JEE Practice Test

Q1: Three projectiles A, B and C are thrown from the same point in the same plane. Their trajectories are shown in the figure. Which of the following statements is true?

• The time of flight is same for all the three projectiles.
• The launch speed is greatest for projectile C.
• The horizontal velocity component is greatest for projectile C.
• All of the above.

Q2: Assertion (A): Path of a projectile with respect to another projectile is straight line. Reason (R): Acceleration of a projectile with respect to another projectile is zero.

• Both, (A) and (R), are true and (R) is the correct explanation of the assertion
• Both, (A) and (R), are true but (R) is not the correct explanation of assertion
• If (A) is true but (R) is false
• If (A) is false but (R) is true

Q3: The x and y coordinates of a particle at any time t are given by x = 7t + 4t² and y = 5t, where x and y are in m and t in s. The acceleration of the particle at 5s is

• zero
• 8 m/s²
• 20 m/s²
• 40 m/s²

Q4: The equation of a projectile is y = √3x - gx²/2. Find the angle of projection.

• 30°
• 60°
• 45°
• None of these

Q5: A ball is thrown up at an angle with the horizontal. Then the total change of momentum by the instant it returns to ground is

• acceleration due to gravity × total time of flight
• weight of the ball × half the time of flight
• weight of the ball × total time of flight
• weight of the ball × horizontal range

Q6: In which of the following graphs, the total change in momentum is zero?

Q7: A block of mass 5 kg resting on a horizontal surface is connected by a cord, passing over a light frictionless pulley to a hanging block of mass 5 kg. The coefficient of kinetic friction between the block and the surface is 0.5. Tension in the cord is (g = 9.8 m/s²)

• 49N
• Zero
• 36.75N
• 12.75N

Q8: Block B is moving towards right with constant velocity v₀. Velocity of block A with respect to block B is - (Assume all pulleys and strings are ideal)

• v₀/2 left
• v₀/2 right
• 3/2 v₀ right
• 3/2 v₀ left

Q9: Figure shows a 5 kg ladder hanging from a string that is connected with a ceiling and is having a spring balance connected in between. A boy of mass 25 kg is climbing up the ladder at acceleration 1 m/s². Assuming the spring balance and the string to be massless and the spring to show a constant reading, the reading of the spring balance is: (Take g = 10 m/s²)

• 30 kg
• 32.5 kg
• 35 kg
• 37.5 kg

Q10: As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring balance will be

• Zero
• 2 kg
• 4 kg
• Between zero and 2 kg

Q11: A projectile is thrown horizontally from a height of 10 m with velocity of √2 m/s. The projectile will fall, from the foot of projection at distance (g = 10 m/s²)

• 1 m
• 2 m
• 3 m
• √2 m

Q12: A body of mass 10 kg is suspended by two massless strings making angles 45° and 30° with horizontal as shown in the figure then

• √2T₁ + 3T₂ = 0
• 2T₁ - √3T₂ = 0
• √2T₁ - 3T₂ = 0
• √2T₁ - √3T₂ = 0

Q13: A wooden block of mass m resting on a rough horizontal table (coefficient of friction = μ) is pulled by a force F as shown in figure. The acceleration of the block moving horizontally is:

• F cos θ / m
• µF cos θ / m
• F / m (cosθ + µ sinθ) - µg
• None

Q14: At a given instant, A is moving with velocity of 5 m/s upwards. What is velocity of B at that time?

• 15 m/s↓
• 15 m/s↑
• 5 m/s↓
• 5 m/s↑

Q15: A force of 100 N is applied on a block of mass 3 kg as shown in figure. The coefficient of friction between the surface and the block is 1/4. Then the friction force acting on the block is

• 15 N downwards
• 20 N downwards
• 25 N upwards
• 30 N upwards

Q16: A block placed on a rough inclined plane of inclination (θ = 30°) can just be pushed upwards by applying a force "F" as shown. If the angle of inclination of the inclined plane is increased to (θ = 60°), the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is

• (√3+1) / (√3-1)
• (2√3-1) / (√3+1)
• (√3-1) / (√3+1)
• None of these

Q17: In the figure shown, the coefficient of static friction between the block A of mass 20 kg and horizontal table is 0.2. What should be the minimum mass of hanging block just beyond which blocks start moving?

• 2 kg
• 3 kg
• 4 kg
• 5 kg

Q18: In the figure shown, the two projectiles are fired simultaneously. Find the minimum distance between them during their flight.

• 10 m
• 20 m
• 30 m
• None of these

Q19: Two trains are each 50 m long moving parallel towards each other at speeds 10 ms⁻¹ and 15 ms⁻¹ respectively, at what time will they pass each other?

• 8s
• 4s
• 2s
• 6s

Q20: An aeroplane is travelling horizontally at a height of 2000 m from the ground. The aeroplane, when at a point P, drops a bomb to hit a stationary target Q on the ground. In order that the bomb hits the target, what angle must the line PQ make with the vertical? (Take, g = 10 ms⁻²)

• 45°
• 30°
• 60°
• 90°

Q21: Three blocks of masses m₁, m₂ and m₃ are connected by massless string as shown kept on a frictionless table. They are pulled with a force T₃ = 40 N. If m₁ = 10 kg, m₂ = 6 kg and m₃ = 4 kg, the tension T₂ (in N) will be

Q22: A man walks in rain with a velocity of 5 km h⁻¹. The rain drops strike at him at an angle of 45° with the horizontal. Velocity of rain if it is falling vertically downward is _________ km/h.

Q23: A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water (in km/hr) is _________

Q24: A football player throws a ball with a velocity of 50 metre /sec at an angle 30 degrees from the horizontal. The ball remains in the air for _________ s. (g = 10 m/s²)

Q25: The velocity of block A (in m/s) is _________

Q26: What is the maximum value of the force F (in N) such that the block shown in the arrangement, does not move? [g = 10 m/s²]

Q27: A projectile fired at 30° to the ground is observed to be at same height at time 3s and 5s after projection, during its flight. The speed of projection of the projectile is _________ ms⁻¹ (Given g = 10 ms⁻²)

Q28: A body is projected with a velocity v₁ from the point A as shown in the figure. At the same time, another body is projected vertically upwards from B with velocity v₂. The point B lies vertically below the highest point. For both the bodies to collide, v₂/v₁ should be 1/x, then x = _________

Q29: An arrow is shot into the air. Its range is 200 metres and its time of flight is 5 s. If the value of g is assumed to be 10 ms⁻², then the horizontal component of the velocity of arrow is 200/x m/s. Find x _________

Q30: A block of mass m placed on an inclined plane of angle of inclination 45° slides down the plane with constant speed. The coefficient of kinetic friction between block and inclined plane is _________

Q31: The octet rule is observed in:

• PCl₅
• CO₂
• BCl₃
• SF₆

Q32: Element X is strongly electropositive and Y is strongly electronegative. Both are univalent. Then the formula of the compound formed would be:

• X⁺Y⁻
• X-Y
• XY'
• X → Y

Q33: Which among the following is an electron deficient compound?

• NH₃
• CO₂
• BH₃
• CH₄

Q34: Which of the following species is tetrahedral?

• SF₄
• ICl₄⁻
• XeF₄
• CH₄

Q35: The correct order of increasing bond angles in the following species is:

• CH₄ < NH₃ < H₂O
• SO₂ < SO₃ < CO₂
• CO₂ < SO₂ < SO₃
• CH₄ < H₂O < NH₃

Q36: Which of the following structures of a molecule is expected to have three bond pairs and one lone pair of electrons?

• Trigonal Planar
• Tetrahedral
• Octahedral
• Pyramidal

Q37: In NO₃⁻ ion, the number of bond pairs and lone pairs of electrons on N atom are:

• 2,2
• 3,1
• 1,3
• 4,0

Q38: A π-bond is formed by the overlap of:

• s-s orbital
• s-p orbital
• p-p orbital in head on manner
• p-p orbitals in sideways manner

Q39: The hybridization of S in SO₄²⁻ is same as:

• I in ICl₄⁻
• S in SO₃
• P in PO₄³⁻
• N in NO₃⁻

Q40: The correct geometry and hybridization for XeF₄ are:

• Trigonal planar, sp³d³
• Square planar, sp³d²
• Octahedral, sp³d²
• Trigonal bipyramidal, sp³d

Q41: Lewis structure of the elements M and Z are shown below. ·M· ·Z· Compound formed is:

• M₅Z₃
• M₂Z₃
• MZ
• MZ₃

Q42: Which of the following is the most polar?

• Cl-Cl
• N-F
• C-F
• O-F

Q43: Nitrogen does not form NF₅ because:

• Nitrogen is a member of V group.
• It does not contain d-orbitals.
• The bond energy of N ≡ N is very high.
• Inert pair effect exists in the molecules.

Q44: Which of the following statements are correct based on given Lewis dot structure? H H 8e 8e 8e 8e 8e 8e 8e

• :N:::N:
• H-C(::)C-H
• :O:C::O:
• H-O-C-O-H
• (i) and (iv) represents formation of triple bond.
• Only (iii) represents formation of double bond.
• Only (ii) represents formation of single bond.
• (ii) and (iii) both represents formation of single bond.

Q45: Among the following molecules: Those having same number of lone pairs on Xe are:

• XeO₃
• XeOF₄
• XeF₆
• (i) and (ii) only
• (i) and (iii) only
• (ii) and (iii) only
• (i), (ii) and (iii)

Q46: Which of the following do(es) not represent correct lewis symbol? :C: :Ö: :Ne: Be ·B· I II III IV V

• I, IV and V
• II, III and IV
• II only
• II and III

Q47: Shape of I₃⁻ ion is:

• Linear
• Angular
• Tetrahedral
• Trigonal planar

Q48: Which of the following species show deviation from the octet's rule?

• AlCl₃
• SF₆
• NO
• All of the above

Q49: Assertion: Dipole moment of NF₃ is less than that of NH₃. Reason: Polarity of N-F bond is less than that of N-H bond.

• Both assertion and reason are true and reason is the correct explanation of assertion.
• Both assertion and reason are true but reason is not the correct explanation of assertion.
• Assertion is true statement but reason is false.
• Both assertion and reason are false statements.

Q50: Which of the following would have a permanent dipole moment?

• BF₃
• SF₄
• SiF₄
• XeF₄

Q51: In the lewis dot structure for NO₂⁺, total number of valence electrons around nitrogen is _________

Q52: Based on VSEPR theory, the number of 90° F-Br-F angles in a molecule of BrF₅ is _________

Q53: The sum of number of lone pairs of electrons present on the central atoms of XeO₃, XeOF₄, XeF₂ and XeF₆, is _________

Q54: Number of molecules from the following which are exceptions to octet rule is _________ CO₂, NO₂, H₂SO₄, BF₃, CH₄, SiF₄, ClO₂, PCl₅, BeF₂, C₂H₆, CHCl₃, CBr₄

Q55: The total number of molecules with zero dipole moment among CH₄, BF₃, H₂O, HF, NH₃, CO₂ and SO₂ is _________

Q56: The number of total electrons shared between nitrogen atoms in N₂ is _________

Q57: Calculate the number of π-d bond(s) present in SO₄²⁻ _________

Q58: The sum of number of sigma and pi bonds formed between two carbon atoms in CaC₂ are: _________

Q59: In OF₂, the sum of the total number of bond pairs and lone pairs are: _________

Q60: The formal charge on the carbon atom in the carbonate ion is: _________

Q61: Let the sequence a₁,a₂, a₃...a₂n₋₁,a₂n form an A.P. Then the value of a₁²-a₂²+a₃²-.....+a₂n₋₁²-a₂n² is

• n / (2n-1) (a₁²-a₂n²)
• n / (2n-1) (a₁²-a₂n)
• n / (n+1) (a₁²+a₂n)
• n / (n-1) (a₁²+a₂n)

Q62: Let a, b, c be distinct complex numbers such that (a/(1-b)) = (b/(1-c)) = (c/(1-a)) = k. Then which of the following is not the value of k?

• -ω
• -ω²
• -1
• None of these

Q63: If z = ((√3+i)/2)⁵ + ((√3-i)/2)⁵ , then

• Re(z)=0
• Im(z)=0
• Re(z)>0,Im(z)>0
• Re(z)>0,Im(z)<0

Q64: The value of sum 3+5+6+9+10+12+15+18+20 + ... + 100 is equal to

• 2418
• 2481
• 2814
• 2184

Q65: The (m+n) th and (m-n) th terms of a G.P. are p and q respectively. Then the m th term of the G.P. is

• p^(m/2n) / q
• √pq
• √p/q
• None of these

Q66: If z = (√3+i)/2, then (z¹⁰¹+i¹⁰³)¹⁰⁵ is equal to

• z
• z²
• z³
• None of these

Q67: The domain of definition of function f(x)= log(x²-5x-24-x-2), is

• (-∞,-3]
• (-∞,-3]∪[8,∞)
• (-∞,-28/9)
• None of these

Q68: Let z = ((2√3+2i)⁸ / (1-i)⁶) + ((1+i)⁸ / (2√3-2i)⁶). Then argument of z is

• 5π/6
• π/6
• -π/6
• -5π/6

Q69: If |z₁|=|z₂|=...=|zₙ|=1, then the value of |z₁+z₂+...+zₙ| is

• 1
• |z₁|+|z₂|+......+|zₙ|
• |(1/z₁)+(1/z₂)+...+(1/zₙ)|
• None of these

Q70: If the pth, qth, rth terms of an A.P. are in G.P., then common ratio of the G.P. is

• (pr)^(1/2) / q
• p/q
• (q+r)/(p+q)
• (q-r)/(p-q)

Q71: The sum of the maximum and minimum values of the function f(x) = 1 / (1+(2cosx-4sinx)²) is

• 22/21
• 21/20
• 22/20
• 21/11

Q72: Let a=111...1 (55 digits), b=1+10+10²+... +10⁴ c=1+10⁵+10¹⁰+10¹⁵+...+10⁵⁰, then

• a=b+c
• a=bc
• b=ac
• c=ab

Q73: If the sum of the first 100 terms of an AP is -1 and the sum of even terms lying in first 100 terms is 1, then which of the following is not true?

• Common difference of the sequence is 3/50
• First term of the sequence is -149/50
• 100th term is 74/25
• None of these

Q74: The domain of f(x) = 1 / (√2x-1 * √(1-x²)) is

• [1/2, 1]
• [-1, ∞)
• [1, ∞)
• None of these

Q75: Let a₁,a₂,... and b₁,b₂,... be arithmetic progression such that a₁ = 25, b₁ = 75 and a₁₀₀+b₁₀₀=100, then the sum of first hundred term of the progression a₁+b₁, a₂+b₂, ... is equal to

• 1000
• 100000
• 10000
• 24000

Q76: The number of integers lying in the domain of the function f(x) = log₀.₅((5-2x)/x) is

• 3
• 2
• 1
• 0

Q77: If R = {(x, y): x, y ∈Z, x² + y² ≤4} is a relation on Z, then domain of R is

• {0,1,2}
• {0,-1,-2}
• {-2,-1, 0, 1, 2}
• none of these

Q78: If sec(α-2β), secα, sec(α+2β) are in arithmetical progression then cos²α = λ cos²β (β≠ nπ, n ∈ I) the value of λ is

• 1
• 2
• 3
• 1/2

Q79: If Sₙ denotes the sum of first n terms of an A.P. then (S₃n-Sₙ₋₁)/(S₂n-S₂n₋₁) is equal to

• 2n
• 2n + 1
• 2n-1
• None of these

Q80: Number of integers in the domain of the function, f(x)=√3-2ˣ-2¹⁻ˣ, is

• 1
• 4
• 2
• 3

Q81: Let x + (1/x) = 1 and a, b and c are distinct positive integers such that x²ᵃ + (1/x²ᵃ) + x²ᵇ + (1/x²ᵇ) + x²ᶜ + (1/x²ᶜ) = 0. Then the minimum value of (a+b+c) is _________

Q82: Let Aₙ be the sum of the first n terms of the geometric series 704 + 704/2 + 704/4 + 704/8 +... and Bₙ be the sum of the first n terms of the geometric series 1984 + 1984/2 + 1984/4 + 1984/8 +... If Aₙ = Bₙ, then the value of n is (where n∈ N ). _________

Q83: Let z=x+iy be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation z³z̄ + z̄³z = 350 is _________

Q84: It is given that 1, 1/(2ⁿ sinα) are in A.P. for some value of α. Let say for n=1, the α satisfying the above A.P. is α₁, for n=2, the value is α₂ and so on. If S = Σᵢ₌₁^∞ sinαᵢ, then the value of S is _________

Q85: The number of integral value(s) in the domain of f(x) = √(ln|ln|x|| + √(7|x|-x²-10)) is equal to _________

Q86: If the domain of the function f(x)= (√(x²-25)/(4-x²)) + log₁₀(x²+2x-15) is (-∞, α) ∪ [β,∞), then α² + β³ is equal to _________

Q87: If (√8+i)⁵⁰ = 3⁴⁹ (a+ib), then the value of a²+b² is _________

Q88: If z = (π/4) (1+i)⁴ ((1-√πi)/(√π+i) + (√π-i)/(1+√πi)), then (a / amp(z)) is equal to _________

Q89: If z₁ and z₂ are unimodular complex numbers that satisfy z₁² + z₂² = 4 then the value of ((z₁+z₁)²+(z₂+z₂)²)/2 is _________

Q90: The value of |2 + (1/z)|² + |2-z²| if |z| = 1 is _________