1
IIT-JEE 1983
Subjective
+2
-0
Evaluate : $$\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right)}^3}}}dx} $$
2
IIT-JEE 1983
Subjective
+4
-0
Find the coordinates of the point on the curve $$y = {x \over {1 + {x^2}}}$$
where the tangent to the curve has the greatest slope.
3
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
Given positive integers $$r > 1,\,n > 2$$ and that the coefficient of $$\left( {3r} \right)$$th and $$\left( {r + 2} \right)$$th terms in the binomial expansion of $${\left( {1 + x} \right)^{2n}}$$ are equal. Then
A
$$n = 2r$$
B
$$n = 2r + 1$$
C
$$n = 3r$$
D
none of these
4
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
The straight lines $$x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$$ form a triangle which is
A
isosceles
B
equilateral
C
right angled
D
none of these
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