\frac{208}{17}$ square cm
4. D.
   $\frac{156}{13}$ square cm

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1. A.
   38.5 square cm
2. B.
   48 square cm
3. C.
   52.5 square cm
4. D.
   66.5 square cm

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1. A.
   $\frac{19}{25}$
2. B.
   $\frac{18}{25}$
3. C.
   $\frac{17}{25}$
4. D.
   $\frac{16}{25}$

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1. A.
   $\frac{3}{8}$ cm
2. B.
   $\frac{5}{8}$ cm
3. C.
   $\frac{9}{8}$ cm
4. D.
   $\frac{15}{8}$ cm

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1. A.
   $\frac{200}{117}$
2. B.
   $\frac{212}{117}$
3. C.
   $\frac{275}{117}$
4. D.
   $\frac{250}{117}$

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1. A.
   1.2 lac
2. B.
   1.25 lac
3. C.
   1.30 lac
4. D.
   1.50 lac

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1. A.
   1.6 lac
2. B.
   1.8 lac
3. C.
   2.4 lac
4. D.
   2.6 lac

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1. A.
   6,000
2. B.
   8,000
3. C.
   12,000
4. D.
   18,000

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1. A.
   $\frac{8}{5}$ square cm
2. B.
   $\frac{5}{4}$ square cm
3. C.
   $\frac{4}{5}$ square cm
4. D.
   $\frac{3}{4}$ square cm

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1. A.
   $\frac{3}{4}$ square cm
2. B.
   $\frac{11}{4}$ square cm
3. C.
   $\frac{3}{2}$ square cm
4. D.
   $\frac{5}{4}$ square cm

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1. A.
   10 cm
2. B.
   12 cm
3. C.
   13 cm
4. D.
   14 cm

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1. A.
   $4 - \sqrt{5}$
2. B.
   $1 + \sqrt{5}$
3. C.
   $2 + \sqrt{5}$
4. D.
   $3 - \sqrt{5}$

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1. A.
   $5 - \sqrt{10}$
2. B.
   $1 + 2\sqrt{5}$
3. C.
   $\frac{22 - 4\sqrt{10}}{9}$
4. D.
   $\frac{22 - 2\sqrt{10}}{9}$

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1. A.
   $12.5\sqrt{3}$ square cm
2. B.
   $6.25\sqrt{3}$ square cm
3. C.
   12.5 square cm
4. D.
   6.25 square cm

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1. A.
   30 square cm
2. B.
   25 square cm
3. C.
   20 square cm
4. D.
   18.75 square cm

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1. A.
   14.75 square cm
2. B.
   14.25 square cm
3. C.
   7.225 square cm
4. D.
   7.625 square cm

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1. A.
   $2\sqrt{3}$ unit
2. B.
   $4\sqrt{3}$ unit
3. C.
   $6\sqrt{3}$ unit
4. D.
   $8\sqrt{3}$ unit

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1. A.
   $6(\pi + \sqrt{3})$ square unit
2. B.
   $3(\pi + 2\sqrt{3})$ square unit
3. C.
   $1.5(3\pi + 8\sqrt{3})$ square unit
4. D.
   $6(\pi + 2\sqrt{3})$ square unit

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1. A.
   $17\pi$ square unit
2. B.
   $16.75\pi$ square unit
3. C.
   $16.5\pi$ square unit
4. D.
   $16.25\pi$ square unit

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1. A.
   $0 < \theta < 30^\circ$
2. B.
   $30^\circ < \theta < 45^\circ$
3. C.
   $45^\circ < \theta < 60^\circ$
4. D.
   $60^\circ < \theta < 90^\circ$

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1. A.
   $\frac{240 - 10\pi - \pi\theta}{24}$ square unit
2. B.
   $\frac{240 - 6\pi - \pi\theta}{24}$ square unit
3. C.
   $\frac{120 - 12\pi - \pi\theta}{24}$ square unit
4. D.
   $\frac{240 - 12\pi - \pi\theta}{24}$ square unit

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1. A.
   2 : 7
2. B.
   2 : 5
3. C.
   3 : 5
4. D.
   5 : 8

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1. A.
   $24\pi$ cm
2. B.
   $18\pi$ cm
3. C.
   $15\pi$ cm
4. D.
   $12\pi$ cm

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