1
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
Change Language
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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2
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
Change Language
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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3
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
+4
-1
Change Language
The sum of all integral values of k (k $$\ne$$ 0) for which the equation $${2 \over {x - 1}} - {1 \over {x - 2}} = {2 \over k}$$ in x has no real roots, is ____________.
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4
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
Change Language
The number of real roots of the equation e4x $$-$$ e3x $$-$$ 4e2x $$-$$ ex + 1 = 0 is equal to ______________.
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