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1

IIT-JEE 1981

MCQ (Single Correct Answer)
Let $$a, b, c$$ be non-zero real numbers such that
$$\int\limits_0^1 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx = \int\limits_0^2 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx.} } $$
Then the quadratic equation $$a{x^2} + bx + c = 0$$ has
A
no root in $$(0, 2)$$
B
at least one root in $$(0, 2)$$
C
a double root in $$(0, 2)$$
D
two imaginary roots
2

IIT-JEE 1981

MCQ (Single Correct Answer)
The value of the definite integral $$\int\limits_0^1 {\left( {1 + {e^{ - {x^2}}}} \right)} \,\,dx$$
A
$$-1$$
B
$$2$$
C
$$1 + {e^{ - 1}}$$
D
none of these

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Class 12