New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Quadratic Equation and Inequalities question

2024 · 1 Feb · Shift 1 · Q39

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Quadratic Equation and Inequalities
2024 · 1 Feb · Shift 1 · Q39

Quadratic Equation and Inequalities question

2024 · 1 Feb · Shift 1 · Q39

JEE MainMathematicsQuadratic Equation and InequalitiesMCQ+4 / −1

Let

\mathbf{S}=\left\{x \in \mathbf{R}:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}

. Then the number of elements in

\mathrm{S}

is :

A
4
B
0
C
2
D
1

More from Quadratic Equation and Inequalities

Let $α$ and $β$ be the roots of the equation $p x^{2} + q x - r = 0$ , where $p e q 0$ . If $p, q$ and $r$ be the consecutive terms of a non constant G.P. and $\frac{1}{α} + \frac{1}{β} = \frac{3}{4}$ , then the value of $(α - β)^{2}$ …2024 · MCQ
If 2 and 6 are the roots of the equation $a x^{2} + b x + 1 = 0$ , then the quadratic equation, whose roots are $\frac{1}{2 a + b}$ and $\frac{1}{6 a + b}$ , is :2024 · MCQ
The number of distinct real roots of the equation $∣ x ∣∣ x + 2∣ - 5∣ x + 1∣ - 1 = 0$ is .2024 · Numerical
The number of real solutions of the equation $x ∣ x + 5∣ + 2∣ x + 7∣ - 2 = 0$ is .2024 · Numerical
Let $α, β$ be the distinct roots of the equation $x^{2} - (t^{2} - 5 t + 6) x + 1 = 0, t \in R$ and $a_{n} = α^{n} + β^{n}$ . Then the minimum value of $\frac{a _{2023} + a _{2025}}{a _{2024}}$ is2024 · MCQ
Let $x_{1}, x_{2}, x_{3}, x_{4}$ be the solution of the equation $4 x^{4} + 8 x^{3} - 17 x^{2} - 12 x + 9 = 0$ and $(4 + x_{1}^{2}) (4 + x_{2}^{2}) (4 + x_{3}^{2}) (4 + x_{4}^{2}) = \frac{125}{16} m$ . Then the value of $m$ is …2024 · Numerical
Let $α, β$ be roots of $x^{2} + 2 x - 8 = 0$ . If $U_{n} = α^{n} + β^{n}$ , then $\frac{U _{10} + 2 U _{9}}{2 U _{8}}$ is equal to .2024 · Numerical
The sum of all the solutions of the equation $(8)^{2 x} - 16 \cdot (8)^{x} + 48 = 0$ is :2024 · MCQ