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NDA Limits PYQs with Solutions

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

80 questionsMathematics2010–2026Answers + solutions

About Limits PYQs

Limits has 80 previous year questions in the Quantrex Academy NDA Mathematics bank. The 80 questions in this list come from NDA (80), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Limits PYQs with Solutions

About Limits PYQs

Questions by year (this list)

Limits questions with solutions

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

What is _ x→0 10^ x -1 x equal to ?

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?

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

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?

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?

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)\

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))

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?

What is ( θ- θ) equal to? x arrow (π)/(2)

Which one of the following is correct regarding _ x arrow 3 (|x-3|)/(x-3) ?

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 arrow 0- h(x)+ _ x arrow 0+ h(x) equal to?

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

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 arrow 0+ h(x) equal to?

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

What is _ x arrow 1 (x^9-1)/(x^3-1) equal to?

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

What is _ x arrow 5 (5-x)/(|x-5|) equal to?

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 arrow 0- h(x) equal to?

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

What is _ x arrow (x)/(2) (4 x-2 π)/( x) equal to?

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

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

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

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

What is _ n arrow ∞ (a^n+b^n)/(a^n-b^n) where a > b > 1 , equal to?

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 ?

What is _ x arrow-1 (x^3+x^2)/(x^2+3 x+2) equal to?

If _ x arrow a (a^x-x^a)/(x^a-a^a)=-1 then what is the value of a ?

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

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

What is _ x arrow 1 (x+x^2+x^3-3)/(x-1) equal to ?

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

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

_ x arrow ∞ (1- ^3 4 x)/(x^2) is equal to

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

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) ?

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

What is _ x arrow 0 ( x)/( 2 x) equal to?

What is _ x arrow (π)/(6) (2 ^2 x+ x-1)/(2 ^2 x-3 x+1) to?

What is _ θ arrow 0 1- θ θ equal to?

If _ x arrow (π)/(2) ( x)/(x)=l and _ x arrow ∞ ( x)/(x)=m , then which one of the following is correct?

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

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

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

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

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?

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

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

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

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

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

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

Consider the function f(x)=\ array ccc (α x)/(π-2 x) & If & x ≠ (π)/(2) 3 & If & x=(π)/(2) array . Which is continuous at x=(π)/(2) , where α is a constant. What is _ x arrow 0

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

What is _ x arrow 0 ( _5(1+x))/(x) equal to?

What is _ x arrow 0 (5^x-1)/(x) equal to?

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

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

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

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

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

What is _ x arrow 0 ( x)/(π-x) equal to?

What is _ x arrow 0 (1- x)/(x) equal to?

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

What is _ x arrow 0 ( 2 x+4 x)/(2 x+ 4 x) equal to?

What is _ x arrow 0 ( x- x)/(x) equal to?

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

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

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

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

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

What is _ x arrow 2 (x-2)/(x^2-4) equal to?

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

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

What is _ x arrow ∞ ( a^2 x²+a x+1 - a^2 x²+1 ) equal to?