JEE Main Test 60

Result

JEE Main Test 60

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Weekly Quiz Competition

Question 1
4 / -1

A real valued function f(x) satisfies the functional equation f(x - y) = f(x)f(y) - f(a - x)f(a + y), where a is a given constant and f(0) = 1. f(2a - x) is equal to

A
f(x)

B
-f(x)

C
f(-x)

D
f(a) + f(a - x)

Solution

Given, f(x - y) = f(x)f(y) - f(a - x)f(a + y) ... (*)

Let x = 0 = y

f(0) = (f(0))² - (f(a))²

1 = 1 - (f(a))²

^⇒f(a) = 0

∴ f(2a - x) = f(a - (x - a))

By using (*), we get

f(2a - x) = f(a - (x - a)) = f(a)f(x - a) - f(a + x - a)f(0)

f(2a - x) = 0 - f(x)(1) = -f(x) (∵ f(a) = 0 and f(0) = 1)
Question 2
4 / -1

Directions For Questions

Directions: The following question has four choices, out of which ONLY ONE is correct.

Xe and F₂ heated in molar ratio 1 : 20 at 400^oC give a compound X. X reacts slowly with atmospheric moisture to give Y and HF. When X reacts with small quantity of water, we get a product Z. Z can also be obtained by the interaction of X with silica. Y reacts with X to give Z. But Y and Z react to give XeO₂F₂.

...view full instructions

The compound X is

A
XeF₂

B
XeF₄

C
XeF₆

D
XeF₈

Solution

Xe and F react in the ratio 1 : 20 to give XeF₆. It undergoes slow hydrolysis to give XeO₃.

XeF₆ + 6H₂O → XeO₃ + 6HF

So, (3) is correct.
Question 3
4 / -1

Photochemical smog can be suppressed by

A
nitrogen oxides

B
peroxyacetyl nitrate

C
radical traps

D
formaldehyde

Solution

Photochemical smog can be suppressed by certain compounds, which act as free radical traps and also by installation of efficient catalytic converters in automobiles.