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Limits — NDA Mathematics PYQs

80 previous year questions from Limits with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

80 questionsMathematicsSolutions on every page
1

What is _ x 1 x^ (n^2-1) -1 x^ (n+1) -1 equal to, where n>1 is a natural number ?

NDA 2026 Solution View → 2

What is _ x 0 10^ x -1 x equal to ?

NDA 2026 Solution View → 3

Consider the following for the two (02) items that follow: Let the function f(x) = x^2 + 9 . What is _ x 0 f(x) - 3 f(x)+7 - 4 equal to?

NDA 2025 Solution View → 4

For the following three (03) items: Consider the function f(x) = x|x| . What is _ x -1 f(x) equal to?

NDA 2025 Solution View → 5

For the following two (02) items: Let f(x) = cases 1 - 2x x^2 , & x 0 cases What is _ x 0^- f(x) equal to?

NDA 2025 Solution View → 6

For the following two (02) items: Let f(x) = cases 1 - 2x x^2 , & x 0 cases What is _ x 0^+ f(x) equal to?

NDA 2025 Solution View → 7

Consider the following for the two (02) items that follow: Let the function f(x) = [x] , where [ ] is the greatest integer function and g(x) = |x| . What is _ x 0 f(x) g(x) equal t

NDA 2025 Solution View → 8

Consider the following for the two (02) items that follow: Let the function f(x) = [x] , where [ ] is the greatest integer function and g(x) = |x| . What is _ x 0 f(x) g(x) equal t

NDA 2025 Solution View → 9

Consider the following for the two (02) items that follow: Let the function f(x) = x^2 - 1 . What is _ x 1 f f(x) equal to?

NDA 2025 Solution View → 10

What is ( - ) equal to? x 2

NDA 2024 Solution View → 11

Which one of the following is correct regarding _ x 3 |x-3| x-3 ?

NDA 2024 Solution View → 12

Let f(x)=|x|+1 and g(x)=[x]-1 , where [.] is the greatest integer function. Let h(x)= f(x) g(x) What is _ x 0- h(x)+ _ x 0+ h(x) equal to?

NDA 2024 Solution View → 13

Let f(x) a^ x-1 b^ x-1 and g(x)=x-1 . What is _ x 1 f(x)-1 g(x) equal to?

NDA 2023 Solution View → 14

Let f(x)=|x| and g(x)=[x]-1 , where [.] is the greatest integer function. Let h(x)= f(g(x)) g(f(x)) . What is _ x 0+ h(x) equal to?

NDA 2023 Solution View → 15

Let f(x) a^ x-1 b^ x-1 and g(x)=x-1 . What is _ x 1 f(x)^ 1 g(x) equal to?

NDA 2023 Solution View → 16

What is _ x 1 x^9-1 x^3-1 equal to?

NDA 2023 Solution View → 17

Let f(x)= array cc a x(x+1)+b, & x 1 x-1 & 1 x 2 array . What is _ x 0 f(x) equal to?

NDA 2023 Solution View → 18

What is _ x 5 5-x |x-5| equal to?

NDA 2023 Solution View → 19

Let f(x)=|x| and g(x)=[x]-1 , where [.] is the greatest integer function. Let h(x)= f(g(x)) g(f(x)) . What is _ x 0- h(x) equal to?

NDA 2023 Solution View → 20

What is _ x 0 x 1- ^4 x equal to?

NDA 2022 Solution View → 21

What is _ x x 2 4 x-2 x equal to?

NDA 2022 Solution View → 22

If f(x)= x 2+x+|x| x then what is _ x 0 f(x) equal to?

NDA 2022 Solution View → 23

What is _ h 0 ^2(x+h)- ^2 x h equal to?

NDA 2022 Solution View → 24

What is _ x 0 x^3( cosec x)^2 equal to?

NDA 2022 Solution View → 25

What is _ x 1 x^3-1 x -1 equal to?

NDA 2022 Solution View → 26

What is _ n a^n+b^n a^n-b^n where a b 1 , equal to?

NDA 2021 Solution View → 27

If f(x)= |x| |x| , x 0 , where [.] denotes the greatest integer function, then what is the right-hand limit of f(x) at x=1 ?

NDA 2021 Solution View → 28

What is _ x -1 x^3+x^2 x^2+3 x+2 equal to?

NDA 2021 Solution View → 29

If _ x a a^x-x^a x^a-a^a =-1 then what is the value of a ?

NDA 2021 Solution View → 30

If a differentiable function f(x) satisfies _ x -1 f(x)+1 x^2-1 =- 3 2 then what is _ x -1 f(x) equal to?

NDA 2021 Solution View → 31

What is _ x 0 3^x+3^ -x -2 x equal to?

NDA 2020 Solution View → 32

What is _ x 1 x+x^2+x^3-3 x-1 equal to ?

NDA 2020 Solution View → 33

What is _ x 0 x (1-x) x^2 equal to?

NDA 2020 Solution View → 34

If _ x 1 x^4-1 x-1 = _ x k x^3-k^3 x^2-k^2 , where k 0 , then what is the value of k ?

NDA 2020 Solution View → 35

_ x 1- ^3 4 x x^2 is equal to

NDA 2019 Solution View → 36

What is the value of _ x 0 x^ 3 x^ ?

NDA 2019 Solution View → 37

If the function f(x)= 2 x- ⁻¹ x 2 x+ ⁻¹ x is continuous at each point in its domain, then what is the value of f(0) ?

NDA 2018 Solution View → 38

What is _ h 0 2 x+3 h - 2 x 2 h equal to?

NDA 2018 Solution View → 39

What is _ x 0 x 2 x equal to?

NDA 2018 Solution View → 40

What is _ x 6 2 ^2 x+ x-1 2 ^2 x-3 x+1 to?

NDA 2018 Solution View → 41

What is _ 0 1- equal to?

NDA 2018 Solution View → 42

If _ x 2 x x =l and _ x x x =m , then which one of the following is correct?

NDA 2017 Solution View → 43

What is _ x 0 e^x-(1+x) x^2 equal to?

NDA 2017 Solution View → 44

Consider the following statements: 1. If _ x a f( x ) and _ x a g ( x ) both exist, then _ x a f( x ) g ( x ) exists. 2. If _ x a f(x) g(x) exists, then both _ x a f(x) and _ x a g

NDA 2017 Solution View → 45

Consider the function f(x)= a ^ [x]+x -1 [x]+x where [ ] denotes the greatest integer function. What is _ x 0⁺ f(x) equal to?

NDA 2016 Solution View → 46

What is _ x 0 e^ - 1 x^2 equal to?

NDA 2016 Solution View → 47

Paragraph: Let f(x)=[x] , where [.] is the greatest integer function and g(x)= x be two real valued functions over R . Question: Which one of the following statements is correct?

NDA 2016 Solution View → 48

If _ x 0 (x)=a^2 , where a 0 , then what is _ x 0 ( x a ) equal to?

NDA 2016 Solution View → 49

Consider the function f ( x )= a ^ [ x ]+ x -1 [ x ]+ x where [ ] denotes the greatest integer function. What is _ x 0⁻ f(x) equal to?

NDA 2016 Solution View → 50

If f(x)= (e^ x-2 -1 ) (x-1) , then _ x 2 f(x) is equal to

NDA 2015 Solution View → 51

Given that _ x ( 2+x^2 1+x -A x-B )=3 . What is the value of A?

NDA 2015 Solution View → 52

Given that _ x ( 2+x^2 1+x -A x-B )=3 . What is the value of B?

NDA 2015 Solution View → 53

If G(x)= 25-x^2 , then what is _ x 1 G(x)-G(1) x-1 equal to?

NDA 2015 Solution View → 54

Consider the function f(x)= array ccc x -2 x & If & x 2 3 & If & x= 2 array . Which is continuous at x= 2 , where is a constant. What is _ x 0 f(x) equal to?

NDA 2015 Solution View → 55

Consider the function f(x)= aligned x^2-5, & x 3 x+13 , & x 3 aligned . What is _ x 3 f(x) equal to?

NDA 2014 Solution View → 56

What is _ x 0 ₅(1+x) x equal to?

NDA 2014 Solution View → 57

What is _ x 0 5^x-1 x equal to?

NDA 2014 Solution View → 58

What is _ x 0 (1+x)^n-1 x equal to?

NDA 2014 Solution View → 59

Paragraph : Consider the function f(x)= 1- x ( -2 x)^2 , where x 2 and f ( 2 )= . Question : What is _ x 2 f(x) equal to?

NDA 2014 Solution View → 60

Paragraph : Consider the function f(x)= 1- x ( -2 x)^2 , where x 2 and f ( 2 )= . Question : What is the value of if the function is continuous at x= 2 ?

NDA 2014 Solution View → 61

What is _ x 0 x 1- x equal to?

NDA 2014 Solution View → 62

If f(9)=9 and f^ (9)=4 , then what is _ x 9 f(x) -3 x -3 equal to?

NDA 2014 Solution View → 63

What is _ x 0 x -x equal to?

NDA 2013 Solution View → 64

What is _ x 0 1- x x equal to?

NDA 2013 Solution View → 65

Consider the following statements : 1. _ x 0 1 x does not exist. 2. _ x 0 1 x exists. Which of the above statements is/are correct?

NDA 2013 Solution View → 66

What is _ x 0 2 x+4 x 2 x+ 4 x equal to?

NDA 2013 Solution View → 67

What is _ x 0 x- x x equal to?

NDA 2013 Solution View → 68

What is _ x 2 2-x x^3-8 equal to?

NDA 2013 Solution View → 69

What is _ x 0 1- 1+x x equal to?

NDA 2013 Solution View → 70

What is _ x 0 2(1- x) x^2 equal to?

NDA 2012 Solution View → 71

Consider the following: 1. _ x 0 1 x exists. 2. _ x 0 e^ 1 x does not exist. Which of the above is/are correct?

NDA 2012 Solution View → 72

What is _ x 0 1+x -1 x equal to?

NDA 2012 Solution View → 73

What is _ x 2 x-2 x^2-4 equal to?

NDA 2012 Solution View → 74

What is _ x -2 ( x+2 x^3+8 ) equal to?

NDA 2012 Solution View → 75

What is _ x 0 x^2 ( 1 x ) equal to?

NDA 2012 Solution View → 76

What is _ x ( a^2 x^2+a x+1 - a^2 x^2+1 ) equal to?

NDA 2011 Solution View → 77

What is the value of _ x 1 (x-1)^2 (x-1) ?

NDA 2010 Solution View → 78

What is value of _ x 0 (a x)- (b x) x^2

NDA 2010 Solution View → 79

What is the value of _ x ( x+6 x+1 )^ x+4 ?

NDA 2010 Solution View → 80

What is _ x 0 a^x-b^x x equal to?

NDA 2010 Solution View →
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