Global Challenge

Question 1

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

Question 2

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?

Accepted Answer

660 m/s

Answer

110 m/s

Answer

55 m/s

Answer

550 m/s

Question 3

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

Accepted Answer

4 : 1

Answer

1 : 2

Answer

1 : 4

Answer

4 : 3

Question 4

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

Accepted Answer

tan⁻¹(1/2√3)

Answer

tan⁻¹(1/4√3)

Answer

tan⁻¹(2/3)

Answer

tan⁻¹(3/4)

Question 5

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

Accepted Answer

The horizontal range of a projectile is proportional to the square root of the speed with which it is projected

Answer

The time of flight of a projectile is proportional to the speed with which it is projected

Answer

For a given speed of projection, the angle of projection for maximum range is 45°

Answer

At maximum height, the acceleration due to gravity is perpendicular to the velocity of the projectile

Question 6

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

Accepted Answer

-10x+10

Answer

-10x

Answer

-10x²+10x+10

Answer

10x-10

Question 7

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)

Accepted Answer

√(u²+2gh)

Answer

√(2gh)

Answer

2√gh

Answer

√(u²-2gh)

Question 8

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

Accepted Answer

-8 m/s²

Answer

Zero

Answer

8 m/s²

Answer

4 m/s²

Question 9

The outermost electronic configuration of the most electronegative element is

Accepted Answer

2s² 2p⁵

Answer

2s² 2p³

Answer

2s² 2p⁴

Answer

2s² 2p⁶

Question 10

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

Accepted Answer

III, I, II

Answer

I, II, III

Answer

II, III, I

Answer

II, I, III

Question 11

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

Accepted Answer

1 and 2

Answer

1 and 4

Answer

1 and 3

Answer

2 and 3

Question 12

The second ionization energy is maximum for

Accepted Answer

Beryllium

Answer

Boron

Answer

Magnesium

Answer

Aluminium

Question 13

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

Accepted Answer

Na

Answer

Mg

Answer

F

Answer

None of these

Question 14

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

Accepted Answer

Principal quantum number

Answer

Atomic number

Answer

Atomic mass

Answer

Azimuthal quantum number

Question 15

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

Accepted Answer

8 valence electrons in an atom

Answer

5 valence electrons in an atom

Answer

6 valence electrons in an atom

Answer

4 valence electrons in an atom

Question 16

The element with atomic number 56 belongs to which block?

Accepted Answer

s-Block

Answer

p-Block

Answer

d-Block

Answer

f-Block

Question 17

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

Accepted Answer

x² - 3x + 2 = 0

Answer

x² + 3x + 2 = 0

Answer

x² - 3x - 2 = 0

Answer

None of these

Question 18

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

Accepted Answer

0 < α < β

Answer

0 < |α| < β < α

Answer

0 < |α| < α < β

Question 19

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

Accepted Answer

5

Answer

15

Answer

40

Answer

25

Question 20

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

Accepted Answer

p ≤ -2

Answer

3 < p < 10

Answer

p ≥ 10

Answer

-2 < p < 3

Question 21

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

Accepted Answer

α < γ < β

Answer

(α + β)/2

Answer

β/α + 1

Answer

γ = α

Question 22

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

Accepted Answer

0

Answer

2

Answer

1

Answer

None of these

Question 23

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

Accepted Answer

both non-real

Answer

both positive

Answer

both negative

Answer

of opposite signs

Question 24

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

Accepted Answer

-1/c, 0

Answer

1/c + 1, -1/c - 1

Answer

-1/c - 1, -1/c

Answer

-1/c, 1

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