The polygon in which sum of all exterior
Question: The polygon in which sum of all exterior angles is equal to the sum of interior angles is called __________. Solution: The polygon in which sum of all exterior angles is equal to the sum of interior angles is called Quadrilateral....
Read More →In trapezium ABCD with AB||CD,
Question: In trapezium ABCD with AB||CD, if A = 100o, then D = __________. Solution: In trapezium ABCD with AB||CD, if A = 100o, then D =80o. We know that, in trapezium adjacent angles of non parallel sides are supplementary. A + D = 180o 100o+ D = 180o D = 180o 100o D = 80o...
Read More →If only one diagonal of a quadrilateral
Question: If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as. Solution: kite This is a property of kite, i.e. only one diagonal bisects the other....
Read More →If the solve the problem
Question: If $y=3 e^{2 x}+2 e^{3 x}$, prove that $\frac{d^{2} y}{d x^{2}}-5 \frac{d y}{d x}+6 y=0$ Solution: Formula: - (i) $\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y}_{1}$ and $\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=\mathrm{y}_{2}$ (ii) $\frac{d\left(e^{a x}\right)}{d x}=a e^{a x}$ (iii) $\frac{\mathrm{d}}{\mathrm{dx}} \mathrm{x}^{\mathrm{n}}=\mathrm{n} \mathrm{x}^{\mathrm{n}-1}$ Given: - $y=3 e^{2 x}+2 e^{3 x}$ $\Rightarrow \frac{d y}{d x}=6 e^{2 x}+6 e^{3 x}$ $\Rightarrow \frac{d^{...
Read More →Adjacent angles of a parallelogram
Question: Adjacent angles of a parallelogram are. Solution: supplementary By property of a parallelogram, we know that, the adjacent angles of a parallelogram are supplementary....
Read More →Find the arithmetic mean between:
Question: Find the arithmetic mean between: (i) 9 and 19 (ii) 15 and -7 (iii) $-16$ and $-8$ Solution: (i) 9 and 19 To find: Arithmetic mean between 9 and 19 The formula used: Arithmetic mean between a and $\mathrm{b}=\frac{a+b}{2}$ We have 9 and 19 A.M. $=\frac{9+19}{2}$ $=\frac{28}{2}$ $=14$ (ii) 15 and -7 To find: Arithmetic mean between 15 and -7 The formula used: Arithmetic mean between a and $\mathrm{b}=\frac{a+b}{2}$ We have 15 and -7 A.M. $=\frac{(15)+(-7)}{2}$ $=\frac{15-7}{2}$ $=\frac{...
Read More →If one diagonal of a rectangle is 6 cm long,
Question: If one diagonal of a rectangle is 6 cm long, length of the other diagonal is. Solution: 6 cm Since both the diagonals of a rectangle are equal. Therefore, length of other diagonal is also 6 cm....
Read More →A rectangle whose adjacent
Question: A rectangle whose adjacent sides are equal becomes a . Solution: square If in a rectangle, adjacent sides are equal, then it is called a square....
Read More →If the solve the problem
Question: If $y=\sin (\log x)$, prove that $x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0$ Solution: Formula: - (i) $\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y}_{1}$ and $\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=\mathrm{y}_{2}$ (ii) $\frac{\mathrm{d}(\log \mathrm{x})}{\mathrm{dx}}=\frac{1}{\mathrm{x}}$ (iii) $\frac{d}{d x} \cos x=\sin x$ (iv) $\frac{\mathrm{d}}{\mathrm{dx}} \sin \mathrm{x}=-\cos \mathrm{x}$ (v) $\frac{d}{d x} x^{n}=n x^{n-1}$ (vi) chain rule $\frac{\mathrm{df}}{\ma...
Read More →A polygon having
Question: A polygon having 10 sides is known as. Solution: decagon A polygon with 10 sides is called decagon....
Read More →Diagonals of a rectangle are————.
Question: Diagonals of a rectangle are. Solution: equal We know that, in a rectangle, both the diagonals are of equal length....
Read More →A nonagon has————sides.
Question: A nonagon hassides. Solution: 9Nonagon is a polygon which has 9 sides....
Read More →The adjacent sides of a parallelogram
Question: The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is __________. Solution: The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is 28 cm. We know that, perimeter of Parallelogram = 2 (sum of lengths of adjacent sides) = 2 (5 + 9) = 2 14 = 28 cm...
Read More →If the diagonals of a quadrilateral
Question: If the diagonals of a quadrilateral bisect each other, it is a __________. Solution: If the diagonals of a quadrilateral bisect each other, it is a Parallelogram....
Read More →If the solve the problem
Question: If $y=\log (1+\cos x)$, prove that $\frac{d^{3} y}{d x^{3}}+\frac{d^{2} y}{d x^{2}} \cdot \frac{d y}{d x}=0$ Solution: Formula: - (i) $\frac{d y}{d x}=y_{1}$ and $\frac{d^{2} y}{d x^{2}}=y_{2}$ (ii) $\frac{\mathrm{d}}{\mathrm{dx}} \cos \mathrm{x}=\sin \mathrm{x}$ (iii) $\frac{d}{d x} \sin x=-\cos x$ (iv) $\frac{d}{d x} x^{n}=n x^{n-1}$ (v) chain rule $\frac{\mathrm{df}}{\mathrm{dx}}=\frac{\mathrm{d}(\text { wou })}{\mathrm{dt}} \cdot \frac{\mathrm{dt}}{\mathrm{dx}}=\frac{\mathrm{dw}}{\...
Read More →The number of sides in a regular polygon
Question: The number of sides in a regular polygon having measure of an exterior angle as 72ois __________. Solution: The number of sides in a regular polygon having measure of an exterior angle as 72ois 5. We know that, the measure of each exterior angle of a regular pentagon is 360o/n. Where n is the number of sides in the polygon, Then, pentagon has exterior angle = 72o So, 72o= 360o/n n = 360o/72o n = 5...
Read More →A diagonal of a quadrilateral is a line
Question: A diagonal of a quadrilateral is a line segment that joins two vertices of the quadrilateral. Solution: opposite Since the line segment connecting two opposite vertices is called diagonal....
Read More →The measure of——– angle of concave
Question: The measure of angle of concave quadrilateral is more than 180. Solution: one Concave polygon is a polygon in which at least one interior angle is more than 180....
Read More →A rhombus is a parallelogram
Question: A rhombus is a parallelogram in whichsides are equal. Solution: all As length of each side is same in a rhombus....
Read More →A farmer buys a used for ₹180000.
Question: A farmer buys a used for ₹180000. He pays ₹90000 in cash and agrees to pay the balance in annual instalments of ₹9000 plus 12% interest on the unpaid amount. How much did the tractor cost him? Solution: Given: - The amount that is to be paid to buy a tractor $=₹ 180000$. An amount that he paid by cash $=₹ 90000$. Remaining balance $=₹ 90000$ Annual instalment $=₹ 9000+$ interest @12\% on unpaid amount. Thus, our instalments are 19800, 18720, 17640 Total number of instalments = $=\frac{...
Read More →A quadrilateral can be constructed uniquely,
Question: A quadrilateral can be constructed uniquely, if its three sides andangles are given. Solution: two included We cap determine a quadrilateral uniquely, if three sides and two included angles are given....
Read More →———measurements can determine
Question: measurements can determine a quadrilateral uniquely. Solution: 5 To construct a unique quadrilateral, we require 5 measurements, i.e. four sides and one angle or three sides and two included angles or two adjacent sides and three angles are given....
Read More →If the solve the problem
Question: If $x=4 z^{2}+5, y=6 z^{2}+7 z+3$, find $\frac{d^{2} y}{d x^{2}}$ Solution: Formula: - (i) $\frac{d y}{d x}=y_{1}$ and $\frac{d^{2} y}{d x^{2}}=y_{2}$ (ii) $\frac{\mathrm{d}}{\mathrm{dx}} \mathrm{x}^{\mathrm{n}}=\mathrm{nx}^{\mathrm{n}-1}$ (iii) chain rule $\frac{\mathrm{df}}{\mathrm{dx}}=\frac{\mathrm{d}(\text { wou })}{\mathrm{dt}} \cdot \frac{\mathrm{dt}}{\mathrm{dx}}=\frac{\mathrm{dw}}{\mathrm{ds}} \cdot \frac{\mathrm{ds}}{\mathrm{dt}} \cdot \frac{\mathrm{dt}}{\mathrm{dx}}$ (iv) pa...
Read More →In a rhombus, diagonals intersect
Question: In a rhombus, diagonals intersect at angles. Solution: right The diagonals of a rhombus intersect at right angles....
Read More →If all sides of a quadrilateral
Question: If all sides of a quadrilateral are equal, it is a. Solution: rhombus or square As in both the quadrilaterals all sides are of equal length....
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