Limits: JEE Main Mathematics Previous Year Questions

130 previous year questions from Limits. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. $Let f (x) = sin x, g (x) = cos x, h (x) = x^{2} then\dots$
2. $lim x \to 0 \frac{x ( e ^{\frac{( 1 + x ^{2} + x ^{4} - 1 )}{x}} - 1 )}{1 + x ^{2} + x ^{4} - 1}$
3. $Let\dots$
4. $lim_{x \to 1} \frac{tan ( x ^{2} - 1 )}{x - 1} is equal to$
5. $Let f be a differentiable function on R such that f (2) = 1, f^{’} (2) = 4 . Let\dots$
6. $Let denote the fractional part of and…$
7. $Let f : R \to R be a differentiable function satisfying f^{’} (3) + f^{’} (2) = 0 . Then\dots$
8. $For t > - 1, let α_{t} and β_{t} be the roots of the equation\dots$
9. $lim x \to 0 \frac{2 ^{2 x} - 2 ^{x + 1} + 2 - cos 2 x}{x ^{2}} =$
10. $lim x \to 0 (\frac{3 x ^{2} + 2}{7 x ^{2} + 2})^{\frac{1}{x ^{2}}} is equal to:$
11. $Let [\cdot] denote the greatest integer function and\dots$
12. $For each t \in R, let [t] be the greatest integer less than or equal to t . Then,\dots$
13. $lim_{x \to 0} \frac{a x ^{2} e ^{x} - b log _{e} ( 1 + x ) + cx e ^{- x}}{x ^{2} sin x} = 1 then\dots$
14. $If\dots$
15. $If lim x \to 0 \frac{ax - ( e ^{4 x} - 1 )}{ax ( e ^{4 x} - 1 )} exists and is equal to b, then the value of a - 2 b is$
16. $Given below are two statements: Statement I:\dots$
17. $lim_{x \to 0} \frac{2 sin x - sin 2 x}{x ^{3}} is equal to$
18. $The value of\dots$
19. $lim_{x \to 0} (\frac{3 x ^{2} + 2}{7 x ^{2} + 2})^{\frac{1}{x ^{2}}} is equal to$
20. $\dots$
21. $lim_{x \to \frac{π}{2}} (\frac{2 x - π}{cos x}) is equal to$
22. $Let f (x) = ⎩ ⎨ ⎧ (1 + a x)^{1/ x}, 1 + b, \frac{( x + 4 ) ^{1/2} - 2}{( x + c ) ^{1/3} - 2}, x < 0 x = 0 x > 0 be continuous at x = 0 . Then e^{a} b c is equal to:$
23. $Let f : (0, \infty) \to (0, \infty) be a differentiable function such that f (1) = e and\dots$
24. $If\dots$
25. $lim n \to \infty (1 + \frac{1 + \frac{1}{2} + \dots \dots + \frac{1}{n}}{n ^{2}})^{n} is equal to$

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Free questions PDF, 30 questions per set, with the Mere Teacher watermark and a QR code to the site. Answers and step-by-step solutions open after a free sign-up, with a download option too.

Set 1 · Q1-30
Set 2 · Q31-60
Set 3 · Q61-90
Set 4 · Q91-120
Set 5 · Q121-130

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Limits: JEE Main Mathematics Previous Year Questions

Download Limits PYQs as PDF

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