Basic Mathematics — JEE Main PYQs

24 previous year questions on Basic Mathematics (Mathematics), newest first. Open any question for its complete step-by-step solution.

Let $A = {x : x^{2} - 10 \leq 6}$ and $B = {x : ∣ x - 2∣ > 1}$ .

Then
JEE Main 2026View solution →
The number of distinct real solutions of the equation $x ∣ x + 4∣ + 3∣ x + 2∣ + 10 = 0$ is
JEE Main 2026View solution →
The sum of all the real solutions of the equation $lo g_{(x + 3)} (6 x^{2} + 28 x + 30) = 5 - 2 lo g_{(6 x + 10)} (x^{2} + 6 x + 9)$ is equal to :
JEE Main 2026View solution →
The number of the real solutions of the equation :
$x ∣ x + 3∣ + ∣ x - 1∣ - 2 = 0$ is
JEE Main 2026View solution →
The product of all solutions of the equation $e^{5 (l o g_{e} x)^{2} + 3} = x^{8}, x > 0$ , is :
JEE Main 2025View solution →
The number of real solution(s) of the equation $x^{2} + 3 x + 2 = min {∣ x - 3∣, ∣ x + 2∣}$ is :
JEE Main 2025View solution →
The number of real roots of the equation $x ∣ x - 2∣ + 3∣ x - 3∣ + 1 = 0$ is :
JEE Main 2025View solution →
The number of distinct real roots of the equation $∣ x + 1∣∣ x + 3∣ - 4∣ x + 2∣ + 5 = 0$ , is ______.
JEE Main 2024View solution →
The number of real solutions of the equation $x (x^{2} + 3∣ x ∣ + 5∣ x - 1∣ + 6∣ x - 2∣) = 0$ is ______.
JEE Main 2024View solution →
The set of all $a \in R$ for which the equation $x ∣ x - 1∣ + ∣ x + 2∣ + a = 0$ has exactly one real root is :
JEE Main 2023View solution →
The number of real roots of the equation $x ∣ x ∣ - 5∣ x + 2∣ + 6 = 0$ , is
JEE Main 2023View solution →
The number of integral solutions $x$ of $lo g_{(x + \frac{7}{2})} (\frac{x - 7}{2 x - 3})^{2} \geq 0$ is
JEE Main 2023View solution →
Let $λ \in R$ and let the equation E be $∣ x ∣^{2} - 2∣ x ∣ + ∣ λ - 3∣ = 0$ . Then the largest element in the set $S = {x + λ : x$ is an integer solution of E $}$ is
JEE Main 2023View solution →
The domain of $f (x) = \frac{l o g _{(x + 1)} ( x - 2 )}{e ^{2 l o g_{e} x} - ( 2 x + 3 )}, x \in R$ is
JEE Main 2023View solution →
Let $A = {x \in R : ∣ x + 1∣ < 2}$ and
$B = {x \in R : ∣ x - 1∣ \geq 2}$ . Then which one of the following statements is NOT true ?
JEE Main 2022View solution →
The number of the real roots of the equation $(x + 1)^{2} + ∣ x - 5∣ = \frac{27}{4}$ is
JEE Main 2021View solution →
The number of solutions of the equation $lo g_{(x + 1)} (2 x^{2} + 7 x + 5) + lo g_{(2 x + 5)} (x + 1)^{2} - 4 = 0, x > 0$ , is
JEE Main 2021View solution →
The number of elements in the set ${n \in {1, 2, 3, \dots, 100} ∣ (11)^{n} > (10)^{n} + (9)^{n}}$ is ____
JEE Main 2021View solution →
The number of solution of the $lo g_{4} (x - 1) = lo g_{2} (x - 3)$ is ____
JEE Main 2021View solution →
The sum of the roots of the equation, $x + 1 - 2 lo g_{2} (3 + 2^{x}) + 2 lo g_{4} (10 - 2^{- x}) = 0$ , is:
JEE Main 2021View solution →
The number of elements in the set ${x \in R : (∣ x ∣ - 3) ∣ x + 4∣ = 6}$ is equal to :
JEE Main 2021View solution →
If $A = {x \in R : ∣ x ∣ < 2}$ and $B = {x \in R : ∣ x - 2∣ \geq 3}$ ; then:
JEE Main 2020View solution →
The sum of the solutions of the equation $∣ x - 2∣ + x (x - 4) + 2 = 0, (x > 0)$ is equal to:
JEE Main 2019View solution →
The number of real roots of the equation
$5 + ∣ 2^{x} - 1 ∣ = 2^{x} (2^{x} - 2) is$
JEE Main 2019View solution →