Global Challenge

Q1: A man can throw a stone to a maximum distance of 80 m. The maximum height to which it will rise, is

Q2: A particle starts from rest. Its acceleration (a) versus time (t) graph is shown in the figure. What will be the maximum speed of the particle?

• 110 m/s
• 55 m/s
• 550 m/s
• 660 m/s

Q3: A stone is projected at angle 30° to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point will be

• 1 : 2
• 1 : 4
• 4 : 1
• 4 : 3

Q4: The horizontal range of a projectile is 2√3 times its maximum height. What is the angle of projection?

• tan⁻¹(1/2√3)
• tan⁻¹(1/4√3)
• tan⁻¹(2/3)
• tan⁻¹(3/4)

Q5: Which one of the following statements is not true about the motion of a projectile?

• The time of flight of a projectile is proportional to the speed with which it is projected
• The horizontal range of a projectile is proportional to the square root of the speed with which it is projected
• For a given speed of projection, the angle of projection for maximum range is 45°
• At maximum height, the acceleration due to gravity is perpendicular to the velocity of the projectile

Q6: The velocity displacement graph of a particle moving along a straight line is shown in figure. The velocity as function of x (0 ≤ x ≤ 1) is

• -10x
• -10x+10
• -10x²+10x+10
• 10x-10

Q7: An aeroplane is moving with horizontal velocity u at height h. The velocity of a packet dropped from it on the earth's surface will be (g is acceleration due to gravity)

• √(u²+2gh)
• √(2gh)
• 2√gh
• √(u²-2gh)

Q8: If the velocity of a particle is given by v = (180 – 16x)^(1/2) m/s, then its acceleration will be

• Zero
• 8 m/s²
• -8 m/s²
• 4 m/s²

Q9: The outermost electronic configuration of the most electronegative element is

• 2s² 2p³
• 2s² 2p⁴
• 2s² 2p⁵
• 2s² 2p⁶

Q10: Identify the correct order in which the ionic radius of the following ions increases: F⁻, Na⁺, N³⁻

• III, I, II
• I, II, III
• II, III, I
• II, I, III

Q11: The elements with atomic number 119 and 120 are yet to be discovered. In which group would you place these elements when discovered?

• 1 and 2
• 1 and 4
• 1 and 3
• 2 and 3

Q12: The second ionization energy is maximum for

• Boron
• Beryllium
• Magnesium
• Aluminium

Q13: Among Na, Mg and F, which has IE₂/IE₁ < 1?

• Na
• Mg
• F
• None of these

Q14: In the modern periodic table, a period indicates the value of

• Atomic number
• Atomic mass
• Principal quantum number
• Azimuthal quantum number

Q15: A large difference between the fourth and fifth ionization energies indicates the presence of

• 5 valence electrons in an atom
• 6 valence electrons in an atom
• 4 valence electrons in an atom
• 8 valence electrons in an atom

Q16: The element with atomic number 56 belongs to which block?

• s-Block
• p-Block
• d-Block
• f-Block

Q17: If α, β are the roots of the equation x² - 2x + 3 = 0, then the equation whose roots are P = α³ - 2α² + 3α - 5 and Q = β³ - 2β² + 3β + 5 is

• x² + 3x + 2 = 0
• x² - 3x - 2 = 0
• x² - 3x + 2 = 0
• None of these

Q18: If α and β (α < β) are the roots of the equation x² + bx + c = 0, where 0 < c < b, then

• 0 < |α| < β < α
• 0 < α < β
• 0 < |α| < α < β
• 0 < α < β

Q19: Let α and β are roots of x² - 3x + 5 = 0, then the value of (α²β + αβ²)/(α + β) is

• 5
• 15
• 40
• 25

Q20: The values of p for which one root of the equation (x - 2)² + p(x - 2) + p² = 0 exceeds 2 and the other is lesser than 2 are given by

• 3 < p < 10
• p ≤ -2
• p ≥ 10
• -2 < p < 3

Q21: Let a, b, c be real numbers, a ≠ 0. If α is a root of a²x² + bx + c = 0. β is the root of a²x² – bx – c = 0 and 0 < α < β, then the equation a²x² + 2bx + 2c = 0 has a root γ that always satisfies

• (α + β)/2
• β/α + 1
• γ = α
• α < γ < β

Q22: If the equations ax² + bx + c = 0 and cx² + bx + a = 0, a ≠ c have a negative common root, then the value of a - b + c is

• 2
• 0
• 1
• None of these

Q23: If α and β are the roots of the equation x² + px + q = 0 and α⁴ and β⁴ are the roots of x² - rx + q = 0, the roots of x² – 4qx + 2q² – r = 0 are always

• both non-real
• both positive
• both negative
• of opposite signs

Q24: If α and β are the roots of the equation (x - 1)² + p(x - 1) + c = 0 then the values of (1/α + 1/β) and (α²/(α² + 2) + β²/(β² + 2)) are

• 1/c + 1, -1/c - 1
• -1/c - 1, -1/c
• -1/c, 1
• -1/c, 0