the length of line segment..?
TRANSCRIPT
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..?
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(4 ́4 = 16)
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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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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?