Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · JEE Main & Advanced · Mathematics · Basics of Mathematics

Basics of Mathematics — JEE Main & Advanced Mathematics PYQs

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

90 questionsMathematicsSolutions on every page
1

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 ________.

JEE Main 2026 Solution View → 2

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

JEE Main 2026 Solution View → 3

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

JEE Main 2026 Solution View → 4

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

JEE Main 2025 Solution View → 5

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 . ________.

JEE Advanced 2024 Solution View → 6

The number of integral solution x of log x + 7 2 x - 7 2 x - 3 2 ≥ 0 is

JEE Main 2023 Solution View → 7

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

JEE Main 2023 Solution View → 8

If the solution of the equation log cos x cot x + 4 log sin x tan x = 1 , x ∈ 0 , π 2 is sin - 1 α + β 2 , where α , β are integers, then α + &#

JEE Main 2023 Solution View → 9

The product of all positive real values of x satisfying the equation x 16 log 5 x 3 - 68 log 5 x = 5 - 16 is

JEE Advanced 2022 Solution View → 10

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

JEE Main 2022 Solution View → 11

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

JEE Main 2022 Solution View → 12

The sum of the roots of the equation, x + 1 - 2 log 2 3 + 2 x + 2 log 4 10 - 2 - x = 0 , is :

JEE Main 2021 Solution View → 13

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

JEE Main 2021 Solution View → 14

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

JEE Main 2021 Solution View → 15

If for x ∈ 0 , π 2 , log 10 sin x + log 10 cos x = - 1 and log 10 sin x + cos x = 1 2 log 10 n - 1 , n > 0 , then the value of n is equal to :

JEE Main 2021 Solution View → 16

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

JEE Main 2021 Solution View → 17

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

JEE Main 2020 Solution View → 18

The number of distinct solutions of the equation, log 1 2 ⁡ sin ⁡ x = 2 - log 1 2 ⁡ cos ⁡ x in the interval 0 , 2 π , is ________

JEE Main 2020 Solution View → 19

The value of log 2 ⁡ 9 2 1 log 2 ⁡ log 2 ⁡ 9 × 7 1 log 4 ⁡ 7 is_____.

JEE Advanced 2018 Solution View → 20

Let S = x ∈ R : x ≥ 0 & 2 x - 3 + x x - 6 + 6 = 0 . Then S :

JEE Main 2018 Solution View → 21

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

JEE Advanced 2013 Solution View → 22

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

JEE Main 2013 Solution View → 23

Let (x₀, y₀ ) be the solution of the following equations (2 x)^ 2 =(3 y)^ 3 , 3^ x =2^ y , then x₀ is equal to

JEE Advanced 2011 Solution View → 24

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

JEE Advanced 2008 Solution View → 25

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 .

JEE Main 2008 Solution View → 26

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

JEE Main 2002 Solution View → 27

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

99 Percentile Qs Bank for JEE Main Solution View → 28

If ₂ x+ ₄ x+ _y x+ ₁₆ x- 25 36 and x=2^k , then k is

99 Percentile Qs Bank for JEE Main Solution View → 29

The number of integral values of a for which the inequality 3 - x - a &#62; x 2 is satisfied by atleast one negative x, must be equal to

99 Percentile Qs Bank for JEE Main Solution View → 30

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= ?

99 Percentile Qs Bank for JEE Main Solution View → 31

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

99 Percentile Qs Bank for JEE Main Solution View → 32

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

99 Percentile Qs Bank for JEE Main Solution View → 33

1 2 3 + 1 4 5 + 1 6 7 + 1 8 9 + is equal to

99 Percentile Qs Bank for JEE Main Solution View → 34

Number of integral values of x satisfying the inequality x 2 + 6 x - 7 x + 2 x + 3 &#60; 0 is

99 Percentile Qs Bank for JEE Main Solution View → 35

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=

99 Percentile Qs Bank for JEE Main Solution View → 36

x R: 14 x x+1 - 9 x-30 x-4 < 0 is equal to

99 Percentile Qs Bank for JEE Main Solution View → 37

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

99 Percentile Qs Bank for JEE Main Solution View → 38

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

99 Percentile Qs Bank for JEE Main Solution View → 39

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

99 Percentile Qs Bank for JEE Main Solution View → 40

The smallest negative integer satisfying both the quadratic inequalities x 2 &#60; 4 x + 77 and x 2 &#62; 4 is

99 Percentile Qs Bank for JEE Main Solution View → 41

Set of all real values of x satisfying the in equation log 2 x 2 &#8722; 5 x + 4 log 2 x 2 + 1 &#62; 1 is

99 Percentile Qs Bank for JEE Main Solution View → 42

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

99 Percentile Qs Bank for JEE Main Solution View → 43

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

99 Percentile Qs Bank for JEE Main Solution View → 44

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

99 Percentile Qs Bank for JEE Main Solution View → 45

If m , &#160; n are any two integers and m &#160; &#38; &#160; n are related as m = n 2 - n , Then the expression m 2 - 2 m is always divisible by

99 Percentile Qs Bank for JEE Main Solution View → 46

12- 68+48 2 is equal to :

99 Percentile Qs Bank for JEE Main Solution View → 47

Number of integers satisfying the inequality, x 4 - 29 x 2 + 100 &#8804; 0 is

99 Percentile Qs Bank for JEE Main Solution View → 48

Let n N which one of the following is true?

99 Percentile Qs Bank for JEE Main Solution View → 49

If 6 x 2 - 5 x - 3 x 2 - 2 x + 6 &#8804; 4 , then the least and highest values of 4 x 2 are

99 Percentile Qs Bank for JEE Main Solution View → 50

Number of integral solutions of inequality 1 10 log x - 3 &#8289; x 2 - 4 x + 3 &#8805; 1 are

99 Percentile Qs Bank for JEE Main Solution View → 51

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

99 Percentile Qs Bank for JEE Main Solution View → 52

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

99 Percentile Qs Bank for JEE Main Solution View → 53

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

99 Percentile Qs Bank for JEE Main Solution View → 54

₄ 2- ₈ 2+ ₁₆ 2- is equal to

99 Percentile Qs Bank for JEE Main Solution View → 55

Solve log 10 2 x + 1 + x = log 10 6 + x log 10 5 .

99 Percentile Qs Bank for JEE Main Solution View → 56

If &#945; and &#946; are the greatest divisors of n n 2 - 1 and 2 n n 2 + 2 respectively for all n &#8712; N , then &#945; &#946; =

99 Percentile Qs Bank for JEE Main Solution View → 57

The solution of the equation |x-1|^ ₃ x^2-2 ₈ 9 =(x-1)^7 is/are

Most Important Selected Qs for JEE Advanced Solution View → 58

Which of the following is equal to integer?

Most Important Selected Qs for JEE Advanced Solution View → 59

The solution(s) of the equation 2 ₃(x-2)+ ₃(x-4)^2=0 , is/are

Most Important Selected Qs for JEE Advanced Solution View → 60

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

Most Important Selected Qs for JEE Advanced Solution View → 61

Let x and y are positive real number such that ₉ x+ ₂₇ y= 7 2 and ₂₇ x+ ₉ y= 2 3 , then:

Most Important Selected Qs for JEE Advanced Solution View → 62

Let equation x^ ₂ x-4 =32 has two real solutions x₁ and x₂ (x₁>x₂ ) , then which of the following is correct?

Most Important Selected Qs for JEE Advanced Solution View → 63

Let , , are positive real numbers such that _ (2 )= 1 3 , _ (5 )= 1 6 and _ ( )= 3 2 , then:

Most Important Selected Qs for JEE Advanced Solution View → 64

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

Most Important Selected Qs for JEE Advanced Solution View → 65

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:

Most Important Selected Qs for JEE Advanced Solution View → 66

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

Most Important Selected Qs for JEE Advanced Solution View → 67

The value(s) of x satisfying 1- ₉(x+1)^2= 1 2 _ 3 ( x+5 x+3 ) is/are

Most Important Selected Qs for JEE Advanced Solution View → 68

Which of the following is correct?

Most Important Selected Qs for JEE Advanced Solution View → 69

Positive number x, y and z satisfy x y z=10⁸¹ and ( ₁₀ x ) ( ₁₀ y z )+ ( ₁₀ y ) ( ₁₀ z )=468 . Find ( ₁₀ x )^2+ ( ₁₀ y )^2+ ( ₁₀ z )^2 .

Most Important Selected Qs for JEE Advanced Solution View → 70

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

Most Important Selected Qs for JEE Advanced Solution View → 71

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:

Most Important Selected Qs for JEE Advanced Solution View → 72

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) .

Most Important Selected Qs for JEE Advanced Solution View → 73

Let | _ 2 30- | ₂ 9+ | ₄ 9- | _ 1 / 2 5||||=x . Then the smallest integer greater than or equal to x , is:

Most Important Selected Qs for JEE Advanced Solution View → 74

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 |

Most Important Selected Qs for JEE Advanced Solution View → 75

If x₁ and x₂ are the solutions of the equation 5^ ( ₅ x )^2 +x^ ₅ x =1250 , then x₁ x₂ is equal to:

Most Important Selected Qs for JEE Advanced Solution View → 76

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 |

Most Important Selected Qs for JEE Advanced Solution View → 77

If 9^ 1+ x =3^ 1+ x +210 (where base of is 3 ) then integral value of x is:

Most Important Selected Qs for JEE Advanced Solution View → 78

Paragraph: The loganthmic function is defined as _a x = y ( a )^y= x where x 0 . a 0 and a 1 ₁₀ x is called common logarithm, while _e x is called natural logarithm where c is an i

Most Important Selected Qs for JEE Advanced Solution View → 79

Paragraph: Let a denotes number of digits in 2⁵⁰, b denotes number of zero's after decimal and before first significant digit in 3⁻⁵⁰ and c denotes number of natural numbers have c

Most Important Selected Qs for JEE Advanced Solution View → 80

Paragraph: Consider a= ₂ 3, b= ₃ 5 and c= ₅ 7 . Question: ₁₄ 63 equals:

Most Important Selected Qs for JEE Advanced Solution View → 81

Paragraph: Let a denotes number of digits in 2⁵⁰, b denotes number of zero's after decimal and before first significant digit in 3⁻⁵⁰ and c denotes number of natural numbers have c

Most Important Selected Qs for JEE Advanced Solution View → 82

Paragraph: The loganthmic function is defined as _a x = y ( a )^y= x where x 0 . a 0 and a 1 ₁₀ x is called common logarithm, while _e x is called natural logarithm where c is an i

Most Important Selected Qs for JEE Advanced Solution View → 83

Paragraph: Consider a= ₂ 3, b= ₃ 5 and c= ₅ 7 . Question: Which of the following is incorrect?

Most Important Selected Qs for JEE Advanced Solution View → 84

Paragraph: If a x b then 1 a 1 x 1 ~b provided a & ~b are of same sign but if a and b are of opposite sign then 1 x (- , 1 a ] [ 1 ~b ,- ) . On the basis of above information, answ

Most Important Selected Qs for JEE Advanced Solution View → 85

Paragraph: If a x b then 1 a 1 x 1 ~b provided a & ~b are of same sign but if a and b are of opposite sign then 1 x (- , 1 a ] [ 1 ~b ,- ) . On the basis of above information, answ

Most Important Selected Qs for JEE Advanced Solution View → 86

Paragraph: If a x b then 1 a 1 x 1 ~b provided a & ~b are of same sign but if a and b are of opposite sign then 1 x (- , 1 a ] [ 1 ~b ,- ) . On the basis of above information, answ

Most Important Selected Qs for JEE Advanced Solution View → 87

Find the number of real solutions of the equation _ x+1 (2x^2 + 7x + 5) + _ 2x+5 (x^2 + 2x + 1) = 4 .

JEE Main Solution View → 88

Let A = x R : |x - a| 0 and d > 0 . If A B = (1, 2] [6, 7) , then the value of a + 2b + 3c + 4d is

JEE Main Solution View → 89

If the solution of the equation _ x ( x) + 4 _ x ( x) = 1, x (0, 2 ) 4 is x = ⁻¹ ( + 2 ) , where , are integers, then + is equal to:

JEE Main Solution View → 90

Let A = x R : |x^2 - 5x + 5| < 1 and B = x R : x - 2 x - 4 0 . Then A B is equal to

JEE Main Solution View →
Practice all Basics of Mathematics questions in the app →