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Practice Test - Mathematics 19

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Question 1

The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l² = m² + n² is

Question 2

Consider

A normal to y = f(x) at

also passes through the point:

Question 3

The coefficient of xⁿ in the expansion of (1+x)(1-x)ⁿ is

Question 4

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for

Question 5

The value of

Question 6

The locus of the foot of perpendicular drawn from the centre of the ellipse x² + 3y² = 6 on any tangent to it is

Question 7

If f(a + b − x) = f (x), then f (x) dx is equal to

Question 8

The system of equations
αx + y + z = α - 1,
x + αy + z = α - 1,
x + y + αz = α - 1
has no solution, if α is

Question 9

Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation

, where k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is

Question 10

If dy/dx= y + 3 > 0 and y(0) = 2, then y(ln 2) is equal to

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Feb 3JEE & BITSAT