JEE Main Test 32

Result

JEE Main Test 32

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

For x > 0, which of the following function is not monotonic -

A
x + | x |

B
e^x

C
log x

D
sin x

Solution

For x>o,

x + | x | = 2x which is monotonic increasing function (derivative is always positive)

e^xis also a monotonic increasing function (derivative is always positive)

log x is also a monotonic increasing function (derivative is always positive)

sinx is increasing from 0 to pi/2 and then decreases till 3pi/2. It is periodic function and hence NOT monotonic.

For greater clarity, check the graph of all the functions.
Question 2
4 / -1

Function f(x) = log sin x is monotonic increasing when -

A
x ∈ (π/2, π)

B
x ∈ (–π/2, 0)

C
x ∈ (0, π)

D
x ∈ (0, π/2)

Solution

f(x) = log sinx is monotonic
When x ∈ (0, π/2)
Question 3
4 / -1

'M' effect is the resonance of -

A
πelectrons only

B
σelectrons only

C
πand σ both

D
(+) ve and (–) charge.

Solution

M effect is the delocalization of π electron which is called as resonance.
Question 4
4 / -1

Which of the following can stabilize the carbon free radicals -

A
+ I effect

B
+ M effect

C
Hyperconjugation

D
All of these

Solution

Free radical stabilize by electron donating
∴+ I, +m, Hyperconjugation
Question 5
4 / -1

Singlet carbene is

A
Electrophile

B
Nucleophile

C
Very strong base

D
Both electrophile and nucleophile

Solution

The structure of carbene is :CH₂. Singlet carbene acts as both electrophile and nucleophile. A carbene has empty p-orbital which is electron deficient while the an unshared pair of electrons on carbon acts as a nucleophile.