1. The series of natural numbers is divided into groups as (1), (2, 3, 4), (3,...

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1. The series of natural numbers is divided into groups as (1), (2, 3, 4), (3, 4, 5, 6, 7), (4, 5, 6, 7, 8, 9, 10).............. If sum of elements in the 20th group is, then is equal to (a) 1368 (b) (38) 2. The lines L: x = y=z, L: x = Y 2 = Z 3 (c) (39) (d) 38 x39 and a line L3 is passing through (1, 1, 1) form a triangle of area 6 units, (1, 1, 1) being one of the vertices of the triangle. Then the point of intersection of the L3 with L is (a) (1, 2, 3) 3. 4. (b) (2,4,6) 48 (c) 3 3 (d) (1, 5, 7) The combined equation of 2 altitudes of an equilateral triangle is x - 3y - 4x+63y-5=0. The third altitude has equation. (a)x+2=0 (b) y = 3 (c) x = 2 (d) None of these The mean marks of students of a school is 56. The mean marks of girls is 60 and that of boys is 50. If 9n number of boys and girls are n and m respectively, then equals m 5. C and C are two circles whose equations are given as x + y = 25 and x + y+10x + y + 1 = 0. Now C is a variable circle which cuts C and C orthogonally. Tangents are drawn from the centre of C3 to C, if the locus of the mid point of the chord of contact of tangents is ax + 3y + b 13(x + y)=0, (where a, b = Z, and a and b are relative prime), then b (a) 1 (b) 2 (c) 4 is a (d) 5 1. The series of natural numbers is divided into groups as (1), (2, 3, 4), (3, 4, 5, 6, 7), (4, 5, 6, 7, 8, 9, 10).............. If sum of elements in the 20th group is, then is equal to (a) 1368 (b) (38) 2. The lines L: x = y=z, L: x = Y 2 = Z 3 (c) (39) (d) 38 x39 and a line L3 is passing through (1, 1, 1) form a triangle of area 6 units, (1, 1, 1) being one of the vertices of the triangle. Then the point of intersection of the L3 with L is (a) (1, 2, 3) 3. 4. (b) (2,4,6) 48 (c) 3 3 (d) (1, 5, 7) The combined equation of 2 altitudes of an equilateral triangle is x - 3y - 4x+63y-5=0. The third altitude has equation. (a)x+2=0 (b) y = 3 (c) x = 2 (d) None of these The mean marks of students of a school is 56. The mean marks of girls is 60 and that of boys is 50. If 9n number of boys and girls are n and m respectively, then equals m 5. C and C are two circles whose equations are given as x + y = 25 and x + y+10x + y + 1 = 0. Now C is a variable circle which cuts C and C orthogonally. Tangents are drawn from the centre of C3 to C, if the locus of the mid point of the chord of contact of tangents is ax + 3y + b 13(x + y)=0, (where a, b = Z, and a and b are relative prime), then b (a) 1 (b) 2 (c) 4 is a (d) 5