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JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x3) + x g(x3) is divisible by x2 + x + 1, then P(1) is equal to ___________.
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2
JEE Main 2021 (Online) 24th February Evening Slot
Numerical
+4
-1
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If a + $$\alpha$$ = 1, b + $$\beta$$ = 2 and $$af(x) + af\left( {{1 \over x}} \right) = bx + {\beta \over x},x \ne 0$$, then the value of the expression $${{f(x) + f\left( {{1 \over x}} \right)} \over {x + {1 \over x}}}$$ is __________.
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3
JEE Main 2020 (Online) 6th September Evening Slot
Numerical
+4
-0
Suppose that a function f : R $$ \to $$ R satisfies
f(x + y) = f(x)f(y) for all x, y $$ \in $$ R and f(1) = 3.
If $$\sum\limits_{i = 1}^n {f(i)} = 363$$ then n is equal to ________ .
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4
JEE Main 2020 (Online) 6th September Morning Slot
Numerical
+4
-0
Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is ______.
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