1
IIT-JEE 2005
MCQ (Single Correct Answer)
+2
-0.5
In an equilateral triangle, $$3$$ coins of radii $$1$$ unit each are kept so that they touch each other and also the sides of the triangle. Area of the triangle is IIT-JEE 2005 Mathematics - Properties of Triangle Question 7 English
A
$$4 + 2\sqrt 3 $$
B
$$6 + 4\sqrt 3 $$
C
$$12 + {{7\sqrt 3 } \over 4}$$
D
$$3 + {{7\sqrt 3 } \over 4}$$
2
IIT-JEE 2005
Subjective
+2
-0
If $$\left| {f\left( {{x_1}} \right) - f\left( {{x_2}} \right)} \right| < {\left( {{x_1} - {x_2}} \right)^2},$$ for all $${x_1},{x_2} \in R$$. Find the equation of tangent to the cuve $$y = f\left( x \right)$$ at the point $$(1, 2)$$.
3
IIT-JEE 2005
Subjective
+4
-0
If $$p(x)$$ be a polynomial of degree $$3$$ satisfying $$p(-1)=10, p(1)=-6$$ and $$p(x)$$ has maxima at $$x=-1$$ and $$p'(x)$$ has minima at $$x=1$$. Find the distance between the local maxima and local minima of the curve.
4
IIT-JEE 2005
Subjective
+2
-0
Evaluate $$\,\int\limits_0^\pi {{e^{\left| {\cos x} \right|}}} \left( {2\sin \left( {{1 \over 2}\cos x} \right) + 3\cos \left( {{1 \over 2}\cos x} \right)} \right)\sin x\,\,dx$$
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