Functions – Problems 1. f: R → R defined by f (x) = sinx and g: R → R defined by g (x) = x², fog (x) =? Solution: Given that f (x) = sin x g (x) = x² fog (x) = f [g (x)] = f [x²] = sin x². 2. If f: Read more about Functions – Problems[…]
Circle Problems 1) Show that the line x + y + 1 = 0 touches the circle x² + y² – 3x + 7y + 14 = 0 and find the point of contact. Solution: Centre of the circle is C (3/2, -7/8) Radius of the circle (r) = Perpendicular distance from the centre to Read more about Circle Problems[…]
Limits – Problems I. Solving the following limits 1) Solution: Given that , , , a + a = 2a 2. Solution: Given 1² + 2 (1) + 3 = 6 3. Solution: Given = 0. k where |K| ≤ 1 = 0 II) Find the right and left-hand limits of the function Solution: Given Read more about Limits – Problems[…]
Perpendicular Distance from a Point to the Line – Problem Formula: The perpendicular distance from a point p (x, y) to the line ax + by + c = 0 is . 1) 5x – 2y + 4 = 0. (-2, -3) Solution: Given that 5x – 2y + 4 = 0 … (1) Length Read more about Perpendicular Distance from a Point to the Line – Problem[…]
Pair of Straight Lines -Problems 1. Find the acute angle between the pair of line represented by the following equation x² – 7xy + 12y² = 9. Solution: Given that, x² – 7xy + 12y² = 9 Comparing with ax² + 2hxy + by² = 0 a = 1, b = 12 and h = Read more about Pair of Straight Lines -Problems[…]
Straight Lines (Circumcenter) Problems 1) Find the circumcenter of the triangle whose vertices are (1, 0), (-1, 2) and (3, 2). Solution: Vertices of the triangle are A (1, 0), B (-1, 2), C (3, 2). Let S (x, y) be the circumcenter of triangle ABC, Then SA = SB = SC, Let SA = Read more about Straight Lines (Circumcenter) Problems[…]
Rotation of Axes (Change of Direction) 1) When the axes rotated through an angle 60, then new co-ordinates of three points are the following (3, 4). Solution: Given that, New co-ordinates are (3, 4) X = 3, Y = 4 x = X cos θ – Y sin θ = 3 cos60 – 4 sin60 = Read more about Rotation of Axes (Change of Direction)[…]
Translation of Axes – Problems 1) Find the point to which the origin is be shifted so as remove the first degree term from the equation 4x² + 9y² – 8x + 36y + 4 =0 Solution: The given equation is 4x² + 9y² – 8x + 36y + 4 = 0 comparing with ax² Read more about Translation of Axes – Problems[…]
Locus – Problems 1) Find the equation of locus of a point which is a distance 5 from A (4, -3) Solution: Let p (x, y) be a point in the locus Given, A (4, -3) CP = 5 (x – 4)² + (y + 3)² = 25 x² – 8x + 16 + y² Read more about Locus – Problems[…]
Porbability Distribution Functions – Problems 1) A p.d.f of a discrete random variable is zero except at the points x = 0, 1, 2 at these points it has the value p(0) = 3c³, p(1) = 4c – 10c², p(2) = 5c – 1 for some c > 0 find the value. Solution: P (X Read more about Porbability Distribution Functions – Problems[…]