Definition : Two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal. This is Known as AAS Congruency. For given two triangles, \(\angle\) A = \(\angle\) X and \(\angle\) C = \(\angle\) Y, AB = XZ , then using AAS rule, \(\Delta\) ABC ≅ \(\Delta\) XYZ. Similar Questions […]
What is AAS (Angle Angle Side) Congruence Rule ? Read More »
Definition : Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle. This is Known as ASA Congruency. For given two triangles, AB = XZ , \(\angle\) A = \(\angle\) X and \(\angle\) B = \(\angle\) Z, then using
What is ASA (Angle Side Angle) Congruence Rule ? Read More »
Solution : Circumradius Formula (R) = \(abc\over 4\Delta\) where R = radius of circumcircle described about a given triangle with sides a, b, c. \(\Delta\) = \(\sqrt{s(s – a)(s – b)(s – c)}\) and s = \(a + b + c\over 2\) where a, b and c are the sides of triangle.
What is the Formula for Circumradius ? Read More »
Solution : Inradius Formula (r) = \(\Delta\over s\) Where r = radius of the circle inscribed in a given triangle \(\Delta\) = area of the given triangle \(\Delta\) = \(\sqrt{s(s – a)(s – b)(s – c)}\) s = half perimeter of the given triangle s = \(a + b + c\over 2\) for all a,
What is the Formula for the Inradius ? Read More »
Solution : Here radius = 10 cm We know that the surface area of hemisphere = \(3 \pi r^2\) = \(3 \times 3.14 \times 10 \times 10\) = 942 \(cm^2\)
Find the total surface area of hemisphere of radius 10cm ? Read More »
Question : In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person has 4 sq. meters of the space on ground and 20 cubic meters of air to breath.
What should be the height of the conical tent ? Read More »
Solution : The locus of the intersection of tangents which are at right angles is known as director circle of the hyperbola. The equation to the director circle is : \(x^2+y^2\) = \(a^2-b^2\) If \(b^2\) < \(a^2\), this circle is real ; If \(b^2\) = \(a^2\) the radius of the circle is zero & it
What is the Equation of Director Circle of Hyperbola ? Read More »
Solution : The equation x = acos\(\theta\) & y = bsin\(\theta\) together represent the parametric equation of ellipse \({x_1}^2\over a^2\) + \({y_1}^2\over b^2\) = 1, where \(\theta\) is a parameter. Note that if P(\(\theta\)) = (acos\(\theta\), bsin\(\theta\)) is on the ellipse then ; Q(\(\theta\)) = (acos\(\theta\), bsin\(\theta\)) is on auxilliary circle. A circle described on
What is the parametric equation of ellipse ? Read More »
Solution : Let y = \(x^{sinx}\). Then, Taking log both sides, log y = sin x.log x \(\implies\) y = \(e^{sin x.log x}\) By using logarithmic differentiation, On differentiating both sides with respect to x, we get \(dy\over dx\) = \(e^{sin x.log x}\)\(d\over dx\)(sin x.log x) \(\implies\) \(dy\over dx\) = \(x^{sin x}{log x {d\over dx}(sin
Differentiate \(x^{sinx}\) with respect to x. Read More »
Solution : Since by deleting a single term from an infinite series, it remains same. Therefore, the given function may be written as y = \(\sqrt{sin x + y}\) Squaring on both sides, \(\implies\) \(y^2\) = sin x + y By using differentiation of infinite series, Differentiating both sides with respect to x, 2y \(dy\over
If y = \(\sqrt{sinx + \sqrt{sinx + \sqrt{sinx + ……. to \infty}}}\), find \(dy\over dx\). Read More »
