1
JEE Main 2021 (Online) 16th March Morning Shift
Numerical +4 -1
Let f : R $$ \to $$ R be a continuous function such that f(x) + f(x + 1) = 2, for all x$$\in$$R.
If $${I_1} = \int\limits_0^8 {f(x)dx} $$ and $${I_2} = \int\limits_{ - 1}^3 {f(x)dx} $$, then the value of I1 + 2I2 is equal to ____________.
If $${I_1} = \int\limits_0^8 {f(x)dx} $$ and $${I_2} = \int\limits_{ - 1}^3 {f(x)dx} $$, then the value of I1 + 2I2 is equal to ____________.
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2
JEE Main 2021 (Online) 16th March Morning Shift
Numerical +4 -1
If the normal to the curve y(x) = $$\int\limits_0^x {(2{t^2} - 15t + 10)dt} $$ at a point (a, b) is parallel to the line x + 3y = $$-$$5, a > 1, then the value of | a + 6b | is equal to ___________.
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3
JEE Main 2021 (Online) 26th February Evening Shift
Numerical +4 -1
Let the normals at all the points on a given curve pass through a fixed point (a, b). If the curve passes through (3, $$-$$3) and (4, $$-$$2$$\sqrt 2 $$), and given that a $$-$$ 2$$\sqrt 2 $$ b = 3,
then (a2 + b2 + ab) is equal to __________.
then (a2 + b2 + ab) is equal to __________.
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4
JEE Main 2021 (Online) 26th February Evening Shift
Numerical +4 -1
If $${I_{m,n}} = \int\limits_0^1 {{x^{m - 1}}{{(1 - x)}^{n - 1}}dx} $$, for m, $$n \ge 1$$, and
$$\int\limits_0^1 {{{{x^{m - 1}} + {x^{n - 1}}} \over {{{(1 + x)}^{m + 1}}}}} dx = \alpha {I_{m,n}}\alpha \in R$$, then $$\alpha$$ equals ___________.
$$\int\limits_0^1 {{{{x^{m - 1}} + {x^{n - 1}}} \over {{{(1 + x)}^{m + 1}}}}} dx = \alpha {I_{m,n}}\alpha \in R$$, then $$\alpha$$ equals ___________.
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Questions Asked from Definite Integrals and Applications of Integrals (Numerical)
Number in Brackets after Paper Indicates No. of Questions
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