KCET Karnataka Common Entrance Test Latest Edition Practice Kit

30 Tests 30 Mock Test

Based On Real Exam Pattern

Thoroughly Revised and Updated Detailed Analysis of all MCQs

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Mathematics : Mock Test

1-188

Mathematics : Mock Test - 1

1-18

Mathematics : Mock Test - 2

19-37

Mathematics : Mock Test - 3

38-56

Mathematics : Mock Test - 4

57-75

Mathematics : Mock Test - 5

76-92

Mathematics : Mock Test - 6

93-113

Mathematics : Mock Test - 7

114-133

Mathematics : Mock Test - 8

134-151

Mathematics : Mock Test - 9

152-171

Mathematics : Mock Test - 10

172-188

Chemistry : Mock Test

189-322

Chemistry : Mock Test - 1

189-201

Chemistry : Mock Test - 2

202-214

Chemistry : Mock Test - 3

215-227

Chemistry : Mock Test - 4

228-241

Chemistry : Mock Test - 5

242-254

Chemistry : Mock Test - 6

255-268

Chemistry : Mock Test - 7

269-282

Chemistry : Mock Test - 8

283-295

Chemistry : Mock Test - 9

296-309

Chemistry : Mock Test - 10

310-322

Physics : Mock Test

323-490

Physics : Mock Test - 1

323-338

Physics : Mock Test - 2

339-353

Physics : Mock Test - 3

354-372

Physics : Mock Test - 4

373-388

Physics : Mock Test - 5

389-404

Physics : Mock Test - 6

405-420

Physics : Mock Test - 7

421-439

Physics : Mock Test - 8

440-456

Physics : Mock Test - 9

457-471

Physics : Mock Test - 10

472-490

Q.1 The area bounded by

𝑦 = log𝑥, 𝑥-axis and ordinates

𝑥 = 1, 𝑥 = 2 is: A.

1

C.

log ( ) sq. unit

2

(log2)2 sq. unit 4

A. 5𝑝 = 2𝑞

2

B.

log ( ) sq. unit 𝑒

𝑋 be a binomial random variable with mean 1 and 3 variance . The probability that 𝑋 takes the value of 3 is: 4 Q.2 Let

3

A.

3

B.

64

C.

16

27

D.

64

B. 2𝑝 = 5𝑞

C. 𝑝 = 2𝑞

D. 5𝑝 = 𝑞

Q.11 If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?

D. log 4 sq. unit

𝑒

𝑝 and 𝑞 so that the maximum of 𝑍 occurs at both the points (25,20) and (0,30) is: Condition on

3 4

2 −1 (1−𝑥 ) Q.3 What is cos equal to? 1+𝑥 2 −1 A. sin 𝑥 B. 2cot−1𝑥 −1 C. 2tan 𝑥 D. tan−1 𝑥

A. 10

B. 12

Q.12 If 𝑓 (2𝑎 − 𝑥) 2𝑎 ∫0 𝑓 (𝑥)𝑑𝑥 is: A. 2𝜆 B. 0 Q.13 Solve:

C. 13

=

D. 15

𝑎 𝑓 (𝑥) and ∫0 𝑓 (𝑥)𝑑𝑥 C. 2𝜆

= 𝜆 then

D. 𝜆

𝑑𝑦

𝑥 𝑑𝑥 − 𝑦 = 𝑥 2 for 𝑦(2), given 𝑦(1) = 1

A. 1

B. 2

C. 3

D. 4

Q.4

𝑛(𝑛 + 1)(𝑛 + 5) is a multiple of 3 is true for:

Q.14 A bag contains

A. B. C. D.

All natural numbers Only natural number All natural numbers Only natural number

both sides, whereas 𝑛 + 1 coins are fair. A coin is picked on random from the bag and tossed. If the probability that toss in 31 tail is , total numbers of coins in the bag are: 42 A. 20 B. 21 C. 25 D. 33

𝑛>5 3 ≤ 𝑛 < 15 𝑛 −3 ≤ 𝑛 < 5

→ → → Q.5 If 𝛽 is perpendicular to both 𝛼 and 𝛾 where 𝛼 → and 𝛾 = 2𝑖̂ + 3𝑗̂ + 4𝑘, then what is 𝛽 equal to? A. C.

B. D.

3ı̂ + 2ȷ̂ 2𝑖̂ − 3𝑗̂

= 𝑘̂

−3𝑖̂ + 2𝑗̂ −2ı̂ + 3𝑗̂

Q.6 What is the value of A. 1

B. 6 𝑥2

Q.7 If A.

lim

𝑥→0

𝑎2

𝑏 2𝑥 𝑎2𝑦

𝑦2

+ 𝑏2 = 1, then B. −

𝑏 2𝑥 𝑎2𝑦

𝑑𝑦 𝑑𝑥

𝑥sin𝑥 C. 4

C.

? D. 8

=? C. −

𝑏 2𝑦

D.

𝑎2𝑥

𝑏 2𝑦 𝑎2𝑥

Q.8 What is the equation of the right bisector of the lines segments joining A. C.

B. D.

80𝑥 − 40𝑦 + 103 80𝑥 + 40𝑦 + 103 80𝑥 + 40𝑦 − 103 80𝑥 − 40𝑦 − 103

𝑦= 4𝑥 − 2𝑦 +

=0 =0 =0 =0

Q.10 The corner points of the feasible region determined by

(0,10), (5,5), (25,20) 𝑍 = 𝑝𝑥 + 𝑞𝑦 , where 𝑝, 𝑞 > 0.

the system of linear constraints are

(0,30). Let

1 3𝑥 2

coefficient in the expansion of 10

)

4580

B.

17 5580

−

896 27

D. None of these

17

Q.16 Of the members of three athletic teams in a school, 21 are in the cricket team, 26 are in the hockey team and 29 are in the football team. Among them, 14 play hockey and cricket, 15 play hockey and football, 12 play football and cricket and 8 play all three games. The total number of members in the three athletic teams is: A. 76

B. 49

C. 43

D. 41

and

, find

2𝑥 − 4𝑦 − 5 = 0 𝑥−𝑦+1= 0

√5𝑥 − 3 − 2, which is parallel to the line 3 = 0?

and

−

6th

(1,1) and (2,3)?

2𝑥 + 4𝑦 − 11 = 0 2𝑥 − 4𝑦 − 11 = 0

Q.9 Find the equation of tangent to the curve

A. B. C. D.

(2𝑥 2 A.

2

(𝑒 4𝑥 −1)

Q.15 The

2𝑛 + 1 coins, 𝑛 coins have tails on

Q.17 If A.

B.

C.

D.

Q.18 Find the area under the curve between

(𝐴𝐵)𝑇 .

𝑦 = 𝑥 and 𝑦 =

2𝑥 + 6. A. 72

B. 18

Q.19 In the expansion of

C. 36

(𝑥 3 −

D. 54

1 15 𝑥2

)

, the constant term, is:

1

Mathematics : Mock Test - 1 A.

15

B. 0

𝐶9

C. -

15

D. 1

𝐶9

Q.33 Find the points on the curve

Q.20 The negation of the statement "The product of 3 and 4 is 9" is: A. B. C. D.

It is false that the product of 3 and 4 is 9 The product of 3 and 4 is 12 The product of 3 and 4 is not 12 It is false that the product of 3 and 4 is not 9

of the tangent is equal to the A. C.

(0,0) and (2,3) (0,0) and (2,4)

𝑦 = 𝑥 2 at which the slope

𝑦 coordinate of the point. B. D.

(0,0) and (3,4) (0,1) and (2,4)

Q.34 Find the angle between the line the plane

𝑥+1

𝑦

=3=

2

8

B.

70%. Company's forecast are only correct 60% of the time.

C.

D. None of these

21

23

B.

50

26

C.

50

29

D.

50

50

Q.22 What is the number of different messages that can be represented by three a’s and two b’s? A. 7

B. 8

Q.23 The value of

C. 9

D. 10

𝑥 for which |𝑥 + 1| + √(𝑥 − 1) = 0

A. 0 C. -1

B. 1 D. No value of x

Q.24 Find the radius of the circle,

and

2

A. sin−1 ( )

A.

6

10𝑥 + 2𝑦 − 11𝑧 − 3 = 0.

Q.21 Weather Forecast Company makes a forecast of raining at Find the probability of it correctly forecasting rain?

𝑧−3

21 5

sin−1 ( ) 21

sin−1 ( ) 21

4𝑥 + 7𝑦 with the 3𝑥 + 8𝑦 ≤ 24, 𝑦 ≤ 2, 𝑥 ≥ 0 and 𝑦 ≥ 0.

Q.35 Find the maximum value of conditions A. 32

B. 42

Q.36 For all positive integrals by: A. 8

B. 9

C. 39

D. 30

10𝑛 + 34𝑛+2 + 8 is divisible C. 7

D. 6

Q.37 The factorized form of the following determinant is:

5𝑥 2 + 5𝑦 2 − 20𝑥 −

6𝑦 + 15 = 0. A.

B.

√34 5

C.

√37 5

Q.25 Find the coefficient of (1 + 𝑥 + 𝑥 2 + 𝑥 3 )11 . A. 567 Q.26 If

𝑥

4

B. 990

6 5

D. √

6 5

in the expansion of C. 365

D. 459

6sin2 𝑥 − 2cos2 𝑥 = 4, then find the value of

tan𝑥. A. √3

B. √2

C. √5

D. 0

Q.27 Three planes x + y = 0, y + z = 0, and x + z = 0: A. B. C. D.

Meet in a line Meet in a unique point Meet taken two at a time in parallel lines None of these

Q.28 If A. 24

𝑛

C. 21

D. 20

(𝑚 − 𝑛)(𝑛 − 1)(𝑛) (𝑚 − 𝑙)(𝑛 − 𝑙)(𝑛 − 𝑚) (𝑙 − 𝑚)(𝑛 − 𝑙)(𝑛 − 𝑚) (𝑚 − 1)(𝑛 − 1)(𝑛 − 1)

Q.38 The integrating factor of the differential equation 𝑑𝑥 2𝑦 𝑑𝑦 + 𝑥 = 5𝑦 2 is, (𝑦 ≠ 0): A. √𝑦

B. 𝑦 2

C. 𝑦

D.

Q.39 Which of the following functions, one? A. 𝑓(𝑥) = |𝑥|, ∀𝑥 ∈ 𝑅 B. C. D.

𝐶15 = 𝑛 𝐶8 , then find the value of 𝑛. B. 23

A. B. C. D.

𝑓: 𝑅 → 𝑅 is one-

𝑓(𝑥) = 𝑥 2 , ∀𝑥 ∈ 𝑅 𝑓(𝑥) = −𝑥, ∀𝑥 ∈ 𝑅 None of these

Q.40 The angle between the lines x – 2y = y and y – 2x = 5 is: 1

3

Q.29 How many two-digit numbers are divisible by 4?

A. tan−1 ( )

B.

tan−1 ( )

A. 21

C.

D.

tan−1 ( )

B. 22

C. 24

D. 25

𝛼 , what is the value of (𝛼. 𝑖̂)𝑖̂ + (𝛼. 𝑗̂)𝑗̂ + (𝛼. 𝑘̂ )𝑘̂

1 √𝑦

4 5

tan−1 ( ) 4

5 2 3

Q.30 For any vector

Q.41 In any discrete series (when all values are not same) if

A. 3𝛼

represent mean deviation about mean and 𝑦 represent standard deviation, then which one of the following is correct?

B. 2𝛼

Q.31 Evaluate the integral A.

1 8

B.

2 8

Q.32 For which value(s) of

C. 𝛼

D. −𝛼

A. 𝑦 ≥ 𝑥

𝜋 4

∫0 sin3 2𝑡cos2𝑡 𝑑𝑡. C.

1 7

D.

1 9

𝑘 will the roots of 3𝑥 2 + 3 =

2

B. ±4

C. ±3

D. ±5

𝑝

C. 𝑥 = 𝑦 𝑞

D. 𝑥 < 𝑦

cos −1 (𝑎) + cos −1 (𝑏) = 𝛼, then 𝑞2

𝑝2 𝑎2

+

𝑘cos𝛼 + 𝑏2 = sin2 𝛼 where 𝑘 is equal to: A. −

2𝑘𝑥 be real and equal? A. ±2

Q.42 If

B. 𝑦 ≤ 𝑥

2𝑝𝑞 𝑎𝑏

B.

2𝑝𝑞 𝑎𝑏

𝑝𝑞

C. − 𝑎𝑏

D.

𝑝𝑞 𝑎𝑏

𝑥

Mathematics : Mock Test - 1 tan2𝑥

𝑥→0 B. 1

A. -1

B. C. D.

log(1+2𝑥)

lim

Q.43 Evaluate

C. 2

D. 4

Q.44 The coordinates of the foot of the perpendicular drawn from the point A(1,0,3) to the join of the points B(4,7,1) and C(3,5,3) are: 5 7 17

A. ( , , )

B.

C.

D. (− , , −

3 3 3 5 7 17

( ,− , ) 3

3

3

(5,7,17) 5 7

17

3 3

3

)

𝑦𝑦 ′ + 𝑥𝑦𝑦 ′′ + 𝑥(𝑦 ′ )2 = 0 𝑦𝑦 ′ + 𝑦𝑦 ′′ − 𝑥(𝑦 ′)2 = 0 𝑦𝑦 ′ − 𝑥𝑦𝑦 ′′ − 𝑥(𝑦 ′ )2 = 0

Q.55 XY-plane divides the line joining the points and

A. 2: 1 internally C. 5: 3 internally A. B. C. D.

Q.46 If the feasible region for a solution of linear inequations is bounded, it is called as:

√1 − √1 − √1 − 𝑥 2 is:

Q.47 A set containing subsets. A. 𝑛 2 Q.48 If

B. Finite Region D. None of the above

lim

C. 𝑛

log(1+sin𝑥) 𝑥

A. 0

B.

D. 𝑛 + 1

3

C.

2

B. 5

−3

D. 1

2

C. -4

D. -5

Q.50 Find the equation of the parabola with vertex at the origin, the axis along the x-axis and passing through the point P(3, 4). C.

4

B.

𝑦2 = 𝑥 3

2

𝑦 =−

9 16

A. 7

𝑦2 =

D.

𝑥

Q.51 Find the value of

2

𝑦 =

3 16 16

B.

9

Q.53 If A. C.

3

Q.58 What is the value of the determinant

𝑖 = √−1 ? B. −2

C. 4𝑖

Q.59 The roots of the equation A. Imaginary C. Real and distinct

𝑥2 +

D. −4𝑖 𝑥

+ 1 = 0 are:

√3 B. Real and equal D. Real and distinct

Q.60 How many three- digits numbers are there which are divisible by 9. A. 98

B. 99

C. 100

D. 101

𝑥

C. 6

1

C.

4

2 3

D. −6

9 from two D.

3 4

1

𝑥 = tan−1 (5) then sin2𝑥 is equal to?

4 13 12 13

B.

5 13

D. None of the above

Q.54 Form the differential equation of the following 𝑎(𝑏2 − 𝑥 2 ): A.

{𝑥 ∣ 𝑥 > −1} [−1,1]

𝑦 − 𝑥 from the following equation:

B. −7

1

B. D.

{𝑥 ∣ 𝑥 < 1} [0,1]

𝑓 (𝑥) =

𝑥

Q.52 What is the probability of getting a sum throws of a dice? A.

A. C.

A. 0

2(3𝑥 − 4) − 2 < 4𝑥 − 2 ≥ 2𝑥 − 4; then the possible value of 𝑥 can be:

A.

Q.57 The domain of the function

where

= 𝑘 , the value of 𝑘 is:

Q.49 If A. 2

The function is one-one into The function is many-one into The function is one-one onto The function is many-one onto

𝑛 elements, has exactly ___________

B. 2𝑛

𝑥→0

B. 3: 2 externally D. 5: 3 externally

Q.56 Which one of the following is correct?

Q.45 If 𝑃2 𝑄 and 𝑅 are three sets, then which of the following is correct? A. 𝑃 ∪ (𝑄 ∩ 𝑅) = (𝑃 ∪ 𝑄) ∩ (𝑃 ∩ 𝑅) 𝑃 ∩ (𝑄 ∪ 𝑅) = (𝑃 ∪ 𝑄) ∩ (𝑃 ∪ 𝑅) B. 𝑃 ∪ (𝑄 ∩ 𝑅) = (𝑃 ∪ 𝑄) ∩ (𝑃 ∪ 𝑅) C. 𝑃 ∩ (𝑄 ∪ 𝑅) = (𝑃 ∩ 𝑄) ∩ (𝑃 ∩ 𝑅) D.

A. Concave Polygon C. Convex Polygon

𝐴(2,3, −5)

𝐵(−1, −2, −3) in the ratio:

𝑦2 =

𝑦𝑦 ′ − 𝑥𝑦𝑦 ′′ + 𝑥(𝑦 ′ )2 = 0

3

Mathematics : Mock Test - 1

Smart Answer Sheet Indicates percentage of students who answered questions correctly. Indicates percentage of students who skipped questions. Correct

Q.

Ans.

1

C

2

A

3

C

4

C

5

B

6

C

7

B

8

A

9

D

10

A

11

D

12

A

Skipped 37.5 % 22.66 % 28.12 % 20.32 % 38.28 % 20.31 % 28.12 % 23.44 % 28.91 % 17.97 % 29.69 % 14.84 % 32.03 % 17.19 % 28.12 % 20.32 % 22.66 % 18.75 % 40.62 % 7.82 % 17.19 % 14.06 % 30.47 % 25.0 %

Q.

Correct Ans.

13

D

14

B

15

B

16

C

17

18

19

20

21

22

23

24

B

B

C

A

A

D

D

A

Skipped 23.44 % 23.44 % 23.44 % 17.97 % 17.19 % 22.65 % 20.31 % 7.03 % 33.59 % 21.1 % 38.28 % 21.1 % 32.03 % 20.31 % 27.34 % 18.75 % 25.78 % 23.44 % 38.28 % 23.44 % 27.34 % 22.66 % 28.12 % 23.44 %

Performance Analysis Avg. Score (%) Toppers Score (%) Your Score

4

28.33% 100.0%

Q.

Correct Ans.

25

B

26

A

27

B

28

B

29

30

31

32

33

34

35

36

B

C

A

C

C

A

A

B

Skipped 35.16 % 15.62 % 15.62 % 7.82 % 16.41 % 23.43 % 24.22 % 14.06 % 29.69 % 21.87 % 25.0 % 22.66 % 25.0 % 16.41 % 19.53 % 23.44 % 33.59 % 21.1 % 20.31 % 3.13 % 10.16 % 10.93 % 39.84 % 7.82 %

Q.

Correct Ans.

37

B

38

A

39

C

40

C

41

42

43

44

45

46

47

48

D

A

B

A

C

C

B

D

Skipped 10.94 % 21.87 % 27.34 % 11.72 % 21.09 % 19.53 % 21.09 % 18.75 % 31.25 % 23.44 % 25.0 % 20.31 % 26.56 % 21.88 % 32.81 % 20.31 % 27.34 % 22.66 % 31.25 % 21.87 % 25.78 % 22.66 % 16.41 % 23.43 %

Q.

Correct Ans.

49

A

50

D

51

A

52

A

53

B

54

D

55

D

56

D

57

D

58

D

59

A

60

C

Skipped 21.88 % 17.18 % 37.5 % 5.47 % 42.19 % 17.97 % 21.09 % 24.22 % 21.88 % 23.43 % 18.75 % 21.87 % 34.38 % 8.59 % 14.06 % 23.44 % 32.81 % 6.25 % 40.62 % 13.29 % 25.78 % 21.1 % 28.12 % 15.63 %

Mathematics : Mock Test - 1

Hints and Solutions

1

3

𝑃 (𝑋 = 3) = 4 × 64 × 4 3

1. We know that: Area bounded by function f(x) and g(x) is given as,

= 64 Hence, the correct option is (A). 3. Given, 1−𝑥 2

cos −1 (1+𝑥 2 ) Put

𝑥 = tan𝜃

We have to find the value of Put

1−𝑥 2

cos−1 (1+𝑥 2 )

𝑥 = tan𝜃 1−𝑥 2

1−tan2 𝜃

⇒ cos−1 (1+𝑥 2 ) = cos −1 (1+tan2 𝜃 ) Area

=

𝑏 ∫𝑎 [ 𝑓 (𝑥)

𝑏 ∫𝑎 [ Top

− 𝑔(𝑥)]𝑑𝑥 =

cos −1 ( − bottom ]𝑑𝑥

Given:

Hence, the correct option is (C).

Applying by parts rule, we get:

=

[𝑥log𝑥]12

= cos −1 (cos2 𝜃 − sin2 𝜃)

= 2tan−1 𝑥 (∵ 𝑥 = tan𝜃)

2

= ∫1 log 𝑥 𝑑𝑥

=

)   (∵ 1 + tan2 𝜃 = sec 2 𝜃)

= 2𝜃 (∵ cos −1 cos𝑥 = 𝑥)

Then,

[log𝑥𝑥]12

sec2 𝜃

= cos −1 (cos2𝜃) (∵ cos2𝜃 = cos2 𝜃 − sin2 𝜃)

𝑦 = log𝑥 Area

1−tan2 𝜃

−

21 ∫1 𝑥

−

[𝑥]12

4. Given:

× 𝑥𝑑𝑥

𝑃 (𝑛): 𝑛(𝑛 + 1)(𝑛 + 5) is a multiple of 3. For

𝑛=1

= [2log2 − log1] − [2 − 1]

𝑛(𝑛 + 1)(𝑛 + 5) = 1.2 ⋅ 6 = 12 = 3.4

= 2log2 − 1

𝑃 (𝑛) is true for 𝑛 = 1

= log22 − log𝑒

Suppose

= log4 − log𝑒

𝑘 (𝑘 + 1)(𝑘 + 5) = 3𝑚 (let) or 𝑘 3 + 6𝑘 2 + 5𝑘 = 3𝑚 .......(i)

4

= log (𝑒) sq. unit

Replacing

Hence, the correct option is (C).

= 𝑛𝑝 = 1

Variance

= 𝑛𝑝𝑞 = 1

3

4

4

𝑘 3 + 9𝑘 2 + 20𝑘 + 12 = (𝑘 3 + 6𝑘 2 + 5𝑘) + (3𝑘 2 + 15𝑘 + 12)

3 4

= 3 𝑚 + 3𝑘 2 + 15𝑘 + 12  [.......from (i) ]

⇒ 𝑝 = ,𝑞 = ,𝑛 = 4 Binomial distribution

𝑛

𝑟 𝑛−𝑟

𝑃(𝑋 = 𝑟) = 𝐶𝑟 𝑝 𝑞 1 3 3 4−3

𝑃 (𝑋 = 3) = 4 𝐶3 ( ) ( ) 4

𝑃 (𝑋 = 3) =

𝑘 by 𝑘 + 1, we get

(𝑘 + 1)(𝑘 + 2)(𝑘 + 6) = 𝑘(𝑘 2 + 8𝑘 + 12) + (𝑘 2 + 8𝑘 + 12)

2. Given: Mean

𝑝(𝑘) is true for 𝑛 = 𝑘

4×3×2×1 3×2×1

4

1

3

× 64 × 4

= 3( 𝑚 + 𝑘 2 + 5𝑘 + 4) (𝑘 + 1)(𝑘 + 2)(𝑘 + 6) is a multiple of 3 i.e., 𝑃(𝑘 + 1) is multiple of 3 , if 𝑃(𝑘) is a multiple of 3 i.e., 𝑃(𝑘 + 1) is true whenever 𝑃 (𝑘) is true. So,

𝑃(𝑛) is true for all 𝑛 ∈ 𝑁. 5