# math genni sample paper - vidyamandir · 2020. 11. 11. · math genni sample paper . read the...

TRANSCRIPT

1

Vidyamandir Classes : Innovating for your success

Math Genni Sample paper

Read the following Instructions very carefully before you proceed.

The paper contains 24 pages and a total of 50 Objective Type Questions divided into three sections: Section - I, Section - II and Section - III.

Section-I and Section-II contain 20 questions each. Section-III contains 10 questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.

For each question in Section - I, you will be given 3 marks if you have darkened only the bubble corresponding to the correct answer and zero marks if no bubble is darkened. There is NO NEGATIVE MARKING.

For each question in Section - II, you will be given 4 marks if you have darkened only the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one (–1) mark (NEGATIVE MARKING) will be given.

For each question in Section - III, you will be given 6 marks if you have darkened only the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus two (–2) marks (NEGATIVE MARKING) will be given.

For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your Name, Roll No., Seat ID, Date of Birth and the PAPER CODE properly in the space provided in the ANSWER SHEET. IT IS YOUR OWN RESPONSIBILITY TO FILL THE OMR SHEET CORRECTLY.

A blank space has been provided on each page for rough work. You will not be provided with any supplement or rough sheet. However some blank pages for rough work are given at the end of this paper.

The use of log tables, calculator and any other electronic device is strictly prohibited.

There are no errors in the paper. Please do not disturb the invigilator or any other student for any corrections/suggestions in the paper. Violating the examination room discipline will immediately lead to the cancellation of your paper and no excuses will be entertained.

FILL THE FOLLOWING INFORMATION PROPERLY BEFORE YOU PROCEED.

ROLL NUMBER SEAT ID

NAME DATE OF BIRTH

INVIGILATOR’S SIGNATURE ROOM NO.

2

Vidyamandir Classes : Innovating for your success

SUGGESTIONS: • Before starting the paper, spend 2-3 minutes to check whether all the pages are in order and report

any issue to the invigilator immediately. • Try to attempt the Sections in their respective order. • Do not get stuck on a particular question for more than 6-8 minutes. Move on to a new question as

there are 50 questions to solve.

SECTION - I

1. If 2 2

2 213

a ab ba ab b− +

=+ +

, then value of ab

is :

(A) 1 (B) 2 (C) 3 (D) 4 2. A pump can be used either to fill or to empty a tank. The capacity of the tank is 3600m3.

The emptying capacity of the pump is 10m3/min higher than its filling capacity. The emptying capacity of the pump, if pump needs 12 more minutes to fill the tank than to empty it, is :

(A) 50 m3/min (B) 60 m3/min (C) 45 m3/min (D) 90 m3/min

3. If 1 1

2 33 2

a b c db c d e= , = , = , = and

14

ef= , the value of

abcdef

is :

(A) 38

(B) 278

(C) 34

(D) 274

SPACE FOR ROUGH WORK

3

Vidyamandir Classes : Innovating for your success

4. If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B are : (A) 7 and 8 (B) 8 and 0 (C) 5 and 8 (D) None of these

5. Ram purchased a flat at Rs. 1 lakh and Prem purchased a plot of land worth Rs. 1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were 10% and 5%. After two years, they exchanged their belongings and one paid the difference. Then :

(A) Ram paid Rs. 275 to Prem (B) Ram paid Rs. 475 to Prem (C) Ram paid Rs. 375 to Prem (D) Prem paid Rs. 475 to Ram

6. Neeraj has agreed to mow a rectangular lawn, whose length is 40 m and breadth is 20 m. The mower mows a 1 m wide strip. If Neeraj starts at one corner and mows around the lawn towards the centre, the number of rounds before he has mowed half the lawn are :

(A) 2.5 (B) 3.5 (C) 3.8 (D) 4.0

SPACE FOR ROUGH WORK

4

Vidyamandir Classes : Innovating for your success

7. Karan and Arjun run a 100 m race, where Karan beats Arjun by 10 m. Karan starts 10 m behind the starting line in a second 100 m race. They both run at their earlier speeds. The statement which is true with respect to the second race is :

(A) Karan and Arjun reach the finishing line simultaneously (B) Arjun beats Karan by 1 m (C) Arjun beats Karan by 11 m (D) Karan beats Arjun by 1 m

8. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is divided by 2, the quotient is 33. The other number is :

(A) 66 (B) 132 (C) 198 (D) 99

9. A man invests Rs. 10,000 in some shares in the ratio 2 : 3 : 5 which pays dividends of 10%, 25% and 20% (on his investment) for that year respectively. His dividend income is :

(A) Rs.1900 (B) Rs.2000 (C) Rs.2050 (D) Rs.1950

SPACE FOR ROUGH WORK

5

Vidyamandir Classes : Innovating for your success

10. The compound interest on Rs. 1000 at the rate of 20% per annum for 18 months when interest is compounded half-yearly is :

(A) Rs. 331 (B) Rs. 1331 (C) Rs. 320 (D) Rs. 325

11. If = =+ + +a b c

b c c a a b, then each fraction is equal to :

(A) ( )2a b c+ + (B) 1/2 (C) 1/4 (D) 0

12. Nishu and Archana can do a piece of work in 10 days and Nishu alone can do it in 12 days. Archana can do it alone in :

(A) 60 days (B) 30 days (C) 50 days (D) 45 days

SPACE FOR ROUGH WORK

6

Vidyamandir Classes : Innovating for your success

13. A boat goes 40km upstream in 8h and a distance of 49 km downstream in 7h. The speed of the boat in still water is :

(A) 5 km/h (B) 5.5 km/h (C) 6 km/h (D) 6.5 km/h

14. In a race of 600 metres, Ajay beats Vijay by 60 metres and in a race of 500 meters Vijay beats Anjay by 25 metres. The distance by which Ajay will beat Anjay in 400 metre race is :

(A) 48 m (B) 52 m (C) 56 m (D) 58 m 15. The value of x(PA) in the given figure is : (A) 16 cm (B) 9 cm (C) 12 cm (D) 15 cm

SPACE FOR ROUGH WORK

7

Vidyamandir Classes : Innovating for your success

16. In the given figure, A, B, C and D are the concyclic points. The value of x is : (A) 130° (B) 50° (C) 60° (D) 30° 17. In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers

joined the garrison. The soldiers will be able to carry on with the remaining food for : (A) 25 days (B) 20 days (C) 15 days (D) 10 days

18. A village having a population of 4000 requires 150 L of water per head per day. It has a tank measuring 20 m× 15 m× 6 m. The water of this tank will last for :

(A) 2 days (B) 3 days (C) 4 days (D) 5 days

SPACE FOR ROUGH WORK

8

Vidyamandir Classes : Innovating for your success

19. If 1 2 1 2 1 2 0+ − =a b c , then the value of ( )2a b c+ − is :

(A) 2ab (B) 2bc (C) 4ab (D) 4ac

20. A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller sphere has a radius, that is 1/9th of the larger sphere. If 10 litres of paint were needed to paint the larger sphere, paint (in litres) needed to paint all the smaller spheres is :

(A) 90 (B) 81 (C) 900 (D) 810

SPACE FOR ROUGH WORK

9

Vidyamandir Classes : Innovating for your success

SECTION - II 21. A rectangular plot of lawn shown in the figure, has

dimensions x and y and is surrounded by gravel pathway of width 2m. The total area of the pathway is :

(A) 2 2 4x y+ + (B) 2 2 8x y+ + (C) 4 4 8x y+ + (D) 4 4 16x y+ +

22. 4 litres of wine is drawn from a cask containing 40 litres of wine. It is replaced by water. The process is repeated 3 times. The final quantity of wine left in the cask is :

(A) 10.84 litres (B) 29.16 litres (C) 28 litres (D) 29.76 litres

23. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. The sum of the digits in N is :

(A) 4 (B) 5 (C) 6 (D) 8

SPACE FOR ROUGH WORK

10

Vidyamandir Classes : Innovating for your success

24. A spherical pear of radius 4 cm is to be divided into eight equal parts by cutting it in halves along the same axis. The surface area (in cm2) of each of the final piece is :

(A) 20π (B) 25π (C) 24π (D) 19π

25. The value of 6 6 6 . . . .+ + + is :

(A) 4 (B) 3 (C) 3.5 (D) 2.5

26. If p and q are the roots of the equation 2 0x px q+ + = then :

(A) p = 1 (B) p = 1 or 0 or 12

−

(C) 2p = − (D) 2p = − or 0

SPACE FOR ROUGH WORK

11

Vidyamandir Classes : Innovating for your success

27. If 3 4cotθ = , then value of ( )( )5 3

5 3

+

−

sin cos

sin cos

θ θ

θ θ is :

(A) 13

(B) 3 (C) 19

(D) 9

28. The value of ( ) ( )4 4 2 2 22 130 45 3 60 45 30

3 4° − ° − ° − ° + °cos sin sin sec cot is :

(A) 5312

(B) 7324

(C) 11324

(D) 8312

29. If ( )sin cos aθ θ+ = and ( )3 3sin cos bθ θ+ = , then value of ( )3 2−a b is :

(A) 3a (B) 3b (C) 0 (D) 1

SPACE FOR ROUGH WORK

12

Vidyamandir Classes : Innovating for your success

30. If ( ) 0cos α β+ = , then the value of ( )−sin α β is :

(A) cos β (B) 2cos β (C) sinα (D) 2sin α

31. The sum of first p terms of an AP is ( )2ap bp+ . The common difference of the AP is :

(A) a (B) 2a (C) (a + b) (D) 3a + b

32. The numbers lying between 10 and 300, which when divided by 4 leave a remainder 3 are : (A) 71 (B) 72 (C) 73 (D) 74

SPACE FOR ROUGH WORK

13

Vidyamandir Classes : Innovating for your success

33. The number of positive integers between 23 and 100 which are exactly divisible by 6 is : (A) 13 (B) 12 (C) 11 (D) 10

34. If the angles of elevation of a tower from two points at distances a and b, where a b> from its foot and in the same straight line from it are 30° and 60° , then the height of the tower is :

(A) a b+ (B) a b− (C) ab

(D) ab

35. A straight tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point, where the top touches the ground is 10m. The height of the tree is :

(A) 10 3m (B) 10 3

3m (C) ( )10 3 1 m+ (D) ( )10 3 1 m−

SPACE FOR ROUGH WORK

14

Vidyamandir Classes : Innovating for your success

36. One card is drawn at random from a well-shuffled deck of 52 cards. The probability of getting a black face card is :

(A) 126

(B) 326

(C) 3

13 (D)

314

37. The probability that a non-leap year has 53 Mondays is :

(A) 27

(B) 17

(C) 752

(D) 753

38. There are 25 tickets numbered as 1, 2, 3, 4, . . . , 25 respectively. One ticket is drawn at random. The probability that the number on the ticket is a multiple of 3 or 5 is :

(A) 25

(B) 1125

(C) 1225

(D) 1325

SPACE FOR ROUGH WORK

15

Vidyamandir Classes : Innovating for your success

39. A point P divides the join of ( )5 2A , − and B(9, 6) in the ratio 3 : 1. The coordinates of P are :

(A) (4, 7) (B) (8, 4) (C) (12, 8) (D) 11

52

,

40. If the points A(2, 3), B(5, k) and C(6, 7) are collinear, then :

(A) 4k = (B) 6k = (C) 3

2k

−= (D)

114

k =

SPACE FOR ROUGH WORK

SECTION - III

16

Vidyamandir Classes : Innovating for your success

Passage 1

Logarithm in short log, is a function defined as follows : ( ) =blog x y , (read as log of x to base b equals y)

if yx b= be log of an input x gives a output y such that base b to the power that output y gives x.

E.g. ( )2 8log gives 3 as 32 8=

( )2 0 5log . gives 1− as 12 0 5.− =

For ( )blog x to be defined, 0 0 1x , b , b> > ≠

Some identities satisfied by log function For 0 0 0 1x , y , b , b> > > ≠

(i) ( ) ( ) ( )b b blog xy log x log y= + (ii) ( ) ( )b b bx

log log x log yy

= −

(iii) ( ) ( )3 3b blog x log x= (iv) ( ) 1blog b =

(v) ( )1 0blog = (vi) ( )( )

1b

xlog x

log b=

(vii) ( )blog xb x= (viii) cb

c

log xlog x

log b=

(ix) b blog x log yy x= (x) log logzc bb

zx xc

=

Quadratic Equation ( )2 0 0ax bx c a+ + = ≠ has two roots by 2 4

2b b ac

xa

− ± −=

41. ( )3

4 6

3 12a a bb

a b a b

log b log blog a b

log b log b−

−÷ =

−

(A) blog a (B) alog b (C) 1 (D) None of these

42. Product of values of x satisfying ( )22 3 0 0 1x ax a xlog a log a log a a , a+ + = > ≠ is :

(A) 11 6a− (B) 5 6a (C) 7 6a− (D) 4 3a−

43. If 13 4x x−= then x cannot be equal to :

(A) 3

3

2 22 2 1

loglog −

(B) 2

22 3log−

(C) 2

2

2 32 3 1

loglog −

(D) 4

11 3log−

SPACE FOR ROUGH WORK

17

Vidyamandir Classes : Innovating for your success

18

Vidyamandir Classes : Innovating for your success

Passage 2

Consider 3 points ( ) ( ) ( )1 1 2 2 3 3A x , y , B x , y , C x , y in Cartesian plane, AB = c, BC = a, CA = b

( ) ( )2 21 2 1 2AB c x x y y= = − + − (Distance formula)

Area of ABC∆ ( )( )( )2

a b cs s a s b s c , s

+ += − − − =

( ) ( ) ( )1 2 3 2 3 1 3 1 212

x y y x y y x y y= − + − + −

If D(x, y) lies on BC such that BD mDC n

=

Then coordinates of D is given by 2 3 2 3nx mx ny myx , y

n m n m+ +

= =+ +

(section formula)

Slope of AB 1 2

1 2

y ytan

x xθ

−= =

−

If D is mid point of BC then 2 3 2 3

2 2x x y y

x , y+ +

= =

If G is centroid of ABC∆ , i.e. point of intersection of medians then coordinate of G is 1 2 3 1 2 3

3 3

x x x y y y,

+ + + +

I be incentre of ABC∆ , i.e. point of intersection of angle bisectors then coordinate of I is

1 2 3 1 2 3ax bx cx ay by cy,

a b c a b c

+ + + +

+ + + +

44. If A(0, 0), B(3, 0), C(3, 4) be vertices of ABC∆ whose centroid is G and incentre is I then absolute difference of areas of GAB∆ and IAB∆ (in square units) is :

(A) 13

(B) 12

(C) 16

(D) 0

45. The area of the pentagon whose vertices are (4, 1), (3, 6), ( )5, 1− , ( )3 3,− − and ( )3 0,− (in square

units) is : (A) 30 (B) 60 (C) 120 (D) None of these 46. AB is parallel to CD, perpendicular distance of O from AB is

same as perpendicular distance between AB and CD then CE : EB =

(A) 2 : 1 (B) 2 : 3 (C) 1 : 2 (D) 3 : 2

19

Vidyamandir Classes : Innovating for your success

SPACE FOR ROUGH WORK

20

Vidyamandir Classes : Innovating for your success

Passage 3

A sequence of numbers 1 2 3 na , a , a , . . . . , a are said to be in arithmetic progression if

2 1 3 2 4 3 1n na a a a a a . . . . . a a d−− = − = − = = − = (common difference)

Then ( )1 1na a n d= + −

and 1 21

n

n n rr

s a a . . . . a a=

= + + + =∑

( )( ) ( )1 12 12 2 nn n

a n d a a= + − = +

( )

1

11 2 3

2

n

r

n n. . . . n r

=

++ + + + = =∑

( )( )2 2 2 2 2

1

1 2 11 2 3

6

n

r

n n n. . . . n r

=

+ ++ + + + = =∑

( ) 2

3 3 3 3 3

1

11 2 3

2

n

r

n n. . . . n r

=

++ + + + = =

∑

47. Let 1 2 11a , a , . . . . , a be in A.P. such that 1 215 13 5a , a .= < and 2 2 2 21 2 3 11 990a a a . . . . a+ + + + =

then 1 2 3 11a a a . . . . a+ + + + is : (A) 30 (B) 11 (C) 0 (D) 33

48. Sum of natural numbers from 1 to 100 that are divisible by 2 or 5 is A then sum of digits of A is : (A) 8 (B) 9 (C) 10 (D) 11

49. Let Sr denotes the sum of first r terms of an A.P. whose first term is r and common difference is ( )2 1r − , let 1n n nT S S −= − then Tn is always :

(A) an odd number (B) an even number (C) a prime number (D) a composite number

50. If 1 2 ; 3n n nd S kS S n− −= − + ≥ , then k is equal to : (A) 1 (B) 2 (C) 3 (D) 4

SPACE FOR ROUGH WORK

21

Vidyamandir Classes : Innovating for your success

SPACE FOR ROUGH WORK

22

Vidyamandir Classes : Innovating for your success

SPACE FOR ROUGH WORK

23

Vidyamandir Classes : Innovating for your success

SPACE FOR ROUGH WORK

24

Vidyamandir Classes : Innovating for your success

SPACE FOR ROUGH WORK

End of 2Year Mathgenii Scholarship Test/JEE-2021

Vidyamandir/ADMTEST/ACEG/JEE-2018/ANSWERS 1

Vidyamandir Classes : Innovating for your success

ANSWERS to 2Admission Test/IITJEE - 2018 (ACEG)

10/04/2016 ANSWERS IITJEE - 2018

SECTION - I

1 2 3 4 5 6 7 8 9 10

A B A B A C D B D A

11 12 13 14 15 16 17 18 19 20

B A C D B B D B C B

SECTION - II

21 22 23 24 25 26 27 28 29 30

D B A C B B D C A B

31 32 33 34 35 36 37 38 39 40

B C A D A B B C B B

SECTION - III

41 42 43 44 45 46 47 48 49 50

B A A B A C C C D B