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RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code 4 4 Solutions Date: 10 May 2018 1. Diiculty : Easy Topics : Definite integration, Rao IIT Academy Website : www.raoiit.com 1 T arget -2018

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Page 1: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

MHT ­ CET 2018 Mathematics / Code­ 44

Solutions

Date: 10 May 2018

1. Di�iculty : Easy

Topics :

Definite integration,

Rao IIT Academy Website : www.raoiit.com1

Target -2018

Page 2: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

2. Di�iculty : Easy

Topics :

Trigonometric Function,

3. Di�iculty : Medium

Topics :

Di�erentiation,

Rao IIT Academy Website : www.raoiit.com2

Page 3: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

4. Di�iculty : Medium

Topics :

Trigonometrical ratios of Compound angles,

 and 

  have 3 solutions

 have 2 solutions.

Rao IIT Academy Website : www.raoiit.com3

Page 4: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

5. Di�iculty : Easy

Topics :

Trigonometric Function,

 ; 

6. Di�iculty : Easy

Topics :

Determinants & Matrices,

7.Di�iculty : Di�icult

Topics :

Mathematics,

Topic - Mathematical logic

contrapositive 

If my friends do not come or we do not go for picnic then weather will not be fine.

Rao IIT Academy Website : www.raoiit.com4

Page 5: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

8. Di�iculty : Medium

Topics :

Application of derivatives,

as   is always positive

9. Di�iculty : Medium

Topics :

Mathematics,

(OR)

put 

Rao IIT Academy Website : www.raoiit.com5

Page 6: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

10. Di�iculty : Easy

Topics :

Mathematics,

Topic - Mathematical logic

contradiction.

11. Di�iculty : Easy

Topics :

Definite integration,

12. Di�iculty : Easy

Topics :

Conics,

Rao IIT Academy Website : www.raoiit.com6

Page 7: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

13. Di�iculty : Medium

Topics :

Indefinite integration,

14. Di�iculty : Medium

Topics :

Di�erentiation,

 then   and 

15. Di�iculty : Easy

Topics :

SETS, RELATION AND FUNCTIONS,

Rao IIT Academy Website : www.raoiit.com7

Page 8: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

16. Di�iculty : Medium

Topics :

Plane,

17.Di�iculty : Medium

Topics :

Di�erentiation,

 Equation of parabola 

have two arbitary constants   and 

 Order 

Rao IIT Academy Website : www.raoiit.com8

Page 9: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

18. Di�iculty : Easy

Topics :

Straight lines,

19. Di�iculty : Easy

Topics :

Three Dimensional Geometry,

Rao IIT Academy Website : www.raoiit.com9

Page 10: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

20.Di�iculty : Easy

Topics :

Vectors,

 

21. Di�iculty : Easy

Topics :

Trigonometric Ratios & Identities,

22. Di�iculty : Di�icult

Topics :

Plane,

Rao IIT Academy Website : www.raoiit.com10

Page 11: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

23. Di�iculty : Easy

Topics :

Pair of straight lines,

24. Di�iculty : Easy

Topics :

Random Variables & its Probability Distribution,

25. Di�iculty : Medium

Topics :

Binomial Distribution,

 Number on die is perfect square.

Rao IIT Academy Website : www.raoiit.com11

Page 12: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

26. Di�iculty : Medium

Topics :

Application of derivatives,

 Slope of tangent

Given tangent 

 lies on curve 

27. Di�iculty : Easy

Topics :

Circles,

 Eqn. of circle

Rao IIT Academy Website : www.raoiit.com12

Page 13: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

28. Di�iculty : Easy

Topics :

Application of derivatives,

To be min

 also 

  

 is minimum

29. Di�iculty : Medium

Topics :

Binomial Distribution,

 also 

 

Rao IIT Academy Website : www.raoiit.com13

Page 14: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

30. Di�iculty : Easy

Topics :

Di�erential Equations,

Let 

 

 

 

 

 

 

Rao IIT Academy Website : www.raoiit.com14

Page 15: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

31. Di�iculty : Medium

Topics :

Probability,

32. Di�iculty : Easy

Topics :

Sequence & Series,

 

 

 

 

 

Rao IIT Academy Website : www.raoiit.com15

Page 16: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

33. Di�iculty : Easy

Topics :

Factorization,

34. Di�iculty : Easy

Topics :

Indefinite integration,

35. Di�iculty : Easy

Topics :

Indefinite integration,

Rao IIT Academy Website : www.raoiit.com16

Page 17: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

36.Di�iculty : Di�icult

Topics :

Vectors,

Rao IIT Academy Website : www.raoiit.com17

Page 18: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

37. Di�iculty : Medium

Topics :

Three Dimensional Geometry,Vectors,

drs of PQ 

              

              

drs of PR 

             

              

as P - Q  - R collinear 

  and 

                   

                              

Rao IIT Academy Website : www.raoiit.com18

Page 19: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

38. Di�iculty : Medium

Topics :

Pair of straight lines,

 ........(1)

 ........(2)

........(3)

Put (3) in (1)

Put (3) in (2)

 

 

 

39. Di�iculty : Easy

Topics :

Pair of straight lines,

 Rao IIT Academy Website : www.raoiit.com19

Page 20: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

40. Di�iculty : Medium

Topics :

Mathematics,

Topic - Mathematical Logic

Hema gets above   marks but she does not get admission in good college.

41.Di�iculty : Easy

Topics :

ContinuityDi�erentiability & Derivatives,

 

 

Rao IIT Academy Website : www.raoiit.com20

Page 21: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

42. Di�iculty : Medium

Topics :

Di�erentiation,

43. Di�iculty : Medium

Topics :

Pair of straight lines,

As   is abscent in given equation

 first line is   and second is 

Given equation 

      

      

     

Rao IIT Academy Website : www.raoiit.com21

Page 22: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

44. Di�iculty : Medium

Topics :

Determinants & Matrices,

45. Di�iculty : Medium

Topics :

LINES AND ANGLES,

  drs of line

      

or  

Equation of line 

Rao IIT Academy Website : www.raoiit.com22

Page 23: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

46. Di�iculty : Medium

Topics :

Random Variables & its Probability Distribution,

 and

and

and

and

and

and

and

47. Di�iculty : Easy

Topics :

Trigonometrical ratios of Compound angles,

Rao IIT Academy Website : www.raoiit.com23

Page 24: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

48. Di�iculty : Easy

Topics :

Definite integration,

49. Di�iculty : Medium

Topics :

ContinuityDi�erentiability & Derivatives,

Rao IIT Academy Website : www.raoiit.com24

Page 25: T MHT CET 2018 Date: 10 May 2018 Mathematics / Code44 ... · RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions MHT CET 2018 Mathematics / Code44 Solutions Date:

RAO IIT ACADEMY / MHT - CET 2018 / Mathematics / Code-44 / Solutions

50.Di�iculty : Easy

Topics :

Linear Programming,

    at   and 

Rao IIT Academy Website : www.raoiit.com25