The length of line segment..?

Page 1

Instructions:

1) 15 Minutes are allotted for reading the question

paper in addition to 3 hours for writing the answers.

2) All answers should be written in the separate

answer booklet.

3) There are four sections in the question paper.

4) There is internal choice in Section - IV.

SECTION - I

Note:

i) If any question is answered more than once in this

section the earlier answer will only be considered.

ii) Answer all the questions.

iii) Each question carries 1 mark. 12 ´ 1 = 12

1. Expand UNESCO.

2. Write the missing information.

H San H Min H ?

3. The Zionist movement belongs to ........

4. Find the wrong pair.

India adopted - a) Directive principles of State

Policy - France

b) Fundamental Rights - USA

c) Fundamental duties - USSR

(Russia)

5. Complete the second pair with the help of the first

one.

Nazism - Hitler Fascism - ?

7. ...... is a major changed that occurred across the

globe in the late 20th century.

8. Financial year - April 1st or March 31st

Academic Year - ?

9. The theme of the book ‘Before they pass away’ is

10. Arrange the following from West to East.

Patkai range, Malwa plateau, Chotanagpur

plateau, Aravallis.

11. Identify the wrongly matched pair and write it in

the answer booklet

12. One hectare is ........... square meters.

SECTION - II

Note:

i) Answer all the questions.

ii) Each question carries 2 marks. 8 ´ 2 = 16

13. How did USSR escape from the influence of

great depression.

14. Mention any two reasons for not establishing sus-

tainable democracy in Nigeria.

15. Give suggestions of your own to prevent the

spread of corona virus.

16. Give examples of physical and working capital.

17. Appreciate the role of women in Chipko move-

ment.

18. What elements do you incorporate while prepar-

ing a pamphlet on food security to bring about

awareness among the people of India?

19. What are the characteristic features of

Peninsular river system?

20. Write down a brief note of appreciation about the

activities of World Health Organisation.

SECTION - III

Note:

i) Answer all the questions.

ii) Each question carries 4 marks. 8 ´ 4 = 32

21. Write down the measures being taken up by

Government of Andhra Pradesh for the develop-

ment of schools.

22. ‘War is destructive and deeply affects the world’.

Comment.

23. Should ground water be considered a

common pool resource? Explain your view.

24. ‘Coalition governments cause political

instability’. Comment.

25. Write down the problems of migrant workers

faced in the present day scenario.

26. What were the various strategies used by social

movement?

27. Study the below table and answer the following

questions.

Formation of Congress government

led by Indira Gandhi - 1960

Formation of TDP - 1982

Operation Blue Star - 1984

Rajiv Gandhi accords with

Punjab and Assam - 1985

Formation of Janata Dal Government

implementation of Mandal

Commission - 1989

Rama Janmabhoomi Rath Yatra - 1990

Questions

i) The Operation Blue star launched in the state of...

ii) Who was the founder of TDP?

iii) Name the important accords during the period of

Rajiv Gandhi.

iv) When did the Mandal commission report imple-

ment?

28. Look at the map and answer the following ques-

tions.

i) Name any two states in which the river Ganga are

drained.

ii) Name the North flowing rivers.

iii) Write down the South flowing rivers.

iv) Mention any two tributaries of the Ganges.

SECTION - IV

Note:

i) Answer all the questions.

ii) Each question carries 8 marks. 5 ´ 8 = 40

29. a) Plateau regions in India do not support agri-

culture as much as the Plain regions - What

are the reasons for this?

(OR)

b) Describe the mechanism of monsoon in India.

30. a) What aspects of the welfare state do you find

functioning in India Today?

(OR)

b) By the end of the 20th century there is only one

power that dominates the world. In this crucial

juncture what would be the role of NAM?

31. a) Observe the following time line chart and

answer the questions.

PUBLIC EXAMINATIONS - 2020

Time: 3 Hrs. 15 Min. SOCIAL STUDIES PAPER - I & II (English Version) Max. Marks: 100

TENTH CLASS MODEL PAPER

÷ªÙÞœüŒî¦ô¢Ù 2 Wû 2020 n email: [email protected]

17

6.

Primary sector Mining

Secondary sector Industries

Service sector Fishing

The picture given below is

the logo of which

International Organisation.

i) Why did the name Bloody Sunday

come after?

ii) What were the results of Civil war?

iii) Under whose leadership did bolshe-

viks fight in the above incidents and

what did he lead?

iv) What is the reason behind the for-

mation of Russian Democratic

Labour Party?

(OR)

b) Observe the following graph and

answer the questions.

i) What does the above graph indicate?

ii) Name the two countries which

opposed with each other in the arms

race.

iii) Why do you think the year 1945 is

shown as the starting point on the

graph?

iv) What is the reason for the

decrease in Nuclear stock piles

after 1991?

32. a) How are human activities con-

tributing to global warming?

(OR)

b) What do you understand by

under employment? Explain with

an example each from the urban

and rural areas?

33. A) Mark the following on the out

line map of India. 4 M

a) 1) River flowing through rift

valley

2) Coral islands

3) Kanchana Junga

4) Gandhinagar

(OR)

b) 1) Lumi river

2) 82 12

° East longitude

3) Nagaland

4) Malwa plateau

B) Mark the following on the outline

map of the world. 4 M

a) 1) Spain

2) The city that UN head quar-

ters is located

3) Bangladesh

4) China

(OR)

b) 1) The Red sea

2) Pakistan

3) Egypt

4) The head quarters of WHO

-Kanukolanu Srinivasa Rao

Debates over socialism in

Russia.

The Bloody Sunday and the

Revolution

The Civil War.

Formation of Comintern.

Beginning of Collectivisation.

Formation of the Russian

Social Democratic Workers

Party.

2nd March - Abdication of the

Tsar. 24th October - Bolshevik

uprising in Petrograd.

• 1850n

1880

• 1898

• 1905

• 1917

• 1918n20

• 1919

• 1929

USSR/Russia

United States

Nu

mb

er

of

warh

ead

s

45,000

40,000

35,000

30,000

25,000

20,000

15,000

10,000

5,000 1945 1955 1965 1975 1985 1995 2005

US and USSR Nuclear Stockpiles

Straight Objective Type

1. A person of height 2 mts starts from a lamp

post of height 5 mts and walks away at the

rate of 6 km per hour. The rate at which his

shadow increases is

1) 2 kmph 2) 4 kmph 3) 6 kmph 4) 8 kmph

2. The curve y − exy + x = 0 a vertical tangent

at the point

1) (1 1) 2) (0 1) 3) (1 0) 4) at no point

3. The condition that the two curves x = y2,

xy = k cut orthogonally is

1) k2 = 1 2) 2k2 = 1 3) 4k2 = 1 4) 8k2 = 1

4. If the length of subtangent is 9, length of

subnormal is 4 at a point (x y) on y = f(x),

then ordinate of the point is

1) ±4 2) ±6 3) ±8 4) ±3

5. If a + b + c = 0 then the quadratic equation

3ax2 + 2bx + c = 0 has atleast one root in

the interval

1) (0 1) 2) (1 2) 3) (2 3) 4) (−1 0)

6. Through the point (2 3) a straight line is

drown making positive intercept on the

coordinate axes. The area of the triangle

thus formed is least, then the ratio of the

intercepts on line x and y axes is

1) 1 : 2 2) 2 : 3 3) 3 : 4 4) 1 : 4

Answers1-2, 2-3, 3-4, 4-2, 5-1, 6-2.

Straight Lines (2D)

The Plane and 3D - Lines

Straight Objective Type

1. Let ABC be a triangle, if P is a point such

that AP divides BC in the ratio 2 : 3. BP

divides CA in the ratio 3 : 5. Then the ratio

in which CP divides AB is

1) 2 : 5 2) −2 : 5 3) 5 : 2 4) −5 : 2

2. If p, q are the perpendicular distances from

origin to the lines x secα + y cosecα = a;

x cosα − y sinα = a cos 2α respectively,

then 4p2 + q2 =

1) a2 2) 2a2 3) 3a2 4) 4a2

3. The line 3x + 2y = 24 meets the axes in A

and B. The perpendicular bisector of AB

meets the line y + 1 = 0 at C. Then area of

triangle ABC is

1) 61 sq.units 2) 71 sq.units

3) 81 sq.units 4) 91 sq.units

4. If P = (0, 1, 0) Q = (0, 0, 1), then the projec-

tion of PQ on the plane x + y + z = 3 is

1) 1 2) √2 3) √

3 4) 2

x − 1 y + 1 z − 1 x − 35. If the lines = = and =

2 3 4 1

y − k z = intersect then the value of k =

2 1

3 5 7 91) 2) 3) 4)

2 2 2 2

6. A line with positive D.C's passes through

P(2 −1 2) makes equal angels with axes.

The line meets the plane 2x + y + z = 9 at

Q. The length of line segment PQ =

1) 1 2) √2 3) √

3 4) 2

Numerical Value Type

7. Let P(3 2 6) be a point in space and Q be

a point on the line r

= ( i − j

+ 2k

) + µ (−3i

+ 5k). Then the value of µ for which the vec-

tor PQ

is parallel of the plane x − 4y + 3z

= 1

8. P (α, β, γ) lies on the plane x + y + z = 2. Let

a

= αi

+ βj

+ γk

and k × (k

× a

) = 0

then

γ =

9. Let O (0, 0), P (3, 4), Q (6, 0) be the vertices

of triangle OPQ. The point R inside the tri-

angle OPQ the point R inside the triangle

OPQ in which the triangles OPR, PQR,

OQR are equal area. The coordinates of R

are (α, β) then α + β =

x − 4 y − 210. The value of k such that = =

1 1z − k lies on 2x − 4y + z = 7 is

7

Answers

1-3, 2-1, 3-4, 4-2, 5-4, 6-3, 7-0.25,

8-2, 9-5.33, 10-7.

Direction Cosines and Direction

Ratios; Plane

Straight Objective Type

1. if α, β, γ are respectively the acute angle

made by any line with the coordinates

axes, then

1) α + β + γ = 90°2) α + β + γ = 360°3) 0° < α + β + γ < 270°4) 0° < α + β + γ < 180°

2. If the angle between the lines whose

−2 a bd.c' s are ( , , ) and

√21 √

21 √21

3 3 −6

( , , ) is 90°, then a pair of√

54 √54 √

54

possible value of a,b are

1) −1, 4 2) 4, 2 3) 4, 1 4) −4, −2

3. The harmonic conjugate of (2, 3, 4) with

respect to the line joining points (3, −2, 2)

and (6, −17, −4) is

1 1 11) (0, 0, 0) 2) ( )2 3 4

18 43) (1 1 1) 4) (, −5, )5 5

4. The equation ax + by + cz + d = 0 (d≠0)

does not represents a plane if

1) a2 + b2 + c2 = 0 2) a2 + b2 + c2 ≠ 0

3) a + b – c = 0 4) a + b + c = 0

5. The number of line perpendicular to x−axis

lying in yz plane is

1) 0 2) 1 3) 3 4) ∞6. The angle between a line and normal to a

plane is 30°. The angle between line and

plane is

π π 2π π1) 2) 3) 4)

3 2 5 4

7. The planes x = ±3, y = ±4, z = ±6 form a

1) cube 2) Rectangular parallelepiped

3) Tetrahedron

4) Parallelepiped with equal edges

Numerical Value Type

8. The lengths of projection of a line segment

on the coordinate planes are 3, 4, 5 then

length of the segment is

9. Let a line makes an angle θ with x, z axes

and β with y-axes so that √3 sinθ = sinβ

then cos2θ =

10. Image of (1, 2, 3) with respect to a plane

ax + by + cz + d = 0 is (−7/3,−4/3,−1/3) then

a + b + c + d =

Answers

1-3, 2-3, 3-4, 4-1, 5-4, 6-1, 7-2,

8-5, 9-0.60, 10-2.

Application of Differentiation

Straight Objective Type

1. A function f: R → R satisfies the equation

f(x + y) = f(x) f(y) for all x, y ∈ R and f(x) ≠ 0for any x ∈ R. If f is differentiable at '0' and

f(0) = 2 then for all x ∈ R, f'(x) =

1) 0 2) 2 3) 2f(x) 4) −f(x)

2. Let f, g be differentiable functions satisfying

g'(a) = 2, g(a) = b and g = f−

then f'(b) =

1 11) 2) 2 3) 4) 4

2 4

13. If f(x) = x sin () for x ≠ 0 and f(0) = 0 then

x

1) f is continuous at x = 0

2) f is differentiable at x = 0

3) f'(0−) exists but f'(0

+) does not exists

4) f' (0+) exists but f'(0

−) does not exists

1 1− ( + )|x| x4. If f(x) = x e for x ≠ 0 and f(0) = 0

then f(x) is

1) continuous as well as differentiable

2) discontinuous every where

3) continuous for all x, but not differentiable

at x = 0

4) neither differentiable nor continuous at

x = 0

5. If f(x) = x − 2, g(x) = (fof) (x) the g'(x)

when x > 20 is

1) 0 2) 1 3) −1 4) 20

6. If f(x) = (cosx) (cos2x) (cos3x) ... (cos nx)

n

then f'(x) + ∑ (r tan rx) f(x) =r = 1

1) n 2) −n 3)1 4) 0

7. If y = √ tan x + √ tan x + √ tan x + … ∞dy

then dx

tan x tan x1) 2)

2y − 1 2y + 1

sec2x sec

2x

3) 4) 2y − 1 2y + 1

d8. If x < 1 then (1 + 2x + 3x

2+ 4x

3+... ∞)

dx

=

1 21) 2)

(1 − x)2

(1 − x)3

−2 −23) 4)

(1 − x)3

(1 + x)3

dy y9. If xy = (x + y)

nand = then n =

dx x

1) 1 2) 2 3) 3 4) 4

10. Let y be an implicit function of x defined by

x2x − 2xx coty − 1 = 0 then y' (1) =

1) 1 2) log 2 3) log 3 4) −1

11. The function f: R-{0}→ R given by

1 2f(x) = − can be made continuous

x e2x − 1

at x = 0, by defining f(0) as

1) 2 2) −1 3) 0 4) 1

12. Let f be a non zero continuous function sat-

isfying f (x + y) = f(x) f(y) for all x, y ∈ R. If

f(2) = 9 then f(3) =

1) 3 2) 9 3) 27 4) 81

13. The value of f(0) so that the function

1 − cos (1 − cosx)f(x) = is continuous every

x4

where is

1 1 11) 2) 3) 4) 1

8 2 4

14. Lt (log55x)

logx5

=x→1

11) 1 2) e 3) 4) 5

e

1. ∠1 + 2∠2 + 3∠3 + ..... + n.∠n15. Lt =

n→∞ n + 1

1) 0 2) 1 3) −1 4) e

16. Lt (√ x + √ x + √

x − √

x ) =

x→∞

11) 0 2) 2 3) 1 4)

2

Numerical Value Type

17. Lt (sin x)tanx =x→ π

2

18. Let f: R→R is a continuous function such

that f(x + y) = f(x) + f(y) for all x, y ∈ R and

f(1) = 2 then f(2) =

19. The derivative of f(tan x) with respect to

πg (sec x) at x = if f'(1) = 2, g'(√

2 ) = 4 is

4

120. If y = then y

2(0) =

1 + x + x2 + x3

Answers

1-3, 2-1, 3-1, 4-3, 5-2, 6-4, 7-3, 8-2, 9-2, 10-4,

11-4, 12-3, 13-1, 14-2, 15-2 16-4, 17-1, 18-4,

19-0.70, 20-0

JEE MAINMathematics

B. Eswara RaoSubject Expert

Writer

Differentiation, Limits and Continuity

Vector Algebra

Straight Objective Type

1. If (a × b

) × c

= a

× (b × c

) where a

.b

.c

are

any vectors such that a

.b ≠ 0, b

. c

≠ 0,

then a

, c

are

1) Perpendicular 2) Parallel

π3) Inclined at an angle of

3

π4) Inclined at an angle of

4

2. If a, b

, c

be non zero vectors such that

1(a

× b

) × c

= |b

| |c| a

and θ in the

3

acute angle between b

and c

then sin θ =

1 2 2√2 √

2

1) 2) 3) 4) 3 3 3 3

3. Let OA, OB, OC be the coterminous

edges of a rectangular parallelepiped of

volume V and let P be the vector opposite

to ‘0’ then [AP

BP

CP

] =

1) V 2) 2V 3) 3V 4) 4V

4. If b

is a vector whose initial point divides

the join of 5i

and 5j

in the ratio k : 1 and

whose terminal point is the origin and |b

|

= √37 then k lies in the interval

1 11) [−6 − ] 2) (−∞ −6] ∪ [ − ∞)6 6

3) [−6 0] 4) [0 6]

Answers: 1-2, 2-3, 3-2, 4-2.

The length of line segment..?

Page 2

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a) -ë]-è[ª-ö˺E Ô òŰޜ٠òÅ°îËÁ-ë¶y-Þ¥öËìª EóŸªÙ-vA-ú£ªhÙC? b) -ë]-è[ªö˺ ÍE-óŸªÙ-vAêŸ àŸöË-û¦-öËìª EóŸªÙ-vAÙචòÅ°ÞœÙ

ÔC? c) -ë]-è[ªìª ÚÛí‡p ÑÙ# ô¢¤Ûé ÚÛLpÙචð»ô¢ ›íô¢ª .-.-.-.-.-.-.-.-.-.- d) ë]è[ªö˺ ë]”ù‡d öËÙG-ÚÛõ ÞœöË òŰޜ٠.-.-.-.-.-.-.-.-.-

sö˶ë¯z a) í£-æ¨d-ÚÛö˺ Ï#aì Næ-Nª-û-ËÂ-öËö˺ Fæ¨ö˺, Ú•÷±yö˺x ÚÛJ-¸ÞN ÔN? b) Î-þ§\-J(Ú Î÷ªxÙ ö˺í£Ù ÷öËx ÚÛL¸Þ öËºí£ öˤÛ-é°-ö˶N?

PUBLIC EXAMINATIONS - 2020

Time: 2 Hrs. 45 Min. GENERAL SCIENCE PAPER - II Max. Marks: 40

TENTH CLASS MODEL PAPER

÷ªÙÞœüŒî¦ô¢Ù 2 Wû 2020 n email: [email protected]

17

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b) @ô¦g-øŒóŸªÙ êŸìö˺ vú£÷-NÙ-àŸ-ñè˶ sþ»ÙêŸz Î÷«xöË vþ§î¦öË ìªÙ# Óö° ô¢¤¨Ù-àŸª-ÚÛªÙ-åªÙC? 17.- a) šíú‡d-šújèÂq ö°Ùæ¨ vÚ¨Nª-ú£Ù--ô¢ÚÛ ÷ªÙë]ªöË NE-óµ«ÞœÙ ÷öËx ÷«ì-î¦-RÚ¨, ú£÷ªú£h @÷-ô¦-øŒ‰-

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šú¤ÛûÂ - IV

ú£÷ªóŸªÙ:- 30 ENª-ÿ§õª ð§ôÂd - B ÷«ô¢ª\õª:- 5

1.- ø‹yú£-î˶ô¢ªx ÍÙç˶? ( )

A) ÷ªè[ Íè[-÷±-ö˺xE îµ³ÚÛ\ö˺x ÞœöË î¦óŸ³-ÞœêŸ î˶ô¢ªx B) ø‹y-ú£-vÚ¨óŸª NCÅE áJ›í î˶ô¢ªxC) A, B D) ÷«ì-÷±öË ø‹yú£-vÚ¨-óŸªö˺ ÷³Üu-iì òÅ°Þ¥õª

2.- Ô Î÷-ô¢é í‡ô¢-Nªè êŸö-Ú¨Ù-ë]ª-õªÞ¥ ÑÙåªÙC? ( )

A) ú£ÙÝ°u í‡-ô¢-Nªè B) øŒÚ¨h í‡ô¢-Nªè C) Íè[O Î÷-ô¢é ÷u÷-ú£–-ö˺E @÷ vë]÷u-ô¦P í‡ô¢-Nªè D) ÷ªÙ#-Fæ¨ Î÷-ô¢é ÷u÷-ú£–-ö˺E @÷ vë]÷u-ô¦P í‡ô¢-NªèÂ

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A) vÚÛ÷ªÙ êŸí£pE ø‹K-ô¢ÚÛ î¦uóŸ«-÷«õª B) ÍCÅ-ÚÛÙÞ¥ Aìè[Ù C) óµ«Þ¥ D) A, C

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A) êÁÚÛõª ÞœöË Óõª-ÚÛõª B) êÁÚÛõª ö˶E Óõª-ÚÛõª C) Ú•Eo êÁÚÛõªêÁ, ÷ªJ-Ú•Eo êÁÚÛõª ö˶ÚÛªÙè¯ ÑÙæ°ô³ D) Ú•êŸh â°êŸªöË ÑêŸpAh áô¢ª-Þœª-꟪ÙC

5.- Îô¢ î¦ï‡°-ÚÛö˺ šíJ-þ§d-L-ú‡úà àŸöË-û¦Eo Eô¢«-í‡Ùචví£óµ«-ÞœÙö˺ Ñí£-óµ«-TÙ-#ì ñÙÞ¥-ü°-ë]ªÙí£ë¶Eo ú£«#-ú£ªhÙC?( )

A) ÷´uÚÛúà Íû¶ >Þœªô¢ª í£ë¯ô¢–Ù B) @ô¦g-øŒóŸªÙ - C) ò˺öËúà D) Îô¢ î¦ï‡°ÚÛ 6.- Ú¨ô¢-é-áìu ú£Ùóµ«-Þœ-vÚ¨-óŸªö˺ í‡Ùè…-í£-ë¯ô¢–Ù êŸóŸ«-ô¢-÷±-꟪Ù-ë]E Eô¢«-í‡Ùචví£óµ«-ÞœÙö˺ Ñí£-óµ«-

TÙ-#ì ô¢þ§-óŸªìÙ? ( )

A) Í-óµ«-è…-ûË B) þ§víÆ£-E-ûË C) NªCÇ-M-ûË ñ«x D) NªëǵjöËÀ ηôÙ-âËËÀ 7.- Ï#aì í£±ÿ§pEo ÞœªJhÙ-àŸÙè….- ( )

A) í£±ô¢ªù£ í£±ù£pÙ B) úˆY í£±ù£pÙ C) ÷ÙëÅ]u í£±ù£pÙ D) CyLÙ-ÞœÚÛ í£±ù£pÙ

8.- ví£êŸªu-êŸpAh ÎôÁ-Þ¥u-EÚ¨ ú£ÙñÙ-CÅÙ-#ì ö˺ÞÁìª ÞœªJhÙ-àŸÙè….- ( )

9.- Oªô¢ª ëµjìÙ-Cì @N-êŸÙö˺ ඛú Ô àŸô¢u @÷ î˵jNëÅ]u ú£Ùô¢¤Ûé Ú¨ÙCÚ¨ ÷ú£ªhÙC? ( )

A) ð§ôÂ\ö˺ ö°û-ËÂìª šíÙàŸè[Ù- B) J-êŸ--ô¢Ùö˺ òÅ°ÞœÙÞ¥ îµ³ÚÛ\-öËìª šíÙàŸè[Ù- C) Íè[-Nö˺ vÚÛ«ô¢-÷ª”-Þ¥-öËìª ú£Ù-JÙ-àŸè[Ù - D) ÚÛöË-í£ÚÛª ñë]ª-õªÞ¥ ð§xú‡dÚ î¦è[æÙ-

10.- ÷´vêŸ-í‡Ùè[ ú£ÙñÙëÅ] î¦uëÅ]ªõª ô¦ÚÛªÙè¯ Eî¦-JÙ-àŸ-è¯-EÚ¨ Ñí£-óµ«-Þœ-í£-è[-EC? ( )

A) ú£Ù꟪-LêŸ Îô¢Ù Aìè[Ù- B) êŸô¢-àŸªÞ¥ Øù£-ë¯õª î¦è[æÙ- C) êŸT-ìÙ-êŸÞ¥ Fæ¨E ê¦Þœè[Ù- D) í£Ùè[x-ô¢-þ§-öËìª Bú£ª-ÚÁ-÷è[Ù-

A) B) C) D)

Straight Objective Type

1. A function f: R → R satisfies the equation

f(x + y) = f(x) f(y) for all x, y ∈ R and f(x) ≠ 0for any x ∈ R. If f is differentiable at '0' and

f(0) = 2 then for all x ∈ R, f'(x) =

1) 0 2) 2 3) 2f(x) 4) −f(x)

2. Let f, g be differentiable functions satisfying

g'(a) = 2, g(a) = b and g = f−

then f'(b) =

1 11) 2) 2 3) 4) 4

2 4

13. If f(x) = x sin () for x ≠ 0 and f(0) = 0 then

x

1) f is continuous at x = 0

2) f is differentiable at x = 0

3) f'(0−) exists but f'(0

+) does not exists

4) f' (0+) exists but f'(0

−) does not exists

1 1− ( + )|x| x4. If f(x) = x e for x ≠ 0 and f(0) = 0

then f(x) is

1) continuous as well as differentiable

2) discontinuous every where

3) continuous for all x, but not differentiable

at x = 0

4) neither differentiable nor continuous at

x = 0

5. If f(x) = x − 2, g(x) = (fof) (x) the g'(x) when

x > 20 is

1) 0 2) 1 3) −1 4) 20

6. If f(x) = (cosx) (cos2x) (cos3x) ... (cos nx)

n

then f'(x) + ∑ (r tan rx) f(x) =r = 1

1) n 2) −n 3)1 4) 0

7. If y = √ tan x + √ tan x + √ tan x + … ∞dy

then dx

tan x tan x1) 2)

2y − 1 2y + 1

sec2x sec

2x

3) 4) 2y − 1 2y + 1

d8. If x < 1 then (1 + 2x + 3x

2+ 4x

3+... ∞)

dx

=

1 21) 2)

(1 − x)2

(1 − x)3

−2 −23) 4)

(1 − x)3

(1 + x)3

dy y9. If xy = (x + y)

nand = then n =

dx x

1) 1 2) 2 3) 3 4) 4

10. Let y be an implicit function of x defined by

x2x − 2xx coty − 1 = 0 then y' (1) =

1) 1 2) log 2 3) log 3 4) −1

11. The function f: R-{0}→ R given by

1 2f(x) = − can be made continuous

x e2x − 1

at x = 0, by defining f(0) as

1) 2 2) −1 3) 0 4) 1

12. Let f be a non zero continuous function sat-

isfying f (x + y) = f(x) f(y) for all x, y ∈ R. If

f(2) = 9 then f(3) =

1) 3 2) 9 3) 27 4) 81

13. The value of f(0) so that the function

1 − cos (1 − cosx)f(x) = is continuous every

x4

where is

1 1 11) 2) 3) 4) 1

8 2 4

14. Lt (log55x)

logx5

=x→1

11) 1 2) e 3) 4) 5

e

1. ∠1 + 2∠2 + 3∠3 + ..... + n.∠n15. Lt =

n→∞ n + 1

1) 0 2) 1 3) −1 4) e

16. Lt (√ x + √ x + √x − √

x ) =

x→∞

11) 0 2) 2 3) 1 4)

2

Numerical Value Type

17. Lt (sin x)tanx =x→ π

2

18. Let f: R→R is a continuous function such

that f(x + y) = f(x) + f(y) for all x, y ∈ R and

f(1) = 2 then f(2) =

19. The derivative of f(tan x) with respect to

πg (sec x) at x = if f'(1) = 2, g'(√

2 ) = 4 is

4

120. If y = then y

2(0) =

1 + x + x2 + x3

Answers

1-3, 2-1, 3-1, 4-3, 5-2, 6-4, 7-3, 8-2, 9-2, 10-4,

11-4, 12-3, 13-1, 14-2, 15-2 16-4, 17-1, 18-4,

19-0.70, 20-0

Straight Objective Type

1. A person of height 2 mts starts from a lamp

post of height 5 mts and walks away at the

rate of 6 km per hour. The rate at which his

shadow increases is

1) 2 kmph 2) 4 kmph 3) 6 kmph 4) 8 kmph

2. The curve y − exy + x = 0 a vertical tangent at

the point

1) (1 1) 2) (0 1) 3) (1 0) 4) at no point

3. The condition that the two curves x = y2,

xy = k cut orthogonally is

1) k2 = 1 2) 2k2 = 1 3) 4k2 = 1 4) 8k2 = 1

4. If the length of subtangent is 9, length of sub-

normal is 4 at a point (x y) on y = f(x), then

ordinate of the point is

1) ±4 2) ±6 3) ±8 4) ±3

5. If a + b + c = 0 then the quadratic equation

3ax2 + 2bx + c = 0 has atleast one root in the

interval

1) (0 1) 2) (1 2) 3) (2 3) 4) (−1 0)

6. Through the point (2 3) a straight line is drown

making positive intercept on the coordinate

axes. The area of the triangle thus formed is

least, then the ratio of the intercepts on line x

and y axes is

1) 1 : 2 2) 2 : 3 3) 3 : 4 4) 1 : 4

Numerical Value Type

7. The height of the cone of maximum volume

which can be inscribed in a sphere of radius 6

is..

8. The differences of a number and its square is

maximum then the number is

9. The constant c of Lagrange's theorem for f(x)

x= on in [2 4] is

x − 1x2

10. If the rate of decrease of − 2x + 5 is twice 2

the decrease of x then x =

Answers

1-2, 2-3, 3-4, 4-2, 5-1, 6-2, 7-8,

8-0.50, 9-2.73, 10-4.

Differentiation, Limits and Continuity

B. Eswara RaoSubject Expert

Writer

JEE MAINMathematics

Straight Lines (2D)

The Plane and 3D- Lines

Straight Objective Type

1. Let ABC be a triangle, if P is a point such

that AP divides BC in the ratio 2 : 3. BP

divides CA in the ratio 3 : 5. Then the ratio

in which CP divides AB is

1) 2 : 5 2) −2 : 5

3) 5 : 2 4) −5 : 2

2. If p, q are the perpendicular distances from

origin to the lines x secα + y cosecα = a;

x cosα − y sinα = a cos 2α respectively,

then 4p2 + q2 =

1) a2 2) 2a2

3) 3a2 4) 4a2

3. The line 3x + 2y = 24 meets the axes in A

and B. The perpendicular bisector of AB

meets the line y + 1 = 0 at C. Then area of

triangle ABC is

1) 61 sq.units 2) 71 sq.units

3) 81 sq.units 4) 91 sq.units

4. If P = (0, 1, 0) Q = (0, 0, 1), then the pro-

jection of PQ on the plane x + y + z = 3 is

1) 1 2) √2 3) √

3 4) 2

x − 1 y + 1 z − 1 x − 35. If the lines = = and

=2 3 4 1

y − k z = intersect then the value of k =

2 1

3 5 7 91) 2) 3) 4)

2 2 2 2

6. A line with positive D.C's passes through

P(2 −1 2) makes equal angels with axes.

The line meets the plane 2x + y + z = 9 at

Q. The length of line segment PQ =

1) 1 2) √2 3) √

3 4) 2

Numerical Value Type

7. Let P(3 2 6) be a point in space and Q be

a point on the line r

= ( i − j

+ 2k

) + µ (−3i

+ 5k). Then the value of µ for which the

vector PQ

is parallel of the plane x − 4y +

3z = 1

8. P (α, β, γ) lies on the plane x + y + z = 2.

Let a

= αi

+ βj

+ γk

and k × (k

× a

) = 0

then γ =

9. Let O (0, 0), P (3, 4), Q (6, 0) be the vertices

of triangle OPQ. The point R inside the tri-

angle OPQ the point R inside the triangle

OPQ in which the triangles OPR, PQR,

OQR are equal area. The coordinates of R

are (α, β) then α + β =

x − 4 y − 210. The value of k such that = =

1 1z − k lies on 2x − 4y + z = 7 is

7

Answers

1-3, 2-1, 3-4, 4-2, 5-4, 6-3, 7-0.25,

8-2, 9-5.33, 10-7.

Direction Cosines and

Direction Ratios; Plane

Straight Objective Type

1. if α, β, γ are respectively the acute angle

made by any line with the coordinates

axes, then

1) α + β + γ = 90° 2) α + β + γ = 360°3) 0° < α + β + γ < 270°4) 0° < α + β + γ < 180°

2. If the angle between the lines whose

−2 a bd.c' s are ( , , ) and

√21 √

21 √21

3 3 −6

( , , ) is 90°, then a pair of√

54 √54 √

54

possible value of a,b are

1) −1, 4 2) 4, 2 3) 4, 1 4) −4, −2

3. The harmonic conjugate of (2, 3, 4) with

respect to the line joining points (3, −2, 2)

and (6, −17, −4) is

1 1 11) (0, 0, 0) 2) ( )2 3 4

18 43) (1 1 1) 4) (, −5, )5 5

4. The equation ax + by + cz + d = 0 (d≠0)

does not represents a plane if

1) a2 + b2 + c2 = 0 2) a2 + b2 + c2 ≠ 0

3) a + b – c = 0 4) a + b + c = 0

5. The number of line perpendicular to x−axis

lying in yz plane is

1) 0 2) 1 3) 3 4) ∞6. The angle between a line and normal to a

plane is 30°. The angle between line and

plane is

π π 2π π1) 2) 3) 4)

3 2 5 4

7. The planes x = ±3, y = ±4, z = ±6 form a

1) cube 2) Rectangular parallelepiped

3) Tetrahedron

4) Parallelepiped with equal edges

Numerical Value Type

8. The lengths of projection of a line segment

on the coordinate planes are 3, 4, 5 then

length of the segment is

9. Let a line makes an angle θ with x, z axes

and β with y-axes so that √3 sinθ = sinβ

then cos2θ =

10. Image of (1, 2, 3) with respect to a plane

ax + by + cz + d = 0 is (−7/3,−4/3,−1/3)

then a + b + c + d =

Answers

1-3, 2-3, 3-4, 4-1, 5-4, 6-1, 7-2,

8-5, 9-0.60, 10-2.

Application of Differentiation

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The height of the cone?