1

JEE Main 2021 (Online) 20th July Morning Shift

Numerical +4 -1

Let T be the tangent to the ellipse E : x

^{2}+ 4y^{2}= 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = $$\sqrt 5 $$ is $$\alpha$$$$\sqrt 5 $$ + $$\beta$$ + $$\gamma$$ cos^{$$-$$1}$$\left( {{1 \over {\sqrt 5 }}} \right)$$, then |$$\alpha$$ + $$\beta$$ + $$\gamma$$| is equal to ______________.Your input ____

2

JEE Main 2021 (Online) 18th March Evening Shift

Numerical +4 -1

Let P(x) be a real polynomial of degree 3 which vanishes at x = $$-$$3. Let P(x) have local minima at x = 1, local maxima at x = $$-$$1 and $$\int\limits_{ - 1}^1 {P(x)dx} $$ = 18, then the sum of all the coefficients of the polynomial P(x) is equal to _________.

Your input ____

3

JEE Main 2021 (Online) 18th March Morning Shift

Numerical +4 -1

Let f(x) and g(x) be two functions satisfying f(x

^{2}) + g(4 $$-$$ x) = 4x^{3}and g(4 $$-$$ x) + g(x) = 0, then the value of $$\int\limits_{ - 4}^4 {f{{(x)}^2}dx} $$ isYour input ____

4

JEE Main 2021 (Online) 17th March Evening Shift

Numerical +4 -1

Let $${I_n} = \int_1^e {{x^{19}}{{(\log |x|)}^n}} dx$$, where n$$\in$$N. If (20)I

_{10}= $$\alpha$$I_{9}+ $$\beta$$I_{8}, for natural numbers $$\alpha$$ and $$\beta$$, then $$\alpha$$ $$-$$ $$\beta$$ equals to ___________.Your input ____

Questions Asked from Definite Integrals and Applications of Integrals (Numerical)

Number in Brackets after Paper Indicates No. of Questions

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