Major Test 1 Mains

8/13/2019 Major Test 1 Mains

1/24

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INSTRUCTIONS

Do not break the seal of the question paper booklet before instructed to do so by the invigilator

In each part of the paper, Section-A contains 30 questions. Total number of pages are 24. Please ensure that the

Questions paper you have received contains ALL THE QUESTIONS in each section and PAGES.

SECTION - A

1. Q.1to Q.30has four choices (A), (B), (C), (D) out of which only one is correct& carry 3 markseach. 1 markwill be

deducted for each wrong answer.

NOTE : GENERAL INSTRUCTION FOR FILLING THE OMR ARE GIVEN BELOW.

1. Use only HB pencilor blue/black pen (avoid gel pen)for darkening the bubble.

2. Indicate the correct answer for each question by filling appropriate bubble in your OMR answer sheet.

3. The Answer sheet will be checked through computer hence, the answer of the question must be marked by shading the

circles against the question by dark HB pencil or blue/black pen.

4. While filling the bubbles please be careful about SECTIONS [i.e. Section-A (include single correct)]

TARGET IIT - JEE

MAJOR TEST (MAIN)

PAPER I BOOKLET CODE : A

CLASS XI [SPEED]

Date : 06 02 - 2013 Duration :3 Hours Max. Marks : 270

394 - Rajeev Gandhi Nagar Kota, Ph. No. 0744-2209671, 93141-87482, 93527-21564

(IVR No. 0744-2439051, 52, 53) www. motioniitjee.com , [email protected]

For example if only 'A' choice iscorrect then, the correct method

for filling the bubble is

For example if only 'A & C'choices are correct then, thecorrect method for filling thebubble is

the wrong method for filling thebubble are

The answer of the questions inwrong or any other manner willbe treated as wrong.

For example If Correct match

for (A) is P; for (B) is R, S; for

(C) is Q; for (D) is Q, S, T then

the correct method for filling

the bubble is

Ensure that all columns are filled.

Answers, having blank column will be

treated as incorrect. Insert leading zero(s)

if required :

0 0 0 0

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 5

6 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

'6' should be

filled as 0006

'86' should be

filled as 0086

0 0 0 0

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 5

6 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

0 0 0 0

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 5

6 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

0000A

1B 1 1 1

2C 2 2 2

3D 3 3 3

4E 4 4 4

5F 5 5 5

6G 6 6

7H 7 7 7

8I 8 8 8

9J 9 9 9

A B C D E

A B C D E

P Q R S T

6

Booklet

0 0000

1 1 1 1 1

2 2 2 2 2

3 3 3 3 3

4 4 4 4 4

5 5 5 5 5

6 6 6

7 7 7 7 7

8 8 8 8 8

9 9 9 9 9

6 6

Test Code Batch

10+1

10+2

10+3

Crash

Paper

Paper 1

Paper 2

Roll Number

Name

Test Date D D M M Y Y

N A M E M I DD

L E N A M E L A S T N A M E

D 1 0 0 1 10+1

1

2 8 3 2 3

F I R S T


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Page # 2

394,50 - Rajeev Gandhi Nagar Kota, Ph. No. : 93141-87482, 0744-2209671

IVRS No : 0744-2439051, 52, 53, www. motioniitjee.com , [email protected]

(SPACE FOR ROUGH WORK)

MAJOR TEST (MAIN)

PART - I [MATHEMATICS]

SECTION A[STRAIGHT OBJECTIVE TYPE]

Q.1to Q.30has four choices (A), (B), (C), (D) out of which ONLY ONEis correct

1. If the points (0, 0), (2, 2 3 ), and (p, q) are the vertices of an equilateral triangle, then (p, q) is;fn fcUnq (0, 0), (2, 2 3 ), rFkk (p, q) leckgq f=kHkqt ds 'kh"kZ gS] rc (p, q) gS

(A) (0, 4) (B) (4, 4) (C) (4, 0) (D) (5, 0)

2. If x, and x2are the roots of the equation e2. xlnx= x3with x1> x2, then

;fn x, rFkk x2lehdj.k e2. xlnx= x3dsewy gS tgk x1> x2] rc

(A) x1= 2x2 (B) x1= x22 (C) 2x1= x2

2 (D) x12= x2

3

3. The least value of 6 tan2!+ 54 cot2!+ 18 is

I:54 when A.M. "G.M. is applicable for 6 tan2!, 54 cot2!, 18

II:54 when A.M. "G.M. is applicable for 6 tan2!, 54 cot2!and 18 added further.

III:78 when tan2!= cot2!.

(A) I is correct (B) I and II are correct

(C) III is correct (D) none of the above is correct

6 tan2!+ 54 cot2!+ 18 dk U;wure eku gS

I:54 tc A.M. "G.M., 6 tan2!, 54 cot2!, 18 ds fy, iz;qDr gksrk gS

II:54 tc A.M. "G.M., 6 tan2!, 54 cot2!rFkk 18 ;ksx djus ds ckn] iz;qDr gksrk gS

III:78 tc tan2!= cot2!.

(A) I lgh gS (B) I rFkk II lgh gS

(C) III lgh gS (D) mijksDr esa ls dksbZ Hkh lgh ugh gS

4. Value of#$###$

20cot80cot20cot80cot3 is equal to

#$###$

20cot80cot

20cot80cot3dk eku cjkcj gS

(A) cot 20 (B) tan 50 (C) cot 50 (D) cot #20


3/24

Page # 3




MAJOR TEST (MAIN)

5. If in a triangle, %%&

'(()

*+

2

1

r

r1 %%

&

'(()

*+

3

1

r

r1 = 2, then the triangle is

(A) right angled (B) isosceles (C) equilateral (D) None of these

;fn f=kHkqt esa, %%&

'(()

*+

2

1

r

r1 %%

&

'(()

*+

3

1

r

r1 = 2, rc f=kHkqt gS

(A) ledks.kh; (B) lef}ckgq (C) leckgq (D) buesa ls dksbZ ugha

6. Which of the following statement is incorrect ?

(A) Graph of |f (x)| is symmetric about x-axis.

(B) Graph of even function f (x) is same as that of f (|x|).

(C) If a function is symmetric about the line x = a, then f (a x) = f(a + x).

(D) Graph of odd degree polynomial will always cut the x-axis.

fuEu esa ls dkSulk dFku vlR; gS \

(A) |f (x)| dk vkjs[k x-v{k ds lkis{k lfEer gSA

(B) le Qyu f (x) dk vkjs[k] f (|x|) ds leku gSA

(C) ;fn dksbZ Qyu js[kk x = a ds lkis{k lfEer gS] rc f (a x) = f(a + x).

(D) fo"ke ?kkr okys cgqO;atd dk vkjs[k lnSo x-v{k dks dkVrk gSA

7. If O is the circumcentre of ,ABC and R1, R2and R3are the radii of the circumcircles of triangles

OBC, OCA and OAB, respectively, then1R

a+

2R

b+

3R

chas the value equal to

;fnO f=kHkqt ABC dk ifjdsUnzgS rFkk R1, R2o R3e'k% f=kHkqt OBC, OCA rFkk OAB dh f=kT;k,gS ] rc 1Ra

+2R

b+

3R

c

dk eku cjkcj gS

(A) 3R2

abc(B)

abc

R3(C) 2R

4,(D) 2R4

,


4/24

Page # 4




MAJOR TEST (MAIN)

8. If the expression %&

'()

*$+

x

11mx is non-negative for all positive real x, then the minimum value of m

must be

;fn O;atd %&

'()

*$+

x

11mx lHkh /kukRed okLrfod x ds fy, v_.kkRed gS] rc m dk U;wure eku gksuk pkfg,

(A)2

1+(B) 0 (C)

4

1(D)

2

1

9. The product of r consecutive positive integers, divided by r! is -

(A) A proper fraction (B) equal to r (C) A positive integer (D) none of these

r ekxr /kukRed iw.kkZadksa dk xq.kuQy] r! ls Hkkx nsus ij gS &

(A) mfPPr fHkUu (B) r ds cjkcj (C) ,d /kukRed iw.kkZad (D) buesa ls dksbZ ugha

10. A rectangular billiard table has vertices at P (0,0), Q(0, 7), R(10, 7) and S(10, 0). A small billiard

ball starts at M(3,4) and moves in a straight line to the top of the table, bounces to the right side

of the table, then comes to rest at N(7, 1). The y-coordinate of the point where it hits the rightside, is

,d vk;rh; fcfy;MZ Vscy ds 'kh"kZ P (0,0), Q(0, 7), R(10, 7) rFkkS(10, 0)gS A ,d NksVh fcfy;MZ xsan M(3,4) ls 'kq:

gksrh gS rFkk Vscy ds ij ,d ljy js[kk esa xfr djrh gqbZ] Vscy ds nka;h rjQ mNyrh gSA vkSj mlds ckn N(7, 1), ij fojke

ysrh gSA fcUnq dk y-funsZ'kkad tgk bl nk;sa vksj ekjk x;k gks &

(A) 3.7 (B) 3.8 (C) 3.9 (D) 4

11. The number of real roots of the equation 122 xcosxsin22

-+ is

(A) 2 (B) 1 (C) inifnite (D) none of these

lehdj.k 122 xcosxsin22

-+ ds okLrfod ewyksa dh la[;k gS

(A) 2 (B) 1 (C) vuar (D) buesa ls dksbZ ugha

12. A flight of stairs has 10 steps. A person can go up the steps one at a time, two at a time, or any

combination of 1s and 2s. Find the total number of ways in which the person can go up the stairs.

,d gokbZ tgkt esa 10 lhf


5/24

Page # 5




MAJOR TEST (MAIN)

13. The lengths of the sides of a triangle are b + 1, 7 b and 4b 2. The number of values of 'b' for

which the triangle is isosceles is/are

,d f=kHkqt ds Hkqtkvksa dh yEckbZb + 1, 7 b rFkk 4b 2 gSaA f=kHkqt ds lef}ckgqgksus ds fy, 'b' ds ekuksa dh la[;k gS(A) 1 (B) 3 (C) 2 (D) 5

14. Let ABC be a acute angled triangle such that A =3

.and cot B. cot C = P. The possible value of P

can be

ekuk ABC U;wudks.k f=kHkqt gS rkfd A =3

.rFkk cot B. cot C = P gSA P ds laHkor~ eku gks ldrs gS

(A) /0

1()

*3

1,0 (B) (0, 1] (C) %

&

'23

45,

3

1(D) [1, 5)

15. The number of bijective function f : A 6A, where A = {1, 2, 3, 4}such that f(1) 73, f(2) 71, f(3) 74, f(4) 72 is

,dSdh vkPNknd Qyu f : A 6A dh la[;k, tgk A = {1, 2, 3, 4} rkfd f(1) 73, f(2) 71, f(3) 74, f(4) 72 gS

(A) 11 (B) 23 (C) 12 (D) 9

16. The line y = 2x + 4 is shifted 2 units along positive direction of y-axis, keeping parallel to itself and

then 1 unit along negative direction of x-axis in the same manner, then equation of the line in its

new position is,

js[kk y = 2x + 4 dks y-v{k ds lekUrj 2 bdkbZ nwjh ij foLFkkfir fd;k x;k gSA blh izdkj x-v{k dks _.kkRed fn'kk esa ,d

bdkbZ foLFkkfir fd;k gS] rc ubZ fLFkfr esa js[kk dh lehdj.k gksxh &(A) y = 2x + 6 (B) y = 2x + 5 (C) y = 2x + 10 (D) y = 2x + 8

17. The function f satisfies the functional equation, 2f(x) + 3f2x 29

x 2

$* '( %+) &

= 100x + 80 8 real x 72 then

value of f(5) =

(A) 596 (B) 996 (C) 1024 (D) none of these

;fn Qyu f Qyuh; lehdj.k 2f(x) + 3f2x 29

x 2

$* '( %+) &

= 100x + 80 8 okLrfod x 72 dks larq"V djrk gS rc f(5) dk

eku cjkcj gS &

(A) 596 (B) 996 (C) 1024 (D) bueasls dksbZ ugha


6/24

Page # 6




MAJOR TEST (MAIN)

18. Let f : R 6A defined by f(x) = [x 2] + [4 x]. (where [*] denotes the greatest integer function).Then(A) f is many one and even function (B) f is onto if A 9I (set of integers)(C) f is many one and odd function (D) None of these

ekuk f : R 6A ifjHkkf"kr f(x) = [x 2] + [4 x]. (tgk [*] egke iw.kkZad Qyu dks iznf'kZr djrk gS). rc(A) f cgq,dSdh rFkk leQyu gS (B) f vkPNknd gS ;fn A 9I (iw.kkZadksa dk leqPp;)(C) f cgq,dSdh rFkk fo"keQyu gS (D) buesa lsdksbZugha

19. The least value of the expression x2+ 4y2+ 3z2 2x 12y 6z + 14 is(A) 0 (B) 1 (C) no least value (D) None of these

O;atd x2+ 4y2+ 3z2 2x 12y 6z + 14 dk U;wure eku gS(A) 0 (B) 1 (C) dksbZ U;wure eku ugh gS (D) buesa ls dksbZ ugha

20. If f(x) =xe2

log2 n x 2

x

$* '( %+) &

!and g(x) = {x} then exact set of values of g(x) for the existence of

f(g (x)) are (where {*} denotes fractional part function)

(A) %&

'()

*e

1,0

:;?

2e

1(B) %

&

'()

*e

2,0

:;?

2e

1(C) %

&

'()

*e

3,0

:;?

2e

1(D) None of these

;fn f(x) =xe2

log2 n x 2

x$* '( %+) &

!rFkk g(x) = {x} rc f(g (x)) ds vfLrRo ds fy, g(x) ds ekuksa dk leqPp; gS

(tgk {*} fHkUukRed Hkkx Qyu dks iznf'kZr djrk gS)

(A) %&

'()

*e

1,0

:;?

2e

1(B) %

&

'()

*e

2,0

:;?

2e

1(C) %

&

'()

*e

3,0

:;?

2e

1(D) buesals dksbZ ugha

21. sin x + cos x = y2 y + a has not value of x for any y, if a belongs to

(A) (0, 3 ) (B) ( 3 , 0) (C) (5, 3 ) (D) ( 3 , 5)

sin x + cos x = y2 y + a fdlh Hkh y ds fy, x dk dksbZ eku ugh gS] ;fna gS&

(A) (0, 3 ) (B) ( 3 , 0) (C) (5, 3 ) (D) ( 3 , 5)

22. If x satisfies |x 1| + |x 2| + |x 3| > 6, then(A) 0 @x @4 (B) x @2 or x "4 (C) x < 0 or x > 4 (D) None of these;fn x, |x 1| + |x 2| + |x 3| > 6 dks larq"V djrk gS] rc(A) 0 @x @4 (B) x @2 ;kx "4 (C) x < 0 ;k x > 4 (D) buesa ls dksbZ ugha


7/24

Page # 7




MAJOR TEST (MAIN)

23. If tan A, 2 tan A+ 2,3 tan A+ 3 are in G.P., then the value of1sec49

cot57

2 +A+

A+is

;fn tan A, 2 tan A+ 2,3 tan A+ 3 xq.kksRrj Js.kh esa gS] rc1sec49

cot57

2 +A+

A+dk eku gS &

(A) 12/5 (B) 33/28 (C) 33/100 (D) 12/13

24. If sin x + cos x = %%&

'(()

*$

y

1y , x 9[0, .], then

;fn sin x + cos x = %%&

'(()

*$

y

1y , x 9[0, .], rc

(A) x =4

., y = 1 (B) y = 0 (C) y = 2 (D) x =

4

3.

25. Let a, b, c be real numbers and a 7 0. If B is a root of a2x2 + bx + c = 0, C is a root ofa2x2 bx c = 0 and 0 < B< C, then the equation a2x2+ 2bx + 2c = 0 has a root Dthat always

satisfiesekuk a, b, c okLrfod la[;k, gS rFkk a 70A ;fna2x2+ bx + c = 0 dk ewy BgS, a2x2 bx c = 0 dk ewy CgS

rFkk 0 < B< C, rc lehdj.k a2x2+ 2bx + 2c = 0 dk ,d ewy DgS tks fd lnSo larq"V djrk gS &

(A) D=2

1(B+ C) (B) D= B+

2

C(C) D= B (D) B< D< C

26. In a triangle ABC, 2a2+ 4b2+ c2= 4ab + 2ac, then the numerical value of cos B is equal to

fdlh f=kHkqt ABC esa, 2a2+ 4b2+ c2= 4ab + 2ac, rc cos B dk la[;kRed eku gS &

(A) 0 (B)8

3(C)

8

5(D)

8

7

27. Number of positive integers n for which n2+ 96 is a perfect square, is

(A) 4 (B) 8 (C) 12 (D) Infinite

/kukRed iw.kkZad n dh la[;k ftldsfy, n2+ 96 iw.kZ oxZ gS &

(A) 4 (B) 8 (C) 12 (D) vuar


8/24

Page # 8




MAJOR TEST (MAIN)

28. Let p(x) = 0 be a polynomial equation of least possible degree, with rational coefficients, having

3 7 + 3 49 as one of its roots. Then, the products of all the roots of p(x) = 0 is

ekuk p(x) = 0 U;wure yEcor~?kkr okyk cgq O;atd lehdj.k gS] ftldk ,d ewy 3 7 + 3 49 gSA rc p(x) = 0 ds lHkh

ewyksa dk xq.kuQy gS(A) 7 (B) 49 (C) 56 (D) 63

29. If S = {x 9R: (log0.60.216) log5(5 2x) @0}, then S is equal to

;fn S = {x 9R: (log0.60.216) log5(5 2x) @0}, rc S cjkcj gS &(A) [2.5, 5) (B) [2, 2.5) (C) (2, 2.5) (D) (0, 2.5)

30. Let x1, x2, x3be the roots of the equation x3 x2+ Cx + D= 0, which are in AP, then Cx + Dy = 1

passes through the fixed point

ekuk x1, x2, x3lehdj.k x3 x2+ Cx + D= 0 dsewy gS] tks fd lekUrj Js.kh esa gS] rc Cx + Dy = 1 fuf'pr fcUnq ls

gksdj xqtjrk gSA

(A) %&

'()

*2

27,

2

9(B) %

&

'()

*2

7,

2

9(C) %

&

'()

*2

27,

2

5(D) %

&

'()

*2

5,

2

9


9/24

Page # 9




MAJOR TEST (MAIN)

PART - II [PHYSICS]



31. A rocket is fired vertically from the ground with a resultant vertical acceleration of 10m/s2. The fuelfinishes in 1 minute and it continues to move up. After how much time from then (when fuel

finished) will the maximum height be reached (g = 9.8 m/s2)

,d jkWdsV dks /kjkry ls 10m/s2 dsifj.kkeh /okZ /kj Roj.k ls /okZ/kjr% iz{ksfir fd;k tkrk gSA bldk bZa/ku1 feuV esa lekIr

gks tkrk gS rFkk ;g ij dh vksj xfr djrk jgrk gSA rc ls bZ/ku lekIr gksus ds ckn fdrus le; i'pkr ;g vf/kdre pkbZ

ij igqap tk,xk\

(g = 9.8 m/s2)

(A) 61.2 s (B) 64.2 s (C) 68.2 s (D) 70 s

32. A ball is thrown upward at an angle 37 to the horizontal andlands on the top edge of a building that is 20 m away and 10 m

high. How fast was the ball thrown ? (g=10 m/s2)

37O

v0

20m

10m

,d xsan dks /kjkry ls37 ds dks.k ij ij dh vksj iz{ksfir fd;k tkrk gS rFkk

;g 20 m nwj ,oa10 m ph bZekjr dh pksVh ij Vdjkrh gSA xsan ds iz{ksi.k osx

dh x.kuk dhft,A (g=10 m/s2)

(A) 10 m/s (B) 25 m/s (C) 40 m/s (D) 80 m/s

33. A ball rolls off the top of a stairway with a horizontal velocity of magnitude 1.8 m/s. The steps are

0.20 m high and 0.20 m wide. Which step will the ball hit first ?

,d xsan ,d lh


10/24

Page # 10




MAJOR TEST (MAIN)

34. Two blocks each of mass M are connected to the ends of light frame

as shown in fig. The frame is rotated about the vertical line of symmetry.

The rod breaks if the tension in it exceeds T0. Find the maximum

frequency with which the frame may be rotated without breaking the

rod.

M M

M nzO;eku ds nks CykWd fp=kkuqlkj ,d gYds se ls tqM+s gSA se /okZ/kj lefer js[kk ds

lkis{k ?kqerk gSA NM+T0ruko lsvf/kd ruko ij VwV tkrh gSA s e dh og vf/kdre vkofRr

Kkr dhft, ftlls NM+ ds VwVs fcuk se dks?kqek;k tk ldsA

(A) 0T1

2 M. !(B) 0

2T1

2 M. !(C) 0

2T1

2 M.

!(D) 0

T1

2 M.

!

35. The vertical section of a road over a canal bridge in the direction of its length is in the form of a

circle of radius 8.9m. Find the greatest speed at which the car can cross this bridge without losing

contact with the road at the highest point, the centre of gravity of the car being at a height 1.1 m

from the ground. (g = 10 m/s2)

,d ugj ds iqy ij fLFkr lM+d dk /okZ/kj Hkkx yEckbZ dh fn'kk esa 8.9m f=kT;k dk ,d oRrkdkj Hkkx gSA fdlh dkj dh og

vf/kdre pky Kkr dhft, ftlls pyus ij dkj lMd ds mPpre fcUnq ij lEidZ u [kks;sA dkj dk xq:Ro dsUnz /kjkry ls 1.1

m dh pkbZ ij gSA(g = 10 m/s2)(A) 5 m/s (B) 10 m/s (C) 15 m/s (D) 20 m/s

36. The mass string system shown in fig. is in equilibrium. If the

coefficient of friction between A and the table is 0.3, the

frictional force on A is1kg

A

0.2kg

45

B

fp=k esaiznf'kZ r fudk; lkE;koLFkk esa gSA ;fn est rFkk CykWd A ds chp ?k"kZ.k xq.kkad

0.3 gks rks A ij yxus okyk ?k"kZ.k cy gksxkA

(A) 9.8 N (B) 2.04 N

(C) 1.96 N (D) 0.59 N

37. A gramophone record is revolving with an angular velocity EFA coin is placed at a distance r from

the centre of record. The static frictional coefficient is G. The coin will revolve with the record if,d xzkeksQksu fjdksMZj Edks.kh; osx ls?kwe jgk gSA fjdksMZj ds dsUnzls r ij ,d flDdk j[kk gSA LFkSfrd ?k"kZ.k xq.kkad G gSA flDdk

fjdksMZj dslkFk ?kwesxk ;fn &

(A) 2g

r GI

E(B) 2

gr only

G-

E(C) 2

gr only

GJ

E(D) 2

gr

G@

E


11/24

Page # 11




MAJOR TEST (MAIN)

38. A square is made by joining four rods, each of mass M and length L.

Its moment of inertia about an axis PQ, in its plane and is passing

through one of its end is (as shown in the figure)

,d oxZ dks pkj NM+ksa dks tksM+dj cuk;k tkrk gS ftuesa izR;sd dk nzO;eku M rFkk yEckbZ

L gSA blds ry rFkk ,d fljsls xqtjus okyh v{k PQ ds lkis{k tMRo vk?kw.kZ gksxkA

(fp=kkuqlkj)

(A) 6ML2

(B)24

ML3 (C)

2

ML3

8

(D)

2

ML3

10

39. A small disc 'P' starts sliding with zero intial velocity from the top of a

smooth hill of height H having a horizontal portion, (see fig). What

must be the height (h) of the horizontal portion so that disc may

cover the maximum distance s ?

P

Hh

s,d NksVh pdrh 'P' 'kwU; vkjfEHkd osx ls,d fpduh H pkbZ dh igkM+h ds {kSfrt Hkkx ls

fQlyuk izkjEHk djrh gS fp=k esaA

{kSfrt Hkkx dh pkbZ(h) D;k gks rkfd pdrh vf/kdre nwjh s r; djs?(A) H (B) H/2 (C) 2H (D) 3H/2

40. A motor vehicle weighs 9.8 103N. During motion it is acted upon by a constant force of frictionequal to 10% of its weight. What quantity of petrol is spent by the engine to increase the speed of

vehicle from 30 km/h to 40 km/h over a distance of 0.5 km. The efficiency of engine is 20% and the

heating value of petrol is 4.3 107 J/kg.

,d eksVj dkj dk Hkkj 9.8 103N gSA xfr ds nkSjku dkj ij vius Hkkj dk 10% ifjek.k dk fu;r ?k"kZ.k cy dk;Zjr gksrk

gSA batu }kjk okgu dh pky 0.5 km dh nwjh r; djus esa 30 km/h ls40 km/h fdrus isVksy dh ek=kk [kpZ gksxh\ batu dh

n{krk 20% vkSj isVksy dk "eh; eku 4.3 107 J/kg gSA(A) 70 g (B) 60 g (C) 80 g (D) 90 g

41. A square plate of side 20 cm has uniform thickness and density. A

circular part of diameter 8 cm is cut out sysmmterically as shown in

Fig. Find the postion of the centre of mass of the portion from point

O. O

20 cm Hkqtk dh ,d oxkZdkj IysV dh ,d leku eksVkbZrFkk ?kuRo gS A fp=kkuqlkj 8 cm O;kl

dk ,d oRrkdkj lefer Hkkx dkVk tkrk gSA fcUnqO ls 'ks"k Hkkx ls nzO;eku dsUnz dh nwjh

Kkr dhft,A(A) 0.88 cm (B) 1.76 cm (C) 0.88 cm (D) 1.76 cm


12/24

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MAJOR TEST (MAIN)

42. A sand bag of mass M is supended by a rope. A bullet of mass m is fired at it with speed v and gets

embedded in it. The loss of K.E. is

M nzO;eku dk jsr dk cSx ,d jLlh }kjk yVdk gSA m nzO;eku dh ,d xksyh dks v pky ls cSx dh vksj nkxk tkrk gS rFkk ;g

mlesa /kal tkrh gSA xfrt mtkZ eas gkfu gksxh&

(A) 0 (B)21 1mv

2 M m

K

$

(C)21 Mmv

2 M m

K

$

(D)21 mmv

2 M m

K

$

43. A bullet of mass m hits block of mass M0at rest. The transfer of energy is maximum when

m nzO;eku dh ,d xksyh fojke esa fLFkr M0nzO;eku ds CykWd ls Vdjkrh gSA tkZ LFkkukUrj.k vf/kdre gksxk tc &

(A) M0= m (B) M

0= 2m (C) M

0> m

44. A force F acts tangentially at the highest point of a sphere of mass M

kept on a rough horizontal plane. If the sphere rolls without slipping,

find the acceleration of the centre of mass of the sphere.r

F

[kqjnjs {kSfrt ry ij fLFkr M nzO;eku ds xksysds mPpre fcUnq ij ,d cy F Li'kZjs[kh;

fn'kk eas dk;Zjr gSA ;fn xksyk fcuk fQlys yq


13/24

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MAJOR TEST (MAIN)

46. Three spring of force constants K1, K

2and K

3are connected as

shown in fig. and carry a mass M at the free end. M is pulled a

little and then released. The system will oscillate with a

frequency f given by

K3

K2

M

K1

rhu fLizax ftuds cy fu;rkad e'k% K1, K

2rFkk K

3gS] dksfp=kkuqlkj tks M+k tkrk

gS rFkk blds eqDr fljs ls M nzO;eku dk CykWd yVd jgk gSA CykWd dks FkksM+k

foLFkkfir djds NksM+ fn;k tkrk gSA fudk; ds nksyu dh vkofRr f gksxh&

(A)1 2 3

M2

K K K

? ;$ $M M= :

(B)1 2 3

1 2 3

K K K1

2 MK K K

? ;

. M M= :

(C)1 2 3

1 2 2 3 3 1

K K K1

2 M(K K K K K K

? ;

. $ $M M= :(D)

1 2 3

1 2 2 3 3 1

M(K K K )2

K K K K K K

? ;

$ $M M= :

47. The potential energy of a particle in motion along X-axis is given by

U = U0 U

0 cosax

The time period of small oscillations is

X-v{k ds vuqfn'k xfreku ,d d.k dh fLFkfrt tkZ fuEu :i ls iznf'kZr gSU = U

0 U

0 cosax

lw{e nksyuksa dk vkorZdky gksxk&

(A)0

ma2

U. (B) 0

U2

ma. (C)

0

2 m

a U

.(D)

0

m2

aU.

48. A travelling wave in a stretched string is described by the equation

y = A sin (kx Et).The maximum particle velocity is :

[khaph gqbZ Mksjh esa izxkeh rjax dk lehdj.k fuEu gSy = A sin (kx Et).

vf/kdre d.k osx gksxk &

(A) AE (B)k

E(C)

d

dk

E(D)

x

t


14/24

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MAJOR TEST (MAIN)

49. The linear density of a vibrating string is 104kg/m. A transvers wave is propagating in the string,

which is described by the equation y = 0.2 sin (x + 30t) where x and y are in metres and time t in

seconds. The tension in the string is :

dEiUu djrh ,d Mksjh dk js[kh; ?kuRo 104kg/m gSA Mksjh esa ,d vuqizLFk rjax xfreku gS ftldk lehdj.k y = 0.2 sin

(x + 30t) gS tgka x rFkky ehVj esa ,oa le; t lsd.M esa gSA Mksjh esa ruko gS &(A) 0.09 N (B) 0.36 N (C) 0.9 N (D) 3.6 N

50. A uniform wire passes over two pulleys and 9 kg weight is suspended at each end. The length ofwire between the pulleys is 1.5 m and its mass is 12.0 g. Find the frequency of vibration with which

the wire vibrates in two loops, the middle point of wire being at rest.

nksf?kjfu;ksa ls xq tjus okys ,d leku rkj ds izR;sd fljs ij 9 kg Hkkj yVd jgk gSrks f?kjfu;ksa ds e/; fLFkr rkj dh yEckbZ 1.5

m rFkk bldk nzO;eku 12.0 g gSA dEiUu dh og vkofRr Kkr dhft, ftllsrkj nks ywiksa esa dEIkUu djs] tcfd rkj dk e/; fcUnq

fojke esa gSA

9kg 9kg(A) 70 Hz (B) 60 Hz (C) 40 Hz (D) 30 Hz

51. A block of steel heated to 100C is left in a room to cool. Which of the curves shown in Fig.

represents the correct cooling behaviour.

100C rd xeZ ,d LVhy ds CykWd dks BaMk gksusds fy;s ,d dejs esa j[kk tkrk gSA fp=k esa iznf'kZr dkSulk o lgh 'khryu

O;ogkj dks iznf'kZr djrk gSA

(A)Temperature

Time

(B)Temperature

Time

(C)Temperature

Time

(D)Temperature

Time

52. An ideal monoatomic gas is taken round the cycle ABCDA asshown in Fig. The work done during the cycle is

P

V

2P,V 2P,2V

P,2VP,V

A D

CB

,dijek.kqd vkn'kZ xSl ph; ize ABCDA fp=kkuqlkj Hkkx ysrh gSA p ds

nkSjku fd;k x;k dk;Zgksxk&

(A) PV (B) 2PV (C) PV/2 (D) Zero


15/24

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MAJOR TEST (MAIN)

53. During the adiabatic expansion of 2 moles of a perfect gas the internal energy was found to have

decreased by 100J. The work done by the gas in this process is ?

,d vkn'kZxSl ds2 eksyksads :)ks "e izlkj.k esaxSl dh vkUrfjd tkZ100J c< tkrh gSA bl ize esaxSl }kjk fd;k x;k dk;Zgksxk&(A) Zero (B) 100J (C) 200 J (D) 100 J

54. For isothermal expansion of perfect gas, the volume of ,P/P is equal to :

,d vkn'kZxSl ds lerkih; izlkj.k esa ,P/P dk vk;ru cjkcj gksxk&(A) D1/2 .,V/V (B) ,V/V (C) D.,V/V (D) D2.,V/V

55. A system for four masses m1, m

2m

3and m

4and two spring and a fixed pulley

is shown in fig. The system is kept at rest by attaching the lower thread to a

rigid peg. Determine the acceleration of m4mass after the lower thread has

been cut. The springs are massless, pulley is frictionless and massless.

pkj nzO;eku m1, m

2m

3rFkkm

4] nks fLizax ,oa ,d fLFkj f?kjuh ls cuk fudk; fp=k esa iznf'kZr gSA

fudk; dsfupys /kkxs dks ,d n


16/24

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MAJOR TEST (MAIN)

58. The masses of 10 kg and 20 kg respectively are connected by massless spring as shown in the

figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has

acceleration of 12 m/s2. What is the acceleration of 20 kg mass

10 kg rFkk20 kg nzO;eku fp=kkuqlkj nzO;ekughu fLizax ls tqM+sgSaA ,d 200 N dk cy20 kg nzO;eku ds CykWd ij dk;Zjr

gSA iznf'kZr {k.k ij 10 kg nzO;eku dk Roj.k12 m/s2 gSA 20 kg dk Roj.k D;k gksxk \

10kg 20kg 200N

(A) 12 m/s2 (B) 4 m/s2 (C) 10 m/s2 (D) zero 'kwU;

59. A rectangular block weighing 150 N, is lying on a rough inclined plane with inclination angle 45 as

shown in the figure, The block is tied up by a horizontal string which has a tension of 50 N to keep

the block just in equilibrium, then the coefficient of friction between the block and the inclined

surface is

45

W

0

,d vk;rkdkj CykWd ftldk Hkkj 150 N gS] 45 ur dks.k ds [kqjnjs ur ry ij fp=kkuqlkj j[kk gSA CykWd dks lkE;koLFkk esaj[kus ds fy;s ,d {kS frt

Mksjh }kjk bls cka/kk tkrk gS] ftleas 50 N dk ruko gS rc ur ry ,oa CykWd ds chp ?k"kZ .k xq.kkad gksxk&

(A) zero 'kwU; (B) 0.33 (C) 0.5 (D) 0.7

60. An elastic string has a length 'a' when tension in it is 4 N. Its length is 'b' when tension is 5 N.

On subjecting the string to a tension of 9 N its length will be

,d izR;kLFk Mksjh esa 4N ruko gksus ij bldh yEckbZ 'a' gSA tc Mksjh esa ruko 5N gS rks Mksjh dh yEckbZ 'b'gSA Mksjh esa ruko 9N gksusij Mksjhdh yEckbZ gksxh&

(A) a + b (B) b a (C) (5b 4a) (D) (a + b)/(b a)


17/24

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MAJOR TEST (MAIN)

PART - III [CHEMISTRY]



61. In which of the following compounds hydroxylic proton is most acidic ?

fuEu fyf[kr ;kSfxd esa dkSulk gkbMMksfDlfyd izksVku vf/kd vEyh; gS \

(A)

F

O

H

(B) OH

F(C)

F

O

H (D)F

O

H

62. Which of the following is the strongest base

fuEu fyf[kr esa ls dkSulk izcy {kkj gS &

(A)

N

H

(B) (C)N

H

(D)

63. Rank the following radicals in order of Decreasing stability

fuEufyf[kr ewyd dks LFkkf;Rork ds ?kVrs e eas fyf[k,

I II III IV(A) III > II > I > IV (B) III > II < I < IV(C) II > III > II > IV (D) III < II < I < IV

64. Arrange the Stability of following

fuEu fyf[kr dks LFkkf;Rork ds e esa O;ofLFkr dhft,

(I) (II) (III)

(A) I < II < III (B) II < I < III (C) I < III < II (D) II < III < I


18/24

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MAJOR TEST (MAIN)

65. Which allylic carbocation is the most stable carbocation :

(A) CH3CH CH (B) CH3CH CHCHCH3

(C) C6H5CH CH (D) All have same stability

buesa ls dkSulk ,ykbfyd dkcksZdsVk;u lokZf/kd LFkk;h dkcksZdsVk;u gS &

(A) CH3CH CH (B) CH3CH CHCHCH3

(C) C6H5CH CH (D) lHkh leku LFkk;hRo j[krs gSA

66. The numbers of .bonds and Nbonds present in a molecule of benzaldehyde are, respectively-

(A) 4.and 13N (B) 4.and 8N (C) 4.and 14N (D) 8.and 10N

csUtssfYMgkbM esa fdrus flXek (N) rFkk .cU/k ik;s tkrs gS%

(A) 4.rFkk13N (B) 4.rFkk8N (C) 4.rFkk14N (D) 8.rFkk10N

67. The compound which has one isopropyl group is :

(A) 2,2,3,3-tetramethyl pentane (B) 2,2-dimethyl pentane

(C) 2,2,3-trimethyl pentane (D) 2-methyl pentane

fuEu ;kSfxdksa esa ls fdles ,d vkblksizksfiy lewg mifLFkr gS &

(A) 2,2,3,3-VsVkesfFky isUVsu (B) 2,2-MkbZesfFky isUVsu(C) 2,2,3-VkbesfFky isUVsu (D) 2-esfFky isUVsu

68. iso-octane contains

(A) 5 prim. one sec. & two ter. C atoms.

(B) 4 prim. 2 sec. & one ter. C atoms.

(C) 5 (10C). one (20C), one (30C) & one (40C) atoms.

(D) 4 (10C). two (20C), one (30C) & one (40C) atoms.

vkblks vkDVsu j[krk gS %

(A) 5 izkFkfed],d f}rh;d] ,oa nks rrh;d dkcZu ijek.kq(B) 4 izkFkfed] nks f}rh;d],oa ,d rrh;d dkcZu ijek.kq(C) 5 (10C). ,d (20C), ,d (30C) ,oa ,d (40C) ijek.kq(D) 4 (10C). nks (20C), ,d (30C) ,oa ,d (40C) ijek.kq


19/24

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MAJOR TEST (MAIN)

69. Which of the following is NOT correctly matched

(A) d-block element : electronic configuration is ns0(n 1)d1 10

(B) p-block element : electronic configuration is ns1 2np1 6

(C) s-block element : electronic configuration is ns1 2

(D) Ce : first member of f-block.

fuEu fyf[kr tksMh esadkSulk feyku lgh ugh gS %

(A) d-CykWd rRo: bysDVksfud foU;klns0(n 1)d1 10

(B) p-CykWd rRo: bysDVksfud foU;klns1 2np1 6(C) s-CykWd rRo: bysDVksfud foU;klns1 2

(D) Ce : f-CykWd dk izFke lnL;

70. Which of the following is NOT in increasing order of ionic radii?

(A) Al3+< Mg2+< Na+ (B) O2< F< Na+ (C) K+< Cl< S2 (D) (A) and (C) both

fuEu fyf[kr esa lsvk;fud f=kT;k dk c


20/24

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MAJOR TEST (MAIN)

75. In Rutherford scattering experiment, the no. of B-particles scattered at an angle 90 is 28 perminute. Calculate the number of B-particle scattered per minute for angle 60jnjQksMZ izdh.kZu iz;ksx esa 90 dks.k ij] izfr feuV izdhf.kZr B-d.kksadh la[;k 28 gSA 60 dks.k ij izfr feuV izdhf.kZr B-d.kksa dh la[;k Kkr dhft, A(A) 112 (B) 105 (C) 110 (D) 205

76. When 2.0 g of a gas A is introduced into an evacuated flask kept at 25C, the pressure is found to

be 1 atm. If 3 g of another gas B is then added to the same flask, the total pressure becomes 1.5atm. Assuming ideal gas behaviour, the ratio of molecular weights M

A: M

Bwill be

tc 25C ij j[ks fuokZfrr ykLD eas ,d xSl A ds 2.0 g dks izokfgr fd;k x;k] rks nkc 1 atm ik;k x;kA ;fn blh ykLdesa vU; xSl B ds 3g dks feyk;k tk, rc dqy nkc dk eku 1.5 atm gks tkrk gSA vkn'kZ xSl O;ogkj dks ekurs gq, M

A: M

B

ds v.kqHkkj dk vuqikr gksxk &(A) 1 : 3 (B) 4 : 5 (C) 1 : 2 (D) 1 : 9

77. 2244222424 dOOcHMnSOSOKObHSOaHKMnO $$$6$$

The minimum sum of a,b,c,d is (where a, b, c, & d are whole numbers)

(A) 24 (B) 25 (C) 21 (D) none of these

2244222424 dOOcHMnSOSOKObHSOaHKMnO $$$6$$

a,b,c,d dk U;wure ;ksx D;k gksxk tgka ( a, b, c, d iw.kkZd :i esa gSA)(A) 24 (B) 25 (C) 21 (D) buesa ls dksbZ ugh

78. A container 'A' (3 litre) contains a particular gas at 1 atm and 127C another container B (2 litre)contains same gas at 3 atm pressure at 327C. The two containers are connected by a stopcock Ifstopcock is opened and final temperature is 227C then final pressure of the container will becomes.

,d ik=k 'A' (3 yhVj) tks 1 atm o 127C rki ij ,d xSl gS o vU; ik=k B (2 yhVj) ftlesaleku xSl 3 atm vkSj 327Cij gS nksuks ik=k LVkWi dkdZ ls tqM+s gksrs gS ;fn LVkWi dkdZ [kksyrs gS rksifj.kkeh rki 227C gksrk gS rc ik=k dk ifj.kkeh nkcgks tkrk gSA

A B

(A) 7 atm (B) 9/5 atm (C) 1/4 atm (D) 7/4 atm


21/24

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MAJOR TEST (MAIN)

79. There are three closed containers in which equal mole of the gas are filled.

10 cm

(I)

10cm

10cm

(II)

R=10cm

(III)

If the containers are placed at the same temperatures then find the incorrect options:

(A) Pressure of the gas is minimum in (III) container(B) Pressure of the gas is equal in (I) & (II) container

(C) Pressure of the gas is maximum in (I)

(D) The ratio of pressure in II and III container is 4 : 3

;gkaij rhu can ik=k gS ftlesa xSl ds leku eksy Hkjs x;s gSA

10 cm

(I)

10cm

10cm

(II)

R=10cm

(III)

;fn ik=kksa dks leku rki ij j[kk tkrk gS rks xyr dFku pqfu,(A) (III) ik=k esaxSl dk nkc de gksxk

(B) ik=k(I) vkSj(II) esaxSl dk nkc leku gksxk

(C) ik=k(I) esa nkc vf/kdre gksxk

(D) ik=k (II) vkSj(III) esa nkc dk vuqikr4 : 3 gksxk

80. Solutions A and B of H2SO

4have respective molarities to be 5.0 and 1.0. In order to prepare 10 L of

8N H2SO

4,what volumes of A and B solutions need be mixed?

H2SO

4ds foy;u A vkSj B ftudh 5.0 vkSj1.0. eksyjrk gS 8N H

2SO

4,ds 10 L cukus ds fy, A rFkk B dk fdruk vk;ur

feykuk iMs+xk \(A) 7.5L of A + 2.5 L of B (B) 8L of A + 2L of B

(C) 2L of A + 8L of B (D) 2.5 L of A and 7.5 L of B

81. Mole fraction of A in mixture of A and B is 1/3 while mole fraction of B in mixture of B & C is 3/4 if theabove mixture are mixed in 3 : 4 ratio then find mole fraction of C in the mixture thus obtained.

(A) 1/7 (B) 1/4 (C) 3/7 (D) none of these

A vkSj B ds feJ.k esa A dk eksy fHkUu 1/3 gS tcfd B rFkk C ds feJ.k esaB dk eksy fHkUu 3/4 gS ;fn ijh feJ.k dks vuqikr3 : 4 esa feyk;k tkrk gS rc blls izkIr feJ.k esa C dk eksy fHkUu Kkr dhft,A

(A) 1/7 (B) 1/4 (C) 3/7 (D) buesa ls dksbZ ugh


22/24

Page # 22




MAJOR TEST (MAIN)

82. The IUPAC name of this compound is

Cl Br

ClO

NH

Cl

(A) N2 chloro ethyl 3-bromo 4,5 dichloro Hexanamide

(B) 3-Bromo 4,5 dichloroN(2chloro ethyl) Hexanamide

(C) 3Bromo 4,5 dichloro ethyl amino Hexanal(D) None

bl ;kSfxd dk IUPAC uke gS &

Cl Br

ClO

NH

Cl

(A) N2 Dyksjks ,fFky 3-czkseks4,5 MkbDyksjks gsDlsu,ekbM+

(B) 3-czskeks4,5 MkbDyksjksN(2Dyksjks,fFky ) gsDlsuy

(C) 3czkseks4,5 MkbDyksjks ,fFky ,ehukss gsDlsuy

(D) dksbZ ugh

83. After two consecutive flop shows as Dabang-2 and Bodyguard, film star Salman Khan plannedto step into the field of Chemistry. Once he went into the laboratory and mixed the solution ofFeC2O4and FeSO4, taking 75 ml of each. He observed that the mixture completly oxidised by 20 mlof 0.04 M K2Cr2O7in acidic medium. He then treated the same solution with Zn and dil HCl. Usinghis innovation, he again let the solution thus obtained be oxidised by 36 ml of 0.02 M KMnO4.Sincehe was new in Chemistry, he asked RRD Sir for the right answer of normality of FeC2O4 and FeSO4solution then what was the correct answer given by him.

(A) 0.012, 0.03 (B) 0.024, 0.04 (C) 0.15, 0.45` (D) None of these

^^ncax-2 vkSj ^ckWMhxkMZ tSls nks yxkrkj fxjs gq, izn'kZuksa ds ckn fQYeh flrkjs lyeku [kku us jlk;u ds{ks=k esa dwnus dh lksphA,d ckj og iz;ksx'kkyk esax;k Fkk vkS j nksuksa dk 75 feyh ysrsgq, FeC2O4vkSjFeSO4dsfoy;u dks fefJr dj fn;k FkkA mlus

ns[kk fd vEyh; ek/;e esa 0.04 M K2Cr2O7ds 20 ml }kjk ;g feJ.k iw.kZr% vkWDlhr gks x;kArc mlus leku foy;u dksZn rFkk ruq HCl dslkFk vfHkr djk;kA vius vkfo"dkj dk mi;ks x djrs gq,] bl izdkj izkIr foy;u dks vkWDlhdj.k gksus dsfy, [kqyk NksM+fn;k 0.02 M KMnO4. ds 36 feyh }kjkA pwafd og jlk;u esa u;k Fkk] mlusvkj vkj Mh lj dks FeC2O4 rFkkFeSO4 foy;u dh uksjeyrk ds lgh mkj ds fy, iwNk vkSj rc muds }kjk fn;k x;k lgh mkj FkkA

(A) 0.012, 0.03 (B) 0.024, 0.04 (C) 0.15, 0.45` (D) buesa ls dksbZ ugh


23/24

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MAJOR TEST (MAIN)

84. IUPAC name of Neohexyl tert pentyl acetylene.

(A) 2,2,7,7 tetra methyl oct -3-3yne (B) 2,2,7,7-tetra methyl oct-1-yne

(C) 3,3,8,8 tetra methyl Non 4yne (D) Compound is not possible

fu;ksgsfDly rrh;d isfUVy ,flfVyhu dk IUPAC uke gS%

(A) 2,2,7,7 VsVk esfFkyv vkWDV-3-3-vkbu (B) 2,2,7,7-VsVk esfFkyv vkWDV-1-vkbu

(C) 3,3,8,8 VsVk esfFky ukWu4 vkbu (D) ;kSfxd lEHko ugh gS

85. These is no peroxy linkage in

fuEu esa ls ijkWDlhfyadst ugh j[krk gS?(A) H

2S

2O

5(B) H

4P

2O

5(C) H

2S

2O

7(D) N

2O

5

86. Which of the following has been arranged in order of decreasing dipole moment ?

fuEu esa ls f}/kzqo vk?kw.kZdk ?kVrk e gksxk%(A) CH

3Cl > CCl

4>CH

2Cl

2>CHCl

3(B) CH

3Cl > CH

2Cl

2>CHCl

3>CCl

4

(C) CH3Cl>CHCl

3>CH

2Cl

2>CCl

4(D) CH

3Br>CH

3Cl>CH

3F>CH

3I

87. In CuSO4. 5H

2O total number of H

2O molecule which does not form H-bond

CuSO4. 5H

2O esaH

2O v.kq dh dqy la[;k gksxh tks fd H-cU/k ugh cukrs gS%

(A) 2 (B) 3 (C) 1 (D) 4

88. Smallest bond angle in found in

U;wure cU/k dks.k ik;k tkrk gS%-(A) NF

3(B) Cl

2O (C) NH

3(D) CH

4

89. No. of sp3hybridised atom in borax Na2B

4O

7.10H

2O.

Na2B

4O

7.10H

2O (cksjsDl)esa dqy sp3

ladfjr ijek.kqvksa dh la[;k gksxhA

(A) 15 (B) 16 (C) 18 (D) 19

90. In which of the following is hypervalent compound.

(A) I3+

(B) I3

(C) HOCl (D) NonefuEu esa ls dkSuls esavfr la ;ksth ;kSfxd gS A

(A) I3+ (B) I

3 (C) HOCl (D) dksbZ ugh


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