1
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\alpha, \beta$$ be the roots of the equation $$x^{2}-\sqrt{2} x+2=0$$. Then $$\alpha^{14}+\beta^{14}$$ is equal to

A
$$-64$$
B
$$-64 \sqrt{2}$$
C
$$-128 \sqrt{2}$$
D
$$-128$$
2
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$(\alpha, \beta)$$ be the centroid of the triangle formed by the lines $$15 x-y=82,6 x-5 y=-4$$ and $$9 x+4 y=17$$. Then $$\alpha+2 \beta$$ and $$2 \alpha-\beta$$ are the roots of the equation :

A
$$x^{2}-7 x+12=0$$
B
$$x^{2}-13 x+42=0$$
C
$$x^{2}-14 x+48=0$$
D
$$x^{2}-10 x+25=0$$
3
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the system of equations

$$2 x+y-z=5$$

$$2 x-5 y+\lambda z=\mu$$

$$x+2 y-5 z=7$$

has infinitely many solutions, then $$(\lambda+\mu)^{2}+(\lambda-\mu)^{2}$$ is equal to

A
916
B
912
C
920
D
904
4
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the region $$\left\{(x, y): x^{2} \leq y \leq\left|x^{2}-4\right|, y \geq 1\right\}$$ is

A
$$\frac{4}{3}(4 \sqrt{2}+1)$$
B
$$\frac{3}{4}(4 \sqrt{2}+1)$$
C
$$\frac{4}{3}(4 \sqrt{2}-1)$$
D
$$\frac{3}{4}(4 \sqrt{2}-1)$$
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