1
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Change Language
If 1, log10(4x $$-$$ 2) and log10$$\left( {{4^x} + {{18} \over 5}} \right)$$ are in arithmetic progression for a real number x, then the value of the determinant $$\left| {\matrix{ {2\left( {x - {1 \over 2}} \right)} & {x - 1} & {{x^2}} \cr 1 & 0 & x \cr x & 1 & 0 \cr } } \right|$$ is equal to :
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2
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Change Language
Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6 and the mean of the remaining n numbers is 3. A new set is constructed by adding 1 into each of first 2n numbers, and subtracting 1 from each of the remaining n numbers. If the variance of the new set is k, then 9k is equal to __________.
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3
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language
Let P be an arbitrary point having sum of the squares of the distances from the planes x + y + z = 0, lx $$-$$ nz = 0 and x $$-$$ 2y + z = 0, equal to 9. If the locus of the point P is x2 + y2 + z2 = 9, then the value of l $$-$$ n is equal to _________.
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4
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Change Language
Let f : [$$-$$1, 1] $$ \to $$ R be defined as f(x) = ax2 + bx + c for all x$$\in$$[$$-$$1, 1], where a, b, c$$\in$$R such that f($$-$$1) = 2, f'($$-$$1) = 1 for x$$\in$$($$-$$1, 1) the maximum value of f ''(x) is $${{1 \over 2}}$$. If f(x) $$ \le $$ $$\alpha$$, x$$\in$$[$$-$$1, 1], then the least value of $$\alpha$$ is equal to _________.
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