Home · JEE PYQs · Mathematics · Basics of Mathematics

JEE Basics of Mathematics PYQs with Solutions

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

90 questionsMathematics2002–2026Answers + solutions

About Basics of Mathematics PYQs

Basics of Mathematics has 90 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 90 questions in this list come from 99 Percentile Qs Bank for JEE Main (30), Most Important Selected Qs for JEE Advanced (30), JEE Main (24) and 1 other source, spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

JEE Basics of Mathematics PYQs with Solutions

About Basics of Mathematics PYQs

Questions by year (this list)

Basics of Mathematics questions with solutions

The sum of squares of all the real solutions of the equation _ (x+1) (2x^2+5x+3) = 4 - _ (2x+3) (x^2+2x+1) is equal to ________.

If the set of all solutions of |x^2 + x - 9| = |x| + |x^2 - 9| is [α, β] ∪ [γ, ∞) , then (α^2 + β^2 + γ^2) is equal to:

The number of the real solutions of the equation: x|x+3|+|x-1|-2=0 is

The product of all solutions of the equation e^ 5( _ e x)^2+3 =x^8, x 0 , is :

Let a=3 2 and b= 1 5^ 1 / 6 6 . If x, y ∈ ℝ are such that gathered 3 x+2 y= _a(18)^ (5)/(4) 2 x-y= _b( 1080 ) gathered and then 4 x+5 y is equal to . ________.

The number of integral solution x of _ (x + (7)/(2)) ((x - 7)/(2x - 3)) ^ 2 ≥ 0 is

Let a, b, c be the three distinct positive real numbers such that (2a) ^ _ e a = (bc) ^ _ e b and b ^ _ e 2 = a ^ _ e c Then 6a + 5bc is equal to ______.

If the solution of the equation _ cosx (cotx) + 4 _ sinx (tanx) = 1, x ∈ (0, (π)/(2)) is ^ - 1 ( α + β 2 ) , where α, β are integers, then α + β is equal to:

The product of all positive real values of x satisfying the equation x ^ (16 ( _ 5 x) ^ 3 - 68 _ 5 x) = 5 ^ - 16 is

Let S = \ x ∈ [- 6, 3] - \ - 2, 2\ : (|x + 3| - 1)/(|x| - 2) ≥ 0\ and T = \ x ∈ Z: x ^ 2 - 7|x| + 9 ≤ 0\ . Then the number of elements in S ∩ T is

Let A = \ x ∈ R: |x + 1| < 2\ and B = \ x ∈ R: |x - 1| ≥ 2\ . Then which one the following statements is NOT true?

The sum of the roots of the equation, x + 1 - 2 _ 2 (3 + 2 ^ x ) + 2 _ 4 (10 - 2 ^ - x ) = 0, is :

If A = x ∈ R: | x - 2 | > 1 , B = \ x ∈ R: x ^ 2 - 3 > 1\ , C = x ∈ R: | x - 4 | ⩾ 2 and Z is the set of all integers, then the number of subsets of the set ( A ∩ B ∩ C ) ^ c ∩ Z

The number of solutions of the equation _ ( x + 1 ) (2 x ^ 2 + 7x + 5) + _ ( 2x + 5 ) ( x + 1 ) ^ 2 - 4 = 0, x > 0, is

If for x ∈ (0, (π)/(2)), _ 10 sinx + _ 10 cosx = - 1 and _ 10 (sinx + cosx) = (1)/(2)( _ 10 n - 1), n > 0 , then the value of n is equal to :

The number of solutions of the equation _ 4 (x - 1) = _ 2 (x - 3) is ______.

If A = \ x ∈ R: |x| < 2\ and B = \ x ∈ R: |x - 2| ≥ 3\ ; then

The number of distinct solutions of the equation, _ (1)/(2) ⁡ |sin ⁡ x| =2 - _ (1)/(2) ⁡ |cos ⁡ x| in the interval [0, 2π], is ________

The value of ( ( _ 2 ⁡ 9) ^ 2 ) ^ 1 _ 2 ⁡ ( _ 2 ⁡ 9) × ( 7 ) ^ 1 _ 4 ⁡ 7 is_____.

Let S = \ x ∈ R: x ≥ 0 and 2| x - 3| + x ( x - 6) + 6 = 0\ . Then S :

If 3 ^ x = 4 ^ x - 1 , then x =

The least integral value α of x such that (x-5)/(x^2+5 x-14)>0 , satisfies :

Let (x_0, y_0) be the solution of the following equations (2 x)^ 2 =(3 y)^ 3 , 3^ x =2^ y , then x_0 is equal to

Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

Statement - 1: For every natural number n ≥ 2, 1 1 + 1 2 +…+ 1 n > n . Statement -2 : For every natural number n ≥ 2, n(n+1) < n+1 .

If a, b, c are distinct +v e real numbers and a^2+b^2+c^2=1 then a b+b c+c a is

The set \ x ∈ ℝ: 16(2^X)>16^ (-1)/(x) \ =

If _2 x+ _4 x+ _y x+ _ 16 x-(25)/(36) and x=2^k , then k is

The number of integral values of a for which the inequality 3 - |x - a| > x^ 2 is satisfied by atleast one negative x, must be equal to

If a=(x)/(y-z), b=(y)/(z-x) and c=(z)/(x-y) , where x, y and z are not all zero, then what is the value of a b+b c+c a= ?

If (x^ 2 + 5x + 5)x + 5 = 1 and then the number of integers satisfying this equation is

If n is a positive integer, then 2 · 4^ 2 n+1 +3^ 3 n+1 is divisible by

(1)/(2 · 3)+(1)/(4 · 5)+(1)/(6 · 7)+(1)/(8 · 9)+… is equal to

Number of integral values of x satisfying the inequality~ x^ 2 + 6x - 7 |x + 2||x + 3| < 0 is

If the greatest divisor of 30 · 5^ 2 n +4 · 2^ 3 n is p, ∀ n ∈ N and that of 2^ 2 n+1 -6 n-2 is q, ∀ n ∈ N , then p+q=

\ x ∈ ℝ: (14 x)/(x+1)-(9 x-30)/(x-4) < 0\ is equal to

The set of values of x for which the inequalities x^2-3 x-10 < 0, 10 x-x^2-16>0 hold simultaneously, is

Set of all the values of x satisfying the inequality x^ 2 - 7x + 6 > x + 2 is

aligned & 1+x _e a+(x^2)/(2 !)( _e a)^2 & +(x^3)/(3 !)( _e a)^3+…(a>0, x ∈ R) is equal to aligned

The smallest negative integer satisfying both the quadratic inequalities x^ 2 4 & is

Set of all real values of x satisfying the in equation _ 2 (x^ 2 - 5x + 4) _ 2 (x^ 2 + 1) > 1 is

If 12^ 4+2 x^2 =(24 3 )^ 3 x^2-2 , then x is equal to

If a, b, c, ≠ 0 and belong to the set to \ 0,1,2 , 3 … …, 9\ , then _ 10 ( a+10 b+10^2 c 10^ -4 a+10^ -3 b+10^ -2 c )is equal to

A three digit number n is such that the last two digits of it are equal and differ from the first. The number of such n 's is

If m, n are any two integers and~ m and n ~are related as m = n^ 2 - n ,~Then the expression~ m^ 2 - 2m is always divisible by

12- 68+48 2 is equal to :

Number of integers satisfying the inequality,& x^ 4 - 29x^ 2 + 100 ≤ 0 & is

Let n ∈ N which one of the following is true?

If 6x^ 2 - 5x - 3 x^ 2 - 2x + 6 ≤ 4, then the least and highest values of 4x^ 2 are

Number of integral solutions of inequality ((1)/(10)) ^ _ (x - 3) ⁡ (x^ 2 - 4x + 3) ≥ 1 are&

The solution set of the inequation x^2+6 x+5 >(8-x) is

If 2=a, 3=b, 7=c and 6^x=7^ x+4 then x is equal to

If α and β are the least positive integers such that for all n ∈ N, n^3+α n is divisible by 3 and n^3-β n is divisible by 6 , then α+β=

_4 2- _8 2+ _ 16 2-… is equal to

Solve _ 10 ( 2 ^ x +1) + x = _ 10 (6) + x _ 10 (5).

If α and β are the greatest divisors of n (n^ 2 - 1) and 2n (n^ 2 + 2) respectively for all~ n ∈ N , then αβ =

The solution of the equation |x-1|^ _3 x^2-2 _8 9 =(x-1)^7 is/are

Which of the following is equal to integer?

The solution(s) of the equation 2 _3(x-2)+ _3(x-4)^2=0 , is/are

Solution(s) of the equation x^ ( _ 10 x+7 4 ) =10^ _ 10 x+1 , is/are

Let x and y are positive real number such that _9 x+ _ 27 y=(7)/(2) and _ 27 x+ _9 y=(2)/(3) , then:

Let equation x^ _2 x-4 =32 has two real solutions x_1 and x_2 (x_1>x_2), then which of the following is correct?

Let α, β, γ are positive real numbers such that _γ(2 α)=(1)/(3), _γ(5 β)=(1)/(6) and _γ(α β)=(3)/(2) , then:

For the equation 3^x=4^ x^2 , the correct statement(s) is/are:

Let y_i(i=1 to n) are the solution satisfying the equation y^ _3( 3 y ) =y^ _3(3 y) -6 where y>0 . Then:

Which of the following is NOT in the solution set of the inequality |x^2-1|+|2 x^2-3| |2-x^2| ?

The value(s) of x satisfying 1- _9(x+1)^2=(1)/(2) _ 3 \ left((x+5)/(x+3)) is/are

Which of the following is correct?

Positive number x, y and z satisfy x y z=10^ 81 and ( _ 10 x)( _ 10 y z)+( _ 10 y)( _ 10 z)=468 . Find ( _ 10 x)^2+( _ 10 y)^2+( _ 10 z)^2 .

Let x - 1 x =3 and x^3+(1)/(x^3)=k , then characteristic of k with base 10 is:

Let x=(antilog_2 3) · _3 2, y= _2( _3( _2 512)) and z= _5 3 · _7 5 · _2 7 , then x y z is equal to:

If the inequality 1+ _5(x^2+1) ≥ _5(a x^2+4 x+a) holds ∀ x ∈ R , then the range of a is (p, q] , find (p+q) .

Let | _ 2 30-| _2 9+| _4 9-| _ 1 / 2 5||||=x . Then the smallest integer greater than or equal to x , is:

Find the number of integral values of x satisfying the equation: | _2^2 x-5 _2 x+6|=| _2^2 x-7 _2 x+12|-|2 _2 x-6|

If x_1 and x_2 are the solutions of the equation 5^ ( _5 x)^2 +x^ _5 x =1250 , then x_1 · x_2 is equal to:

Find the number of integral values of x satisfying the equation: | _2^2 x-5 _2 x+6|=| _2^2 x-7 _2 x+12|-|2 _2 x-6|