New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Quadratic Equation and Inequalities question

2002 · Shift 0 · Q104

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

PYQ Library
JEE Main
Mathematics
Quadratic Equation and Inequalities
2002 · Shift 0 · Q104

Quadratic Equation and Inequalities question

2002 · Shift 0 · Q104

JEE MainMathematicsQuadratic Equation and InequalitiesMCQ+4 / −1

If

a,\,b,\,c

are distinct

+ ve

real numbers and

{a^2} + {b^2} + {c^2} = 1

then

ab + bc + ca

is

A
less than 1
B
equal to 1
C
greater than 1
D
any real no.

More from Quadratic Equation and Inequalities

Let $P_{n} = α^{n} + β^{n}, n \in N$ . If $P_{10} = 123, P_{9} = 76, P_{8} = 47$ and $P_{1} = 1$ , then the quadratic equation having roots $\frac{1}{α}$ …2025 · MCQ
If the set of all $a \in R - {1}$ , for which the roots of the equation $(1 - a) x^{2} + 2 (a - 3) x + 9 = 0$ are positive is $(- \infty, - α] \cup [β, γ)$ , then $2 α + β + γ$ is equal to .2025 · Numerical
Let $α$ and $β$ be the roots of $x^{2} + 3 x - 16 = 0$ , and $γ$ and $δ$ be the roots of $x^{2} + 3 x - 1 = 0$ . If $P_{n} = α^{n} + β^{n}$ and $Q_{n} = γ^{n} + \overset{o}{^}^{n}$ , then $\frac{P _{25} + 3 P _{24}}{2 P _{23}} + \frac{Q _{25} - Q _{23}}{Q _{24}}$ …2025 · MCQ
Let the equation $x (x + 2) (12 - k) = 2$ have equal roots. Then the distance of the point $(k, \frac{k}{2})$ from the line $3 x + 4 y + 5 = 0$ is2025 · MCQ
Consider the equation $x^{2} + 4 x - n = 0$ , where $n \in [20, 100]$ is a natural number. Then the number of all distinct values of $n$ , for which the given equation has integral roots, is equal to2025 · MCQ
Let the set of all values of $p \in R$ , for which both the roots of the equation $x^{2} - (p + 2) x + (2 p + 9) = 0$ are negative real numbers, be the interval $β - 2 α$ . Then $β - 2 α$ is equal to2025 · MCQ
The number of real roots of the equation $x ∣ x - 2∣ + 3∣ x - 3∣ + 1 = 0$ is :2025 · MCQ
The sum of the squares of the roots of $∣ x - 2 ∣^{2} + ∣ x - 2∣ - 2 = 0$ and the squares of the roots of $x^{2} - 2∣ x - 3∣ - 5 = 0$ , is2025 · MCQ