1
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1

Let p and q be two real numbers such that p + q = 3 and p4 + q4 = 369. Then $${\left( {{1 \over p} + {1 \over q}} \right)^{ - 2}}$$ is equal to _________.

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2
JEE Main 2022 (Online) 26th June Morning Shift
Numerical
+4
-1

The sum of the cubes of all the roots of the equation

$${x^4} - 3{x^3} - 2{x^2} + 3x + 1 = 0$$ is _________.

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3
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
Let f(x) be a polynomial of degree 3 such that
$$f(k) = - {2 \over k}$$ for k = 2, 3, 4, 5. Then the value of 52 $$-$$ 10f(10) is equal to :
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4
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
Let $$\lambda$$ $$\ne$$ 0 be in R. If $$\alpha$$ and $$\beta$$ are the roots of the equation x2 $$-$$ x + 2$$\lambda$$ = 0, and $$\alpha$$ and $$\gamma$$ are the roots of equation 3x2 $$-$$ 10x + 27$$\lambda$$ = 0, then $${{\beta \gamma } \over \lambda }$$ is equal to ____________.
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