How do bonds work
A chemical bond is a force of attraction between the ions, atoms or molecules to form compounds. The bond will... View Article
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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... View Article
Why is radium 226 unstable?
Radium-226 is a heavy nucleus and it is unstable. It emits radon 222 and alpha particle
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... 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.
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.... 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... 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... 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 =... 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... 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... 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... 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... 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... 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... 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 tan2 θ/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... View Article
If a4 + b4 + c4 = 2c2(a2 + b2), then acute value of ∠C is equal to
(1) 300 (2) 600 (3) 450 (4) 750 Solution: Given a4 + b4 + c4 = 2c2 (a2 + b2)... View Article
In a triangle ABC, if cos A/a = tan C/c, then sin (B + C) is equal to
(1) cos B sin A (2) cos A cos C (3) cos A sin B (4) sin B sin C... View Article
In a triangle ABC, if tan (A/2) = p, tan (B/2) = q, then 2(p + q)(1 – pq)/(1 + p2)(1 + q2) is equal to
(1) sin C (2) sin 2C (3) sin A + sin B (4) none of these Solution: Given tan (A/2)... View Article
If in a triangle ABC, the line joining the circumcentre O and the incentre I is parallel to BC, then
1) r = R cos A 2) r = R sin A 3) R = r cos A 4) R... View Article
