for xi foundation - goal institutegoalinstitute.org/imagebag/image264.pdf · 20. the trajectory of...

B-58, BUDDHA COLONY, PATNA - 800 001 , Mob.: 9334594165 / 66 / 67

XI FOUNDATION REVISION - TEST-1 (PCM ) [ 1 ]

Name of the Candidate : ________________________________________

Roll No. : ________________________________________

Centre Code : ________________________________________

Centre Town : ________________________________________

INSTRUCTIONS

(i) This Paper has 60 Objective type questions and 15 Integer

TypeQuestions. All questions are compulsory.

(ii) The Maximum marks for each question is 4.

(iii) 1 mark will be deducted against each negative response from the

total marks.

(iv) Use of calculator, slide rule, graph paper and trignometric tables is

NOT PERMITTED.

[ Time : 3.00 Hours ] [ Max. Marks : 300 ]Test CODE : XI - Foundation - Test - 1st (2019-2020)

Ascent ProgramA Series of Revision Class, Tests, Discussion and Doubt Program

for

XI FoundationTest - 1st

(PCM)

Help Line : 9334594165 / 66 / 67

B-58, BUDDHA COLONY, PATNA - 800 001, Website: www.goalinstitute.org

16.03.2020Date:



01. The van der Waals’ equation of state for some

gases can be expressed as

2

aP (V b) RT

V

where P is the pressure, V the molar volume, T

the absolute temperature of the given sample of

gas, and a, b and R are constants. The dimensions

of a are :

(1) ML5T–2 (2) ML–1T–2

(3) L3 (4) L6

02. A student when discussing the properties of a

medium (except vacuum) writes

Velocity of light in vacuum

= velocity of light in medium

This formula is :

(1) Dimensionally correct

(2) Dimensionally incorrect

(3) Numerically incorrect

(4) Both (1) and (3)

03. If X = a + b, the maximum percentage error in

the measurement of X will be :

(1)a b

100%a b

(2)a b

100%a b a b

(3)a b

100%a b a b

(4)a b

· 100%a b

04. Which of the following have got same

dimensions ?

a. Latent heat

b. Energy per unit mass

c. Gravitational potential

d. Specific heat

(1) “d” and “c” (2) “a” and “d”

(3) “a” and “b” (4) None of these

05. The resultant of two vectors A

and B

is

perpendicular to the vector A

and its magnitude

is equal to half of the magnitude of vector B

.

The angle between A

and B

is :

R

B

90°

A

(1) 120° (2) 150°

(3) 135° (4) None of these

06. The resultant of the three vectors OA, OB

and

OC

, shown in the following figure, is :

45°45°

r

r

A

B

C

r

O

(1) r (2) 2r

(3) r(1 2) (4) r( 2 1)

07. Given 21|A | 2,|A | 3

and 21|A A | 3

. Find

the value of 21 1 2(A 2 A ) · (3 A 4 A )

(1) –64 (2) –60

(3) –62 (4) –61

08. The angle which the vector ^ ^

A 2 i 3 j makes

with y-axis, where ^i and

^j are unit vectors

along x- and y-axes, respectively is :

(1) cos–1 (3/5) (2) cos–1 (2/3)

(3) tan–1 (2/3) (4) sin–1 (2/3)

[Time : 3 Hours] Full Marks : 300

XI FOUNDATION REVISION - TEST-1 (PCM) - 16.03.2020



09. In a two dimensional motion of a particle, the

particle moves from point A, position vector 1r

to point B, position vector 2r

. If the magnitudes

of these vectors are, respectively, r1 = 3 and

r2 = 4 and the angles they make with the

x-axis are 1 = 75° and 2 = 15°, respectively,

then find the magnitude of the displacement

vector.

A

B1r

2r12

(1) 15 (2) 13

(3) 17 (4) 15

10. Two vectors a

and b

are at an angle of 60° with

each other. Their resultant makes an angle of

45° with a

. If |b|

= 2 units, then |a|

is :

(1) 3 (2) 3 1

(3) 3 1 (4) 3/2

11. A thief is running away on a straight road in a

jeep moving with a speed of 9 ms–1. A policeman

chases him on a motor cycle moving at a speed

of 10 ms–1. If the instantaneous separation of

the jeep from the motor cycle is 100 m, how long

will it take for the policeman to catch the thief ?

(1) 1 s (2) 19 s

(3) 90 s (4) 100 s

12. A person is throwing two balls into the air one

after the other. He throws the second ball when

the first ball is at the highest point. If he is

throwing the balls every second, how high do they

rise ?

(1) 5 m (2) 3.75 m

(3) 2.50 m (4) 1.25 m

13. A drunkard is walking along a straight road. He

takes 5 steps forward and 3 steps backward and

so on. Each step is 1 m long and takes 1 s. There

is pit on the road 11 m away from the starting

point. The drunkard will fall into the pit after :

(1) 29 s (2) 21 s

(3) 37 s (4) 31 s

14. A particle is dropped from rest from a large height.

Assume g to be constant throughout the motion.

The time taken by it to fall through successive

distances of 1 m each will be :

(1) All equal, being equal to 2/g second

(2) In the ratio of the square roots of the integers

1, 2, 3, ......

(3) In the ratio of the difference in the square

roots of the integers, i.e., 1, ( 2 1),

( 3 2), ( 4 3) , .....

(4) In the ratio of the reciprocals of the square

roots of the integers, i.e., 1 1 1

, , , ....1 2 3

15. A ball is dropped into a well in which the water

level is at a depth h below the top. If the speed of

sound be c, then the time after which the splash

is heard will be given by :

(1)2 1

hgh c

(2)

2 1h

gh c

(3)2 1

hg c

(4)

2 1h

g c

16. A body is projected up a smooth inclined plane

with velocity u from the point A as shown in the

figure. The angle of inclination is 45° and the

top is connected to a well of diameter 40 m. If

the body just manages to cross the well, what is

the value of u ? Length of inclined plane is

20 2 m.

45°

A 40 m

B C

S

(1) 40 m/s (2) 40 2 m/s

(3) 20 m/s (4) 20 2 m/s

17. A ball rolls off the top of a staircase with a

horizontal velocity u m/s. If the steps are h metre

high and b metre wide, the ball will hit the edge

of the nth step, if :

(1) 2

2hun

gb (2)

22hun

gb

(3)

2

2

2hun

gb (4)

2

2

hun

gb



18. If a stone is to hit at a point which is at a distance

d away and at a height h above the point from

where the stone starts, then what is the value

of initial speed u if the stone is launched at an

angle ?

(1)g d

cos 2(d tan h)

(2)d g

cos 2(d tan h)

h

u

d

(3)

2

2

gd

hcos

(4)

2gd

(d h)

19. A particle is projected from the ground with an

initial speed of v at angle with the horizontal.

The average velocity of the particle between its

point of projection and highest point of trajectory

is :

(1)2v

1 2cos2

(2)2v

1 2cos3

(3)2v

1 3cos2

(4) v cos

20. The trajectory of a projectile in a vertical plane

is y = ax – bx2, where a and b are constants and

x and y are respectively horizontal and vertical

distances of the projectile from the point of

projection. The maximum height attained by the

particle and the angle of projection from the

horizontal are :

(1)2

1b, tan (b)

2a

(2)

21a

, tan (2b)b

(3)2

1a, tan (a)

4b

(4)

212a

, tan (a)b

Q. No. 21 to 25 Integer Type Questions

21. A bullet fired into a fixed target loses half of its

velocity after penetrating 3 cm. How much

further it will penetrate (in cm) before coming

to rest assuming that it faces constant

resistance to motion ?

22. The acceleration–time graph of a particle moving

along a straight line is as shown in figure.

10

y a/ms–2

4t/s

At what time the particle acquires its initial

velocity ?

23. The velocity–time graph of a body moving in a

straight line is shown.

2 4 6 8 10

v/ms–1

2

1

–1

–2

t/s

The displacement of the body in 10 s is :

24. The number of significant figures in 5.69 × 1015 kg

is :

25. The percentage error in the measurement of

mass and speed are 2% and 3%, respectively.

How much will be the maximum error in the

estimation of KE obtained by measuring mass

and speed ?

26. Number of atoms in the following samples of

substances is the largest in :

(1) 4.0 g of hydrogen (2) 71.0 g chlorine

(3) 127.0 g of iodine (4) 48.0 of magnesium

27. The ratio of number of oxygen atoms (O) in 16.0 g

ozone (O3), 28.0 g carbon monoxide (CO) and 16.0

oxygen (O2) is (Atomic mass : C = 12, O = 16 and

Avogadro’s constant NA = 6.0 × 1023 mol–1)

(1) 3 : 1 : 2 (2) 1 : 1 : 2

(3) 3 : 1 : 1 (4) 1 : 1 : 1

28. In a compound C, H and N atoms are present in

9 : 1 : 3.5 by weight. Molecular weight of

compound is 108. Molecular formula of compound

is :

(1) C2H6N2 (2) C3H4N

(3) C6H8N2 (4) C9H12N3

29. 2 3A 2B 3C AB C

Reaction of 6.0 g of A, 6.0 × 1023 atoms of B, and

0.036 mol of C yields 4.8 g of compound AB2C3. If

the atomic mass A and C are 60 and 80 amu,

respectively, the atomic mass of B is

(Avogadro no. = 6 × 1023) :

(1) 50 amu (2) 60 amu (3) 70 amu (4) 40 amu



30. To neutralise completely 20 mL of 0.1 M aqueous

solution of phosphorous acid (H3PO3), the value

of 0.1 M aqueous KOH solution required is :

(1) 40 mL (2) 20 mL

(3) 10 mL (4) 60 mL

31. The orbital angular momentum for an electron

revolving in an orbit is given by h

( 1).2

l l . This

momentum for an s-electron will be given by :

(1) zero (2)h

2

(3)h

2 ·2

(4)1 h

·2 2

32. If the shortest wavelength in Lyman series of

hydrogen atom is A, then the longest wavelength

in Paschen series of He+ is :

(1)5A

9(2)

9A

5

(3)36A

5(4)

36A

7

33. Energy of an electron is given by

218

2

ZE 2.178 10 J

n

.

Wavelength of light required to excite an electron

in an hydrogen atom from level n = 1 to n = 2 will

be :

(h = 6.62 × 10–34 Js and c = 3.0 × 108 ms–1)

(1) 1.214 × 10–7 m (2) 2.816 × 10–7 m

(3) 6.500 × 10–7 m (4) 8.500 × 10–7 m

34. If the radius of first orbit of H atom is a0, the

de-Broglie wavelength of an electron in the third

orbit is :

(1) 4a0 (2) 8a0

(3) 6a0 (4) 2a0

35. Which of the following sets of quantum numbers

is correct for an electron in 4f orbital ?

(1) n = 4, l = 3, m = +1, s = +½

(2) n = 4, l = 4, m = –4, s = –½

(3) n = 4, l = 3, m = +4, s = +½

(4) n = 3, l = 2, m = –2, s = +½

36. Similarity in chemical properties of the atoms

of elements in a group of the Periodic table is

most closely related to :

(1) atomic numbers

(2) atomic masses

(3) number of principal energy levels

(4) number of valence electrons

37. Consider the following ionization enthalpies of

two elements ‘A’ and ‘B’.

Element

1st 2nd 3rd

A 899 1757 14847

B 737 1450 7731

Ionization enthalpy (kJ/mol)

Which of the following statements is correct ?

(1) Both ‘A’ and ‘B’ belong to group–1 where ‘B’

comes below ‘A’.

(2) Both ‘A’ and ‘B’ belong to group–1 where ‘A’

comes below ‘B’.

(3) Both ‘A’ and ‘B’ belong to group–2 where ‘B’

comes below ‘A’.

(4) Both ‘A’ and ‘B’ belong to group–2 where ‘A’

comes below ‘B’.

38. In the long form of the periodic table, the valence

shell e lectronic configuration of 5s25p4

corresponds to the element present in :

(1) Group 16 and period 6




39. Which of the following series correctly

represents relations between the elements from

X to Y ? XY

(1) 3Li 19K Ionization enthalpy increases

(2) 9F 35Br Electron gain enthalpy (negative

sign) increases

(3) 6C 32Ge Atomic radii increases

(4) 18Ar 54Xe Noble character increases

40. Among Al2O3, SiO2, P2O3 and SO2 the correct

order of acid strength is :

(1) Al2O3 < SiO2 < SO2 < P2O3

(2) SiO2 < SO2 < Al2O3 < P2O3

(3) SO2 < P2O3 < SiO2 < Al2O3

(4) Al2O3 < SiO2 < P2O3 < SO2

41. Amongst LiCl, RbCl, BeCl2 and MgCl2 the

compounds with the greatest and the least ionic

character, respectively are :

(1) LiCl and RbCl

(2) RbCl and BeCl2

(3) MgCl2 and BeCl2

(4) RbCl and MgCl2



42. Which one of the following pairs of species have

the same bond order ?

(1) CN– and NO+ (2) CN– and CN+

(3) –2O and CN– (4) NO+ and CN+

43. Which one of the following molecules is polar ?

(1) XeF4 (2) IF5

(3) SbF5 (4) CF4

44. The group having triangular planar structure is :

(1) 23 3 3BF , NF , CO (2) 2

3 3 3CO , NO , SO

(3) 23 3 3NH , SO , CO (4) NCl3, BCl3, SO3

45. The group of molecules having identical shape

is :

(1) PCl5, IF5, XeO2F2 (2) BF3, PCl3, XeO3

(3) SF4, XeF4, CCl4 (4) ClF3, XeOF2, XeF3+


46. Total number of lone pair of electrons in 3I ion

is ________ .

47. In the molecular orbital diagram for the

molecular ion, 2N , the number of electrons in

the 2p molecular orbital is ________ .

48. Dissolving 120 g of a compound of (mol. wt. 60)

in 1000 g of water gave a solution of density 1.12

g/mL. The molarity of the solution is ___ .

49. Experimentally it was found that a metal oxide

has formula M0.98O. Metal M, present as M2+

and M3+ in its oxide. Fraction of the metal which

exists as M3+ would be _______ .

50. In an atom, how many orbitals will have the

quantum numbers; n = 3 and l = 2 ?

51. If 1

Q x : x , y Ny

, then :

(1) 1 Q (2) 0 Q

(3) 2 Q (4) none of these

52. Define Na = {an : n N}, then N3 N5 is equal to :

(1) N15 (2) N5

(3) N10 (4) none of these

53. The domain of the function 2

log(x 5)f(x)

x 4x 3

is :

(1) (–, –1) (2) [–3, –1]

(3) R – [–3, –1] (4) (–5, ) – {–3, –1}

54. For non-empty sets A and B, if A B, then

(A × B) (B × A) equals :

(1) A B (2) A × A

(3) B × B (4) none of these

55. The quotient of the identity function by the

reciprocal function is given by

(1) x2 x R (set of real numbers)

(2) 2

1x R {0}

x

(3) x2 x R – {0}

(4) None of these

56. If sets A and B are defined as

4A {(x, y)|y

x , 0 x R

B = {(x, y)|y = x, x > 0, x R}, then :

(1) A B (2) A B =

(3) A B = A (4) none of these

57. The most general value of satisfying the

equations sin = sin and cos = cos is :

(1) 2n + (2) 2n – (3) n + (4) n –

58. In ABC, if a b c

s2

, then

2 2C Bbcos ccos

2 2

is equal to :

(1) s (2) 2s (3) 3s (4) 4s

59. Consider the set of all determinants of order 3

with entries 0 and 1 only. Let B be the subset of

A consisting of all determinants with value 1.

Let C be the subset of the set of all determinants

with value –1 then :

(1) C =

(2) A = B C

(3) B has as many elements as C

(4) none of these

60. The solution of the equation sin m + sin n = 0

is :

(1)(2K 1)

, K Zm n

(2)2K

, K Zm n

(3) both (1) and (2) are true

(4) none of these

61. If F is function such that F(0) = 2, F(1) = 3,

F(x + 2) = 2F(x) – F(x + 1) for x 0, then F(5) is

equal to :

(1) –7 (2) –3 (3) 17 (4) 13



62. Which of the following is an empty set ?

(1) {x|x is a real numbr and x2 – 1 = 0}

(2) {x|x is a real number and x2 + 3 = 0}

(3) {x|x is a real number and x2 – 9 = 0}

(4) {x|x is a real number and x2 = x + 2}

63. Let Z denote the set of all integers and

A = {(a, b) : a2 + 3b2 = 28, a, b Z} and

B = {(a, b) : a > b, a, b Z}.

Then the number of elements in A B is :

(1) 2 (2) 3 (3) 4 (4) 6

64. Let A = {–1, 0, 1, 2}, B = {–4, –2, 0, 2} and f,

g : A B be the functions defined by f(x) = x2 – x

and 1

g(x) 2 x 12

. Then

(1) f = g (2) f = 2g

(3) g = 2f (4) none of these

65. In the figure, ABC is a triangle in which

C = 90° and AB = 5 cm. D is a point on AB such

that AD = 3 cm and ACD = 60°. Then the length

of AC is :

60°

C

A BD3 cm

5 cm

(1)3

5 cm7

(2)7

cm3

(3)3

cm7

(4) none of these

66. If f : R R satisfies f(x + y) = f(x) + f(y) x, y R

and f(1) = 7, then n

r 1

f(r)

(1)n(n 1)

2

(2)

7n(n 1)

2

(3) 7n(n + 1) (4) none of these

67. The domain and range of the relation R given by

R = {(x, y) : 6

y xx

; where x, y N and x < 6} is

:

(1) {1, 2, 3}, {7, 5} (2) {1, 2}, {7}

(3) {1, 3}, {5} (4) none of these

68. Let a

tana 1

and

1tan

2a 1

, then +

is :

(1)4

(2)

4

(3)

2

(4)

69. When varies over the real numbers, the

maximum value of cos – cos 2 is :

(1) 2 (2)7

8(3)

9

8(4) 0

70. A function f satisfies the relation f(n2) = f(n) + 6 for

n 2 and f(2) = 8. Then the value of f(256) is

(1) 24 (2) 26 (3) 22 (4) 28


71. If n(A) = 3 and B = {3, 4, 5}, then n(A × B) =

72. The value of

tan 3x tan 2x tan x – tan 3x + tan 2x + tan x =

73. If f(x) = x3 – 1, then find [f(3) f(2)]

11

_____ .

74. The number of solutions of sin x = sin2x between

2

and

2

is _____ .

75. If f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then

f(1) is equal to ______ .

If you find any probable mistake in the Question, you can send a mail at:

[email protected] or

whatsapp/ message on 7564901784

with following details:

Date of Test, Name, Roll No., Contact No. and Explanation of the mistake.

Note: All the request will be accepted till

Tomorrow 05 PM.



Space for Rough Work



01.

02.

03.

04.

05.

06.

07.

08.

09.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

(1)

(4)

(3)

(3)

(2)

(3)

(1)

(3)

(2)

(2)

(4)

(1)

(1)

(3)

(1)

(4)

(3)

(2)

(3)

(3)

1

8

6

3

8

(1)

(4)

(3)

(1)

(1)

(1)

(4)

(1)

(3)

(1)

(1)

(3)

(3)

(3)

(4)

(2)

(1)

(2)

(2)

(4)

9

1

2

4

5

(1)

(1)

(4)

(2)

(3)

(1)

(3)

(1)

(3)

(3)

(4)

(2)

(4)

(1)

(1)

(2)

(1)

(1)

(3)

(2)

9

0

3

3

0

XI - Foundation Revision Test -1st

PCM - 16.03.19

01.

02.

03.

04.

05.

06.

07.

08.

09.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

(1)

(4)

(3)

(3)

(2)

(3)

(1)

(3)

(2)

(2)

(4)

(1)

(1)

(3)

(1)

(4)

(3)

(2)

(3)

(3)

1

8

6

3

8

(1)

(4)

(3)

(1)

(1)

(1)

(4)

(1)

(3)

(1)

(1)

(3)

(3)

(3)

(4)

(2)

(1)

(2)

(2)

(4)

9

1

2

4

5

(1)

(1)

(4)

(2)

(3)

(1)

(3)

(1)

(3)

(3)

(4)

(2)

(4)

(1)

(1)

(2)

(1)

(1)

(3)

(2)

9

0

3

3

0

XI - Foundation Revision Test -1st

PCM - 16.03.19

for xi foundation - goal institutegoalinstitute.org/imagebag/image264.pdf · 20. the trajectory of...

Documents