1
IIT-JEE 1996
MCQ (Single Correct Answer)
+1
-0.25
The angle between a pair of tangents drawn from a point P to the circle $${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\, + \,9\,{\sin ^2}\,\alpha \, + \,13\,{\cos ^2}\,\alpha \, = \,0$$ is $$2\,\alpha $$.
The equation of the locus of the point P is
A
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\, + \,4\, = \,0$$
B
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\,\, - \,9\,\, = \,0$$
C
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\,\, - \,4\,\, = \,0$$
D
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\,\, + \,9\,\, = \,0$$
2
IIT-JEE 1996
MCQ (Single Correct Answer)
+1
-0.25
$${\sec ^2}\theta = {{4xy} \over {{{\left( {x + y} \right)}^2}}}\,$$ is true if and only if
A
$$x + y \ne 0\,$$
B
$$x = y,\,x \ne 0$$
C
$$x = y\,$$
D
$$x \ne 0,\,y \ne 0$$
3
IIT-JEE 1996
Fill in the Blanks
+2
-0
The value of the expression
$$1 \bullet \left( {2 - \omega } \right)\left( {2 - {\omega ^2}} \right) + 2 \bullet \left( {3 - \omega } \right)\left( {3 - {\omega ^2}} \right) + \,....... + \left( {n - 1} \right).\left( {n - \omega } \right)\left( {n - {\omega ^2}} \right),$$

where $$\omega $$ is an imaginary cube root of unity, is..........

4
IIT-JEE 1996
MCQ (Single Correct Answer)
+1
-0.25
For positive integers $${n_1},\,{n_2}$$ the value of the expression $${\left( {1 + i} \right)^{^{{n_1}}}} + {\left( {1 + {i^3}} \right)^{{n_1}}} + {\left( {1 + {i^5}} \right)^{{n_2}}} + {\left( {1 + {i^7}} \right)^{{n_2}}},$$
where $$i = \sqrt { - 1} $$ is real number if and only if
A
$${n_1} = {n_2} + 1$$
B
$${n_1} = {n_2} - 1$$
C
$${n_1} = {n_2}$$
D
$${n_1} > 0,\,{n_2} > 0$$
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