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What is the meaning of cooling?

Cooling means the removal of heat which results in a lower temperature or a change in the phase. The decrease in temperature by any other method... View Article

Why is radium 226 unstable?

Radium-226 is a heavy nucleus and it is unstable. It emits radon 222 and alpha particle... View Article

What is the most unstable element?

Francium is the most unstable element that occurs naturally. The longest-lived isotope of francium, francium-223 has a half-life of only 22... View Article

Is the capacitor linear or nonlinear?

An ideal capacitor is a linear electrical element. The current flow is proportional to the applied voltage.... View Article

Are capacitors and inductors linear

Capacitors and inductors show linear characteristics. A linear element is one in which current and the voltage are directly proportional. If the... View Article

If in a triangle ABC, sin C + cos C + sin (2B + C) – cos (2B + C) = 2√2, the the triangle ABC is

(1) equilateral (2) scalene (3) isosceles right angled (4) obtuse angled Solution: Given sin C + cos C + sin (2B + C) - cos (2B + C) = 2√2... View Article

In a triangle ABC, if cos A cos B + sin A sin B sin C = 1 then a : b : c =

1) 1 : 2 : 3 2) 1 : 1 : 2 3) 1 : 1 : √2 (4) 1 : 1 : √3 Solution: Given cos A cos B + sin A sin B sin C = 1 If sin C = 1, then C = 900 Then... View Article

In a triangle, ABC, AD, BE, and CF are the altitudes, and R is the circumradius then the radius of the circle DEF is

1) 2R 2) R 3) R/2 4) none of these Solution: Consider ∆DEF EF = a cos A DE = c cos C DF = b cos B Let R1 is the circumradius of ∆DEF. R1 =... View Article

If the median AD of a triangle ABC divides the angle ∠BAC in the ratio 1:2, then sin B/sin C is equal to

(1) 2 cos A/3 (2) ½ sec A/3 (3) ½ sin A/3 (4) 2 cosec A/3 Solution: From sine rule in ∆ABD, AD/sin B = BD/sin A/3 …(i) Consider ∆ADC. By... View Article

If R and r are the radii of the circumcircle and incircle of a regular polygon of n sides, each side being of length a, then a is equal to

(1) 2(R + r) sin (π/2n) (2) 2(R + r) tan (π/2n) (3) 2(R + r) (4) none of these Solution: We know R = ½ a cosec (π/n) r = ½ a cot (π/n) So... View Article

If α, β are the acute angles of an obtuse-angled triangle, then tan α tan β is

1) < 1 2) > 1 3) = 1 4) None of these Solution: Given α, β are the acute angles of an obtuse-angled triangle. So α + β is also an... View Article

In a triangle ABC, if cos A + cos B + cos C = 7/4, then R/r is equal to

(1) 4/7 (2) 4/3 (3) 3/4 (4) none of these Solution: Given cos A + cos B + cos C = 7/4 If A, B, C are the angles of a triangle, then cos A +... View Article

If d₁, d₂, d₃ are the diameters of the three escribed circles of a triangle, then d₁d₂ + d₂d₃ + d₃d₁ is equal to

(1) 4s2 (2) ∆2 (3) 4∆2 (4) 2∆2 Solution: We know d1 = 2r1, d2 = 2r2,d3 = 2r3 We have r1 = ∆/(s - a) r2 = ∆/(s - b) r3 = ∆/(s - c) d1d2 +... View Article

If in a triangle ABC, c⁴ – 2c²(a² + b²) + a⁴ + a²b² + b⁴ = 0, then the acute angle C is equal to

(1) 300 (2) 600 (3) 450 (4) 750 Solution: From cosine rule, cos C = (a2 + b2 - c2)/2ab cos2 C = (a2 + b2 - c2)2/4a2b2 ..(i) Given c4 -... View Article

The sides of a triangle are in the ratio 5: 8: 11. If θ denotes the angle opposite to the largest side of the triangle, then the value of tan²θ/2 is equal to

(1) 1/21 (2) 7/48 (3) 7/3 (4) 7/12 Solution: Given the sides are in the ratio 5: 8: 11 Let the sides be 5x, 8x, and 11x. Then s = (5x + 8x +... View Article

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