The lengths of the two sides of a right triangle containing the right angle differ by `2cm.` If the area of the triangle is `24cm^2.` Find the perimeter of the triangle.
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The sides of a triangle are in A.P. and its area is `(3)/(5)` th of an equilateral triangle of the same perimeter. Find the greatest angle of the tria
Correct Answer - `120^(@)` Let the sides be `x - d, x, x + d`. Then `s = (3x)/(2), (s -a) = (x)/(2) + d`, `(s-b) = (x)/(2), (s-c) = (x)/(2)...
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If one side of a triangle is double the other, and the angles on opposite sides differ by `60^(@)`, then the triangle is
Correct Answer - C `a = 2b and A - B = 60^(@)` We know that `tan.(A -B)/(2) = (a -b)/(a + b) cot.(C)/(2)` or `tan 30^(@) = (1)/(3) cot.(C)/(2)` or...
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If two sides of a triangle are roots of the equation `x^(2) -7x + 8 = 0` and the angle between these sides is `60^(@)` then the product of inradius an
Correct Answer - B Let a and b the roots of `x^(2) -7 x + 8 = 0` Then `a + b = 7, ab = 8` Also, `C = 60^(@)`...
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Find in each cash whether the sides of the triangle, as given below form a right triangle or not (1) 9 cm, 12 cm and 15 cm (ii) 8 cm,15 cm and 17 cm (
Correct Answer - (ii), (iii), (v)
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Which of the following can be the sides of a right triangle? (i) 2.5 cm,6.5 cm, 6 cm. (ii) 2 cm, 2 cm, 5 cm. (iii) 1.5 cm, 2cm, 2.5 cm. In the case of
Correct Answer - (i) और (iii)
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The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle. Hint Ratio of sides
Correct Answer - `32 sqrt(3) cm^(2)`
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The sides of a quadrilateral ABCD taken in order are 6 cm, 8 cm, 12 cm and 14 cm respectively and the angle between the first two sides is a right ang
Correct Answer - 82.8 `cm^(2)`
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The difference between the lengths of the parallel sides of a trapezium is 8 cm, the perpendicular distance between these sides is 24 cm and the area
Correct Answer - 17 cm, 9 cm
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Consider a particle of mass \( m \) having linear momentum \( P \) at position \( r \) relative to the origin \( O \). Which of the following equations correctly relates \( r , P , L \) ? a) \( \left[\left(\frac{d L}{d t}\right)+r x\left(\frac{d P}{d t}\right)\right]=0 \) b) \( \left[\left(\frac{d L}{d t}\right)-r x\left(\frac{d P}{d t}\right)\right]=0 \) c) \( \left[\left(\frac{d L}{d t}\right) \times\left(\frac{d r}{d t}\right) \times P\right]=0 \) d) \( \left[\left(\frac{d L}{d t}\right)-\left(\frac{d r}{d t}\right) \times P\right]=0 \)
Correct answer is (b) We know that \(\tau\) = r × F ∵ \(\tau\) \(= \frac{dL}{dt},\) \(F = \frac{dP}{dt}\) \(\left(\frac{dL}{dt}\right) = r \times \left(\frac{dP}{dt}\right)\) \(\left(\frac{dL}{dt}\right) - r \times \left(\frac{dP}{dt}\right) = 0\)
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