1
IIT-JEE 1989
Fill in the Blanks
+2
-0
The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle $${x^2} + {y^2} = 4\,\,at\,\,\left( {1,\sqrt 3 } \right)$$ is,..................
2
IIT-JEE 1989
Fill in the Blanks
+2
-0
If $$a,\,b,\,c,$$ are the numbers between 0 and 1 such that the ponts $${z_1} = a + i,{z_2} = 1 + bi$$ and $${z_3} = 0$$ form an equilateral triangle,
then a= .......and b=..........
3
IIT-JEE 1989
MCQ (More than One Correct Answer)
+2
-0.5
The equation $${x^{3/4{{\left( {{{\log }_2}\,\,x} \right)}^2} + {{\log }_2}\,\,x - 5/4}} = \sqrt 2 $$ has
A
at least one real solution
B
exactly three solutions
C
exactly one irrational solution
D
complex roots.
4
IIT-JEE 1989
True or False
+1
-0
If x and y are positive real numbers and m, n are any positive integers, then $${{{x^n}\,{y^m}} \over {(1 + {x^{2n}})\,(1 + {y^{2m}})}} > {1 \over 4}$$
A
TRUE
B
FALSE
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