PREPARED BY M.SRINIVASAN, PGT(MATHS) ZIET, MUMBAI PREPARED BY M.SRINIVASAN, PGT(MATHS) ZIET, MUMBAI

FOR ONE TO ONE FUNCTION EVERY ELEMENT OF A IS MAPPED TO UNIQUE ELEMENT OF A NUMBER OF ONE-ONE FUNCTION = 3! = 6

x = 4

6a – 8 = 0

2-k+15 = 0 k = 17

ORDER OF AB = 2 X 5 ORDER OF (AB)’ = 5 X 2

26 = 6x + 20 x = 1

f(x) is continuous at x = 1 f(1) = 11

f‘(x) = -3 (-1) (-3) < 0 f(x) is strictly decreasing in (- , 1)

f‘(x) = -3 (-0.5) (1.5) > 0 f(x) is strictly increasing in (1, 3) f‘(x) = -3 (2.5) (0.5) < 0 f(x) is strictly decreasing in (3,  )

f(x) is an odd function

u = x ; dv = cos  x

Multiply Numerator and Denominator by

LET M BE THE MID POINT OF AB

If the vectors are parallel, the components are proportional = -3

DIRECTION RATIOS ARE 1 : 1 : 1 DIRECTION COSINES ARE

Direction ratios of the given line 1 : -1 : 3 Equation of the normal to the plane are 1 : -1 : 3 Equation of the plane is : x – y + 3z + d = 0 Plane passes through the point (1, 2, 1) d = -2 Equation of the plane is : x – y + 3z -2 = 0

Direction Ratios of the line PQ are 2 : -1 : 1

The plane contains the line The equation of the plane is: a(x + 3) + b (y – 1) + c(z – 5) = 0 and 3a - b + 5c = 0 The plane passes through the point (1, 1, 1) 4a + 0b - 4c = 0

a(x + 3) + b (y – 1) + c(z – 5) = 0 3a - b + 5c = 0 4a + 0b - 4c = 0 The line is The point is : (-1, 2, 5) The points satisfies the equation of the plane The plane contains the line

MIN COST = Rs.110

Integration Integration Differentiation Differentiation Matrices and determinants Matrices and determinants Relations and functions Relations and functions Probability Probability Limits Limits

Calculus - 44 marks Vectors and 3-D Geometry – 17 marks Algebra – 13 marks Relations and functions – 10 Marks Probability – 10 marks