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# Test: Limit (Competition Level) - 3

## 30 Questions MCQ Test Mathematics for JEE Mains | Test: Limit (Competition Level) - 3

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This mock test of Test: Limit (Competition Level) - 3 for JEE helps you for every JEE entrance exam. This contains 30 Multiple Choice Questions for JEE Test: Limit (Competition Level) - 3 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Limit (Competition Level) - 3 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this Test: Limit (Competition Level) - 3 exercise for a better result in the exam. You can find other Test: Limit (Competition Level) - 3 extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1
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QUESTION: 2
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QUESTION: 3
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limx→0(3sinx−sin3x)/(x3
=limx→0 [d/dx(3sinx−sin3x)][d/dx(x3)]
We have indeterminate form 0/0 L'Hospital's rule applies
=limx→0 (3cosx−3cos3x)/(3x2)
=limx→0 [d/dx(3cosx−3cos3x)]/[d/dx(3x2)]
We have indeterminate form 0/0 L'Hospital's rule applies
=limx→0 (−3sinx+9sin3x)/(6x)
=limx→0 d/dx(−3sinx+9sin3x)/[d/dx(6x)]
We have indeterminate form 0/0 L'Hospital's rule applies
=limx→0 (−3cosx+27cos3x)/(6)
=(−3+27)/6
= 4

QUESTION: 4

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QUESTION: 5

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QUESTION: 7

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QUESTION: 8

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QUESTION: 9

Let α and β be the roots of ax2 + bx + c = 0, then

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QUESTION: 10

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Put x = tanθ. Then x → 0 ⇒ θ → 0

QUESTION: 11

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QUESTION: 12

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QUESTION: 13

Let : R → R be a positive increasing function with

Solution:

As fis a positive increa sin g function, we have f (x) < f (2x)< f (3x)
Dividing by f
we have by squeez theorem or sandwich theorem,

QUESTION: 14

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QUESTION: 15

The values of constants a and b so that

Solution:

Since the lim it is '0', the deg ree of numeration is less than the deg ree of Deno min ator.
∴ Coefficient of x2 = 0, coefficient of x = 0

⇒ 1 - a = 0, a - b = 0

⇒ a = 1, b = -1.

QUESTION: 16

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QUESTION: 17

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QUESTION: 18

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QUESTION: 19

+.......n terms (a > 0,d > 0) =

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QUESTION: 21

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QUESTION: 22

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QUESTION: 23

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QUESTION: 24

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QUESTION: 25

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QUESTION: 26

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Requried limit =

QUESTION: 27

The value of

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[on putting x = 1/h as x → ∞, h → 0]

QUESTION: 28

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= 1/24

QUESTION: 29

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Given limit is

QUESTION: 30

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