NOSEGAY PUBLIC SCHOOL, SGNR
MAJOR TEST COMPETITIVE CELL (2023-24)
Class : XI S & S ACE (JEE)
Date : 02-09-2023
Instructions
1. Question paper contains three Subjects Physics, Chemistry and Maths.
2. Each subject has two sections A and section B.
3. Section A contains 20 Questions. All single choice correct.
4. Section-B contains 05 Questions. All numerical.
5. Total Marks :- 300
6. Marking Scheme : For every correct answer 4 marks will be given. -1 Mark for each incorrect answer.
No negative marking for numericals.
Physics
1. A stone falls freely under gravity it covers distance h1, h2 and h3 in the first 5 seconds, the next 5 seconds
and the next 5 seconds respectively. The relation between h1, h2 and h3 is:
(a) h1=h2=h3
(b) h1=2h2=3h3
(c) ℎ = =
(d) h2=3h1=h3=3h2
2. A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after
some time with a velocity of 80 m/s. the height of the tower is: (g=10m/s 2)
(a) 300m
(b) 360m
(c) 340m
(d) 320m
3. The ratio of the distance travelled by a freely feeling body in the 1st, 2nd, 3rd, and 4th second
(a) 1 : 2 : 3 : 4
(b) 1 : 4 : 9 : 16
(c) 1 : 3 : 5 : 7
(d) 1 : 1 : 1 : 1
4. A ball is projected with a velocity, 10ms-1, at an angel 600 with the vertical direction. Its speed at the highest
point of its trajectory will be
(a) zero
(b) 5√3𝑚𝑠
(c) 5ms-1
(d) 10ms-1
5. Two particles are projected from the same point with the same speed u such that they have the same range
R, but different maximum heights h1 and h2. Which of the following is correct?
(a) R2=4h1h2
(b) R2=2h1h2
(c) R2=16h1h2
(d) R2=h1h2
6. A bullet is fired with a velocity u making an angle of 600 with the horizontal plane. The horizontal component
of the velocity of the bullet when it reaches the maximum height is
(a) u
(b) 0
(c)
√
(d) u/2
7. A ball it thrown upwards and it returns to ground describing a parabolic path. Which of the following remains
constant
(a) Kinetic energy of the ball
(b) speed of the ball
(c) Horizontal component of velocity
(d) vertical component of velocity
8. The path of a projectile in the absence of air drag is shown in the figure by dotted line. If the air resistance is
not ignored then which one of the path shown in the figure is appropriate for the projectile?
(a) B
(b) A
(c) D
(d) C
9.
1
10.
11.
12.
13. We can derive Newtons(a) Second and third laws from the first law
(c) Third and first laws from second law
(b) First and second laws from the third law
(d) All the three laws are independent of each
14. Formula for true force is
(a) 𝐹 = 𝑚𝑎
(b) 𝐹 =
(c) 𝐹 =
(d) 𝐹 =
15. n small balls each of mass m impinge elastically each second on a surface with velocity u. the force
experienced by the surface will be
(a) mnu
(b) 2mnu
(c) 4mnu
(d) 𝑚𝑛𝑢
16.
17.
2
18.
19.
20. A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in
perpendicular directions with velocities of 3 m/s and 4 m/s respectively. The third piece will be thrown off with
velocity of
(a) 1.5 m/s
(b) 2.0 m/s
(c) 2.5 m/s
(d) 3.0 m/s
21. A body starts from rest from the origin with an acceleration of 6 m/s2 along the X-axis and 8 m/s2 along the
Y-axis. Its distance (in meter) from the origin after 4 seconds will be
22. The range of a projectile when fired at 750 with the horizontal is 0.5 km. What will be its range when fired at
450 with the same speed:- [range in km]
23. A batsman deflects a fall by an angle of 450 without changing its initial speed which is equal to 54 km/h.
what is the impulse imparted to the ball (in kg m/s)? Mass of the ball is 0.15 kg
24. A hunter has a machine gun that can fire 50g bullets with a velocity of 500 m/s. A 40 kg tiger springs at him
with a velocity of 10 m/s. how many bullets must the hunter fire into the tiger in order to stop him in track?
25. A particle moves in the x y plane under the action of force → such that the components of its linear
momentum → at any time t are px=2cost, py=2sint. Find the angle between → and → at time t. (angle in
degrees)
Chemistry
26. Lewis dot structure of CO, NO
(i) : 𝐶 ≡ 𝑂:
(ii) : 𝑁 ≡ 𝑂:
Which of the above structure is correct?
(a) Only I
(b) Only II wrong
(c) Only Ill
(d) All of the above
27. In carbon di oxide the formal charge on the carbon atom is
(a) +1
(b) -1
(c) 0
(d) + 0.75
28. Which of the following is not the characteristic of a covalent compound?
(a) No definite geometry
(b) Insoluble in polar solvent
(c) Small difference in electronegativity between the combining atoms
(d) Low melting point
29. Match the compounds given in column I with the hybridization and shape given in column II and
mark the correct option
Column - 1
Column-2
(A) XeF6
(i) distorted octahedral
(B) ХеОз
(ii) Square planar
(C) XeOF4
(iii) Pyramidal
(D) XeF4
(iv) Square pyramidal
3
(A).
(B).
(C).
(D)
(a).
(i).
(iii).
(iv).
(ii)
(b).
(i).
(ii).
(iv).
(iii)
(c).
(iv).
(iii). (i).
(ii)
(d).
(iv).
(i).
(ii).
(iii)
30. The correct order of the lattice energies of the following ionic compounds is
(a) NaCl> MgBr2 >CaO > Al2O3
(b) NaCI >CaO >MgBr2 >Al2O3
(c) Al2O3 >MgBr2 >CaO >NaCl
(d) MgBr2 >Al2O3 >CaO > NaCl
31. The correct order of increasing bond length of C-H, C-0, C-C and C=C is
(a) C-H<C-O<C-C<C=C
(b) C-H<C=C<C-O<C-C
(c) C-C<C= C<C-O<C-H
(d) C-O<C-H<C-C<C=C
32. Which of the following has lowest bond angle?
(a) H2S
(b) NH3
(c) SO2
(d) H20
33. In case of H2O molecule, the molecular geometry is
(a) Tetrahedral
(b) Bent
(c) t shaped
(d) Linear
34. The set representing the correct order of first ionization potential is
(a) K > Na > Li
(b) Be > Mg > Ca
(c) B > C > N
(d) Ge > Si > C
35. The correct order of second ionisation potential of carbon, nitrogen, oxygen and fluorine is
(a) 0 > F > N> C
(b) F > 0 > N> C
(c) C > N> O> F
(d) O > N> F > C
36. The first ionisation potential of Na, Mg, Al and Si follow the order
(a) Na > Mg > Al > Si
(b) Na < Mg > AI < Si
(c) Na < Mg < Al < Si
37. Which of the following molecules have same bond order?
1. H2
2. Cl2
3. CO
4. Br2
Choose the correct option.
(a) 1, 2 and 4 have same bond order
(b) 3 and 5 have same bond order
(c) Both (a) and (b)
(d) None of the above
38. Which of the following has most covalent bond?
(a) Na2S
(b) AlCl3
(c) NaH
(d) Na = Mg = Al > Si
5. N2
(d) MgCl2
39. Molecular shapes of SF4, CF4 and XeF4 are
(a) Same with 2, 0 and 1 lone pairs of electrons respectively
(b) The same with 1, 1 and 1 lone pairs of electrons respectively
(c) Different with 0, 1 and 2 lone pairs of electrons respectively
(d) Different with 1, 0 and 2 lone pairs of electrons respectively.
40. Give the correct order of initials T or F for following statements. Use T if statement is true and F if it
Is false:
(i) The order of repulsion between different pair of electrons is Ip - Ip > Ip - bp > bp - bp
(ii) In general, as the number of lone pair of electrons on central atom increases, value of bond angle
from normal bond angle also increases
(iii) The number of lone pair on O in H2O is 2 while on N in NH3 is 1
(iv) The structures of xenon fluorides and xenon oxyfluorides could not be explained on the basis of
VSEPR theory.
(a) TTTF
(b) TFTF
(c) TFTT
(d) TFFF
41. Which of the following statements is/are not correct for combination of atomic orbitals
(i) The combining atomic orbitals must have the same or nearly the same energy.
(ii) Greater the extent of overlap, the greater will be the electron densitv between the nuclei of a
Molecular orbital.
(iii) 2px orbital of one atom can combine with either of 2Px, 2py or 2pz orbital of other atom as these
orbitals have same energy.
(a) (i) and (ii)
(b) (iii) only
(c) (i) only
(d) (ii) and (iii)
4
42. Matching Type question
1. Match the column
Column I
(A)BeH2
(B)SF6
(C)NO2
Column II
(p) Odd electron molecules
(q) Expanded octet
(r) Incomplete octet of central atom
Maths
43. Which of the following is positive number
(a) sin 1290
(b) cos 570
(c) cot 1200
(d) tan 960
44. 𝑠𝑖𝑛 24 − 𝑠𝑖𝑛 6 is equal to
(a)
√
(b)
45. The range of 𝑓(𝑥) =
(a) [-1, 1]
√
(c)
√
(d)
√
𝑖𝑠
(b)
,
(c)
,
(d)
,
46. The maximum value of the 𝑠𝑖𝑛𝑥 + 2𝑠𝑖𝑛𝑥 + 3𝑠𝑖𝑛𝑥 + − − − − − − +10𝑠𝑖𝑛𝑥
(𝑤ℎ𝑒𝑟𝑒 𝑥 , 𝑥 , 𝑥 , − − − − − − −, 𝑥 ∈ 𝑅)𝑖𝑠
(a) 25
(b) 35
(c) 45
(d) 55
47. log tan 1 + log tan 2 + log tan 3 + − − − − − − − + log tan 89 𝑖𝑠
(a) 1
(b) 0
(c)
(d) log 2
48. if cot ∝= 1, sec 𝛽 = (−5)/3 𝑤ℎ𝑒𝑟𝑒 𝜋 <∝< 3𝜋/2 𝑎𝑛𝑑 𝜋/2 < 𝛽 < 𝜋,
𝑡ℎ𝑒𝑛 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 tan(∝ +𝛽)𝑎𝑛𝑑 𝑞𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝑖𝑛 𝑤ℎ𝑖𝑐ℎ (∝ +𝛽)𝑙𝑖𝑒𝑠 𝑟𝑒𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑦 𝑎𝑟𝑒
(a) and ivth quadrant
(b) 7 and ist quadrant
(c) -7 and ivth quadrant
(d) and ist quadrant
49. If sin (B + C – A), sin(C + A – B), sin(A + B – C) are in A.P, then cot A, cot B, cot C are in
(a) G.P
(b) HP
(c) AP
(d) N.O.T.
50.
51.
52.
5
53.
54.
55. if sin 𝜃 + sin 𝜃 + sin 𝜃 = 3 then cos 𝜃 + cos 𝜃 + cos 𝜃 =
(a) 3
(b) 2
(c) 1
(d) 0
56. if A+B+C=1800 then cos 2 𝐴 + cos 2 𝐵 + cos 2 𝐶 =
(a) -1-4cos 𝐴 cos 𝐵 cos 𝐶
(b) 4cos 𝐴 cos B cos 𝐶
(c) 1+4cos 𝐴 cos 𝐵 cos 𝐶
(d) N.O.T
57. solve (2𝑠𝑖𝑛𝑥 − 𝑐𝑜𝑠𝑥)(1 + 𝑐𝑜𝑠𝑥) = 𝑠𝑖𝑛 𝑥 in [0,2𝜋]
(a)
(b)
(c) 𝜋
(d) all of these
58. if 𝑠𝑖𝑛𝜃, 𝑐𝑜𝑠𝜃, 𝑡𝑎𝑛𝜃 𝑎𝑟𝑒 in G.P then general solution for 𝜃 𝑖𝑠
(a) 2𝑛𝜋 ±
(b) 2𝑛𝜋 ±
(c) 𝑛𝜋 ±
(d) N.O.T
59. if 𝑠𝑖𝑛 ∝ +4𝑐𝑜𝑠 𝛽 + 2 = 4√2𝑠𝑖𝑛 ∝ 𝑐𝑜𝑠𝛽, ∝, 𝛽 ∈ [0, 𝜋] then cos(∝ +𝛽) − cos(∝ −𝛽) is equal to
(a) 0
(b) -1
(c) √2
(d) −√2
60. the value of 𝑐𝑜𝑠
, cos
(a)
(b)
61. value of 𝑐𝑜𝑠
(a)
√
𝑐𝑜𝑠
(b)
− − − − − −𝑐𝑜𝑠
+ 𝑠𝑖𝑛
√
𝑠𝑖𝑛
𝑠𝑖𝑛
is
(c)
(d)
(c)
(d) −
is
62. two poles standing on a horizontal ground are of heights 5 m and 10 m resp. the line joining their tops
marks an angle of 150 with the ground then the distance (n m) between the poles is
(a) 5(√3 + 1
(b) (2 + √3
(c) 10(√3 − 1
(d) 5(2 + √3
63. The number of integral values of ‘k’ for which the equation 3sinx + 4cosx = k + 1 has a solution, k  R is
______.
64. The minimum value of  for which the equation
4
1
 

  has at least one solution in  0,  is
sin x 1  sin x
 2
_____.
65.
6
66. The value of 3
sin 4 t  cos 4 t  1
is equal to ________.
sin 6 t  cos 6  1
67. Suppose A and B are two angles such that A, B  (0,  ) and satisfy sin A + sin B = 1 and cos A + cos B =
0. Then the value of 12 cos 2A + 4 cos 2B is ________.
(a) A - (p), B - (q), C - (r)
(b) A - (q), B - (r), C - (p)
(c) A - (r), B - (q), C - (p)
(d) A - (r), B - (P), C- (q)
68. Which of the following is not a correct statement?
(a) Every AB5 molecule does in fact have square pyramid structure
(b) Multiple bonds are always shorter than corresponding single bonds
(c) The electron-deficient molecules can act as Lewis acids
(d) Expanded octet molecules are also called superoctets.
69. In which of the following pairs, the two species are iso-structural
(a) SF4 and XeF4
(b) SO42- and NO3
(c) BF3 and NF3
(d) BrO3- and XeO3
70. The correct geometry and hybridization for XeF4
(a) Square planar, sp3d3
(b) Octahedral, sp3d2
(c) Trigonal bipyramidal, sp3d
(d) planar triangle, sp3d
71. BF3 is planar and electron deficient compound.Number of electrons around the
Central atom, respectively are:
72. The ionisation energy of sodium is 495 kJ/mol. The energy needed to convert atoms present in 2.3
mg of sodium into sodium ions would be in Joules
73. The number of molecules (s) or ion (s) from the following having non-planar structure is _________
𝑁𝑂 , 𝐻 𝑂 , 𝐵𝐹 , 𝑃𝐶𝐼 , 𝑋𝑒𝐹 , 𝑆𝐹 , 𝑋𝑒𝑂 𝑃𝐻 , 𝑆𝑂 , [𝐴𝐼(𝑂𝐻) ]
74. Number of electron deficient molecules among the following
𝑃𝐻 , 𝐵𝐻 , 𝐶𝐶𝐼 , 𝑁𝐻 , 𝐿𝑖𝐻 𝑎𝑛𝑑 𝐵𝐶𝐼 is
75. Amongst 𝑆𝐹 , 𝑋𝑒𝐹 , 𝐶𝐹 𝑎𝑛𝑑 𝐻 𝑂 the number of species with two lone pairs of electrons________.
7
8