1
WB JEE 2024
+1
-0.25

If $$\mathrm{P}(x)=\mathrm{a} x^2+\mathrm{b} x+\mathrm{c}$$ and $$\mathrm{Q}(x)=-\mathrm{a} x^2+\mathrm{d} x+\mathrm{c}$$ where $$\mathrm{ac} \neq 0$$, then $$\mathrm{P}(x) \cdot \mathrm{Q}(x)=0$$ has (a, b, c, d are real)

A
2 real roots
B
at least two real roots
C
4 real roots
D
no real root
2
WB JEE 2024
+1
-0.25

Let $$\mathrm{N}$$ be the number of quadratic equations with coefficients from $$\{0,1,2, \ldots, 9\}$$ such that 0 is a solution of each equation. Then the value of $$\mathrm{N}$$ is

A
29
B
39
C
90
D
81
3
WB JEE 2024
+1
-0.25

If $$a, b, c$$ are distinct odd natural numbers, then the number of rational roots of the equation $$a x^2+b x+c=0$$

A
must be 0
B
must be 1
C
must be 2
D
cannot be determined from the given data
4
WB JEE 2023
+1
-0.25

If one root of $${x^2} + px - {q^2} = 0,p$$ and $$q$$ are real, be less than 2 and other be greater than 2, then

A
$$4 + 2p + {q^2} > 0$$
B
$$4 + 2p + {q^2} < 0$$
C
$$4 + 2p - {q^2} > 0$$
D
$$4 + 2p - {q^2} < 0$$
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