Archives

A vertical pole PO is standing at the centre 0 of a square ABCD. If AC subtends an ∠90° at the top P of the pole, then the angle subtended by a side of the square at P is

1) 30° 2) 45° 3) 60° 4) None of these Solution: (3) 60° ∠OPA = ∠OPC = π / 4 Let OP = n, OA = n, AC = 2n OP / OA = cos (π / 4) PA = √2 n... View Article

ABCD is a square plot. The angle of elevation of the top of a pole standing at D from A or C is 30° and that from B is θ, then tan θ is equal to

1) √6 2) 1/√6 3) √3/2 4) √2/2 Solution: (2) 1 / √6 In triangle Δ PCD, tan 30° = h / a h / a = 1 / √3 .............. (1) In triangle Δ... View Article

If in a triangle ABC, s – a, s – b, s – c are in GP, then (sin²A + sin²C)/(sin A + sin C) is equal to

(1) sin (A + C) (2) sin (A - C) (3) b/R (4) none of these Solution: Given that s - a, s - b, s - c are in GP. So (s - b)2 = (s - a)(s - c)... View Article

In a triangle ABC, abc/2∆ is equal to

(1) (r1 + r2)/(1 + cos C) (2) (r1 + r2)/(1 + sin C) (3) (r1 + r2)/(1 + tan C) (4) none of these Solution: We know r1 = ∆/(s - a) r2 =... View Article

In a triangle ABC, [latex]frac{a(a+c-b)}{b(b+c-a)}[/latex] is equal to

(1) (1 - cos A)/(1 - cos B) (2) (1 + cos B)/(1 + cos A) (3) (1 - cos A)/(1 + cos B) (4) none of these Solution: a(a + c - b)/b(b + c - a) =... View Article

In a triangle ABC, if A = π/4 and tan B tan C = k, then k must satisfy

(1) k2 + 6k + 1 = 0 (2) k2 - 6k + 1 < 0 (3) k2 - 6k + 1 ≥ 0 (4) none of these Solution: Given tan B tan C = k We know in a triangle ABC,... View Article

If in a triangle ABC, 5 cos C + 6 cos B = 4 and 6 cos A + 4 cos C = 5, then tan(A/2) tan (B/2) is equal to

(1) 3/2 (2) 2/3 (3) 1/5 (4) 5 Solution: Given 5 cos C + 6 cos B = 4 6 cos A + 4 cos C = 5 This is of the form b cos C + c cos B = a and c... View Article

If the sides of a triangle are 3, 5, and 7 and the smallest and greatest angles are α and β respectively, then 4(1 – cos α) (1 – cos β) is equal to

(1) 3/5 (2) 3/7 (3) 3/4 (4) 3/11 Solution: Let a = 3, b = 5 and c = 7 Here a< b<c So A is the smallest angle and C is the greatest... View Article

If in a triangle, a² + b² + c² = ca + ab√3, then the triangle is

(1) equilateral (2) isosceles (3) right angled with A = 900, B = 600 and C = 300 (4) none of these Solution: Given a2 + b2 + c2 = ca +... View Article

The angles of a triangle ABC are in A.P. The largest angle is twice the smallest and the median to the largest side divides the angle at the vertex in the ratio 2 : 3. If the length of the median is 2√3 cm, then the length of the largest side is

1) 2 sin 320 2) 4 sin 320 3) 6 sin 320 4) 8 sin 320 Solution: Let A, B, C are the angles in AP. Then 2B = A + C Also A + B + C = 180 So B... View Article

In a cyclic quadrilateral ABCD; a, b, c, d denote the length of the sides AB, BC, CD, and DA respectively. Then cos A is equal to

(1) (a2 + d2 - b2 - c2)/2(ad + bc) (2) (a2 + d2 - b2 - c2)/2(ab - dc) (3) (a2 - d2 + b2 - 2c2)/2(ad + bc) (4) none of these Solution:... View Article

If the angles of a triangle are in the ratio 1 : 3: 5 and θ denotes the smallest angle, then the ratio of the largest side to the smallest side of the triangle is

(1) (√3 sin θ + cos θ)/2 sin θ (2) (√3 cos θ - sin θ)/2 sin θ (3) ( cos θ + √3 sin θ)/2 sin θ (4) (√3 cos θ + sin θ)/2 sin θ Solution: Given... View Article

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Archives

A vertical pole PO is standing at the centre 0 of a square ABCD. If AC subtends an ∠90° at the top P of the pole, then the angle subtended by a side of the square at P is

ABCD is a square plot. The angle of elevation of the top of a pole standing at D from A or C is 30° and that from B is θ, then tan θ is equal to

If in a triangle ABC, s – a, s – b, s – c are in GP, then (sin²A + sin²C)/(sin A + sin C) is equal to

In a triangle ABC, abc/2∆ is equal to

In a triangle ABC, [latex]frac{a(a+c-b)}{b(b+c-a)}[/latex] is equal to

In a triangle ABC, if A = π/4 and tan B tan C = k, then k must satisfy

If in a triangle ABC, 5 cos C + 6 cos B = 4 and 6 cos A + 4 cos C = 5, then tan(A/2) tan (B/2) is equal to

If the sides of a triangle are 3, 5, and 7 and the smallest and greatest angles are α and β respectively, then 4(1 – cos α) (1 – cos β) is equal to

If in a triangle, a² + b² + c² = ca + ab√3, then the triangle is

The angles of a triangle ABC are in A.P. The largest angle is twice the smallest and the median to the largest side divides the angle at the vertex in the ratio 2 : 3. If the length of the median is 2√3 cm, then the length of the largest side is

In a cyclic quadrilateral ABCD; a, b, c, d denote the length of the sides AB, BC, CD, and DA respectively. Then cos A is equal to

If the angles of a triangle are in the ratio 1 : 3: 5 and θ denotes the smallest angle, then the ratio of the largest side to the smallest side of the triangle is

In a triangle ABC, if c = (a – b) sec θ, then tan θ is equal to

In a triangle ABC, the median AD is perpendicular to AC. If b = 5 and c = 11, then a is equal to

If in a triangle sin A/sin C = sin (A – B)/sin (B – C), then

If the angles A and B of the triangle ABC satisfy the equation sin A + sin B = √3(cos B – cos A), then they differ by

The circumradius of the triangle whose sides are 13, 12, and 5 is

What is a monomer in plastic

Which is the best definition of a wave?

How is fructose a reducing sugar

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