Multiple Choice QuestionsThe normal to the curve x2 + 2xy-3y2 =0 at (1,1)
does not meet the curve again
meets the curve again in the second quadrant
meets the curve again in the third quadrant
meets the curve again in the third quadrant
The number of common tangent to the circles x2+y2-4x-6y-12=0 and x2+y2+6x+18y+26 = 0 is
1
2
3
3
C.
3
Number of common tangents depend on the position of the circle with respect to the each other.
(i) If circles touch externally ⇒C1C2 = r1+ r2,3 common tangents
(ii) If circles touch internally ⇒ C1C2 = r2-r1, 1 common tangents
(iii) If circles do not touch each other, 4 common tangents
Given equations of circles are
x2 +y2-4x-6y-12 = 0 .. (i)
x2+y2+6x+18y+26 =0 ... (ii)
Centre of circle (i) is C1 (2,3) and radius
=
Centre of circle (ii) is C2(-3,-9) and radius
Thus, both circles touch each other externally. Hence, there are three common tangents.
A = 
is a matrix satisfying the equation AAT = 9I, Where I is 3 x 3 identity matrix, then the ordered pair (a,b) is equal to
(2,-1)
(-2,1)
(2,1)
(2,1)
The set of all values of λ for which the system of linear equations
2x1-2x2+x3 = λx1
2x1- 3x2 + 2x3 = λx2
-x1 + 2x2 = λx3
a non- trivial solution.
is an empty set
is a singleton set
contains two elements
contains two elements
Let f (x) be a polynomial of degree four having extreme values at x =1 an x =2. If 
then f(2) is equal to
-8
-4
0
0
If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls, is
is differntiable, then the value of k+m is
Switch
is equal to
where 
.Then, a value of y is
