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NDA Basics of Mathematics PYQs with Solutions

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

63 questionsMathematics2010–2026Answers + solutions

About Basics of Mathematics PYQs

Basics of Mathematics has 63 previous year questions in the Quantrex Academy NDA Mathematics bank. The 63 questions in this list come from NDA (63), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Basics of Mathematics PYQs with Solutions

About Basics of Mathematics PYQs

Questions by year (this list)

Basics of Mathematics questions with solutions

If 1- _ 10 2= _ 10 (5^x+4^x+3^x+2^x+1) , then what is a value of x ?

What is the sum of the binary numbers (101101101)_2 and (100011)_2 ?

For the following two (02) items: Let p = ∑_ j=1 ^ n _ 10 2^j and q = ∑_ j=1 ^ n _ 10 5^j . If p + q = 15 , then what is q - p equal to?

For the following two (02) items: Let p = ∑_ j=1 ^ n _ 10 2^j and q = ∑_ j=1 ^ n _ 10 5^j . If p + q = 66 , then which one of the following is correct?

If p^x = q^y = r^z , where x , y and z are in GP, then consider the following statements: I. p , q and r are in AP. II. p , q and r are in GP. Which of the statements given above

What is the number of solutions of _4(x-1)= _2(x-3) ?

For x ≥ y > 1 , let _x((x)/(y))+ _y((y)/(x))=k , then the value of k can never be equal to:

If _b a=p, _d c=2 p and _f e=3 p , then what is ( ace )^ (1)/(p) equal to?

What is the remainder when 2^ 120 is divided by 7 ?

If x a, a x and b x are in G.P, then what is x equal to?

If 1!+3!+5!+7!+…+199 ! is divided by 24 , what is the remainder?

How many real numbers satisfy the equation |x-4|+|x-7|=15 ?

Consider the following statements: 1. (25)!+1 is divisible by 26 2. (6)! +1 is divisible by 7 Which of the above statement is/are correct?

Let A=\ 7,8,9,10,11,12,13,14,15,16\ and let f: A arrow N be defined by f(x)= the highest prime factor of x . How many elements are there in the range of f ?

Consider the following statements : 1. (n!)/(3!) is divisible by 6 , where n > 3 2. (n!)/(3!)+3 is divisible by 7 , where n > 3 Which of the above statements is/are correct?

If x y=4225 where x, y are natural numbers, then what is the minimum value of x+y ?

If n=100 !, then what is the value of the following? (1)/( _2 n)+(1)/( _3 n)+(1)/( _4 n)+…+ 1 _ 100 n

If _ 10 2 _2 10+ _ 10 (10^x)=2 , then what is the value of x ?

If _ 10 2, _ 10 (2^x-1), _ 10 (2^x+3) are in AP, then what is x equal to?

What is the value of (1)/(10) _5 1024- _5 10+(1)/(5) _5 3125 ?

If x= _c(a b), y= _a(b c), z= _b(c a) , then which of the following is correct?

What is the minimum value of |x-1| , where x ∈ ℝ ?

If 1.5 ≤ x ≤ 4.5 , then which one of the following is correct?

If |x^2-3 x+2| > x^2-3 x+2 , then which one of the following is correct?

Let A ∪ B=\ x (x-a)(x-b) > 0 , where a < b\ . What are A and B equal to?

How many two-digit numbers are divisible by 4 ?

What is the solution of x ≤ 4, y^3 0 and x ≤-4, y ≤ 0 ?

If x^ 7^x > 7 where x > 0 , then which one of the following is correct?

The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What are the number of boys and girls respectively in the

If f(x)= _ 10 (1+x) , then what is 4 f(4)+5 f(1)- _ 10 2 equal to?

What is the value of _9 27+ _8 32 ?

If (0.2)^x=2 and _ 10 2=0.3010 , then what is the value of x to the nearest tenth?

The average age of a combined group of men and women is 25 years. If the average age of the group of men is 26 years and the of the group of women is 21 years, then the percentage

If n ∈ N , then 121^ n -25^ n +1900^ n -(-4)^ n is divisible by which one of the following?

If x+ _ 15 (1+3^x)=x _ 15 5+ _ 15 12 , where x is an integer, then what is x equal to?

What is the greatest integer among the following by which the number 5^5+7^5 is divisible?

If 0 < a < 1 , the value of _ 10 a is negative. This is justified by

What is the value of _7 _7 7 7 7 equal to?

If n=(2017)! , then what is 1 _2 n + 1 _3 n + 1 _4 n +… .+ 1 _ 2017 n equal to

Consider the following expressions: 1. x+x^2- 1 x 2. a x^2+b x+x-c+(d)/(c)-(e)/(x^2) 3. 3 x^2-5 x+a b 4. 2 x^2-ax+b^3 5. (1)/(x)-(2)/(x+5) Which of the above are rational

What is 1 _2 N + 1 _3 N + 1 _4 N +… .+ 1 _ 100 N equal to (N ≠ 1) ?

If x+ _ 10 (1+2^x)=x _ 10 5+ _ 10 6 then x is equal to

If |a| denotes the absolute value of an integer, then which of the following are correct? 1. |ab|=|a||b| 2. |a+b| ≤|a|+|b| 3. |a-b| ≥||a|-|b|| Select the correct answer using the

The sum of all real roots of the equation |x-3|^2+|x-3|-2=0 is

If A=\ x ∈ ℝ: x^2+6 x-7 0\ , then which of the following is/are correct? 1. A ∩ B=\ X ∈ ℝ:-2 < x < 1\ 2. A B=\ x ∈ ℝ :-7 < x < -2\ Select the correct answer using the code given

If _a(a b)=x , then what is _b(a b) equal to?

If y= _ 10 x+ _ x 10+ _ x x+ _ 10 10 then what is ( dy dx )_ x=10 equal to?

If x^ ((y)/(z)) · y^ (X z)^2 · z^ ((x)/(y)) =y^ 4 y for any x > 1, y > 1 and z > 1 , then which one of the following is correct?

If .A= x ∈ R: x^2+6 x-7 0\ and B= \ x ∈ R: x^2+9 x+14 0\ , then which of the following is/ are correct? 1. (A ∩ B)=(-2,1) 2. (A / B)=(-7,-2) Select the correct answer using the

If _8 m+ _8 (1)/(6)=(2)/(3) , then m is equal to

What is the positive square root of 7+4 3 ?

What is the degree of the equation (1)/(x-3)=(1)/(x+2)-(1)/(2) ?

What is the value of _y x^5 _x y^2 _z z^3 ?

What is _ 81 243 equal to?

What is the minimum value of |x| ?

If ( _3 x)( _x 2 x)( _ 2 x y)= _x x^2 , then what is y equal to?

What is the value of 2 _8 2-(1)/(3) _3 9 ?

The monthly family expenditure (in percentage) on different items are as follows : array c Food & Rent & Cloth & Transport & Education & Others 38 & 19 & 18 & - & 9 & 6 array If

What is the value of _2( _3 81) ?

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

What is the value of _ 10 ((9)/(8))- _ 10 ((27)/(32))+ _ 10 ((3)/(4))?

If _3[ _3[ _3 x]]= _3 3 , then what is the value of x ?

What is the value of _ α β (H) _ α β γ (H) ?

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