1

JEE Advanced 2020 Paper 1 Offline

Numerical

+4

-0

In a triangle PQR, let a = QR, b = RP, and c = PQ. If |a| = 3, |b| = 4

and $${{a\,.(\,c - \,b)} \over {c\,.\,(a - \,b)}} = {{|a|} \over {|a| + |b|}}$$, then the value of |a $$ \times $$ b|

and $${{a\,.(\,c - \,b)} \over {c\,.\,(a - \,b)}} = {{|a|} \over {|a| + |b|}}$$, then the value of |a $$ \times $$ b|

^{2}is ......Your input ____

2

JEE Advanced 2020 Paper 1 Offline

Numerical

+4

-0

For a polynomial g(x) with real coefficients, let m

$$S = \{ {({x^2} - 1)^2}({a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3}):{a_0},{a_1},{a_2},{a_3} \in R\} $$;

For a polynomial f, let f' and f'' denote its first and second order derivatives, respectively. Then the minimum possible value of (m

_{g}denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by$$S = \{ {({x^2} - 1)^2}({a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3}):{a_0},{a_1},{a_2},{a_3} \in R\} $$;

For a polynomial f, let f' and f'' denote its first and second order derivatives, respectively. Then the minimum possible value of (m

_{f'}+ m_{f''}), where f $$ \in $$ S, is ..............Your input ____

3

JEE Advanced 2020 Paper 1 Offline

Numerical

+4

-0

let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit

$$\mathop {\lim }\limits_{x \to {0^ + }} {{{{(1 - x)}^{1/x}} - {e^{ - 1}}} \over {{x^a}}}$$

is equal to a non-zero real number, is .............

$$\mathop {\lim }\limits_{x \to {0^ + }} {{{{(1 - x)}^{1/x}} - {e^{ - 1}}} \over {{x^a}}}$$

is equal to a non-zero real number, is .............

Your input ____

4

JEE Advanced 2020 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One
end of the plank is now lifted so that it gets tilted making an angle $$\theta $$ from the horizontal as shown in
the figure below. The maximum value of $$\theta $$ so that the football does not start rolling down the plank
satisfies (figure is schematic and not drawn to scale)

Paper analysis

Total Questions

Chemistry

18

Mathematics

18

Physics

18

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