1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$z_1$$ and $$z_2$$ be two roots of the equation $$z^2+a z+b=0, a^2<4 b$$, then the origin, $$\mathrm{z}_1$$ and $$\mathrm{z}_2$$ form an equilateral triangle if

A
$$\mathrm{a}^2=3 \mathrm{b}^2$$
B
$$\mathrm{a^2=3 b}$$
C
$$\mathrm{b}^2=3 \mathrm{a}$$
D
$$\mathrm{b}^2=3 \mathrm{a}^2$$
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$\cos \theta+i \sin \theta, \theta \in \mathbb{R}$$, is a root of the equation

$$a_0 x^n+a_1 x^{n-1}+\ldots .+a_{n-1} x+a_n=0, a_0, a_1, \ldots . a_n \in \mathbb{R}, a_0 \neq 0,$$

then the value of $$a_1 \sin \theta+a_2 \sin 2 \theta+\ldots .+a_n \sin n \theta$$ is

A
2n
B
n
C
0
D
n + 1
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$\left(x^2 \log _x 27\right) \cdot \log _9 x=x+4$$ then the value of $$x$$ is

A
2
B
$$ -\frac{4}{3} $$
C
$$-$$2
D
$$ \frac{4}{3} $$
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
EXAM MAP