The shape of the top surface of a table is trapezium.
Question: The shape of the top surface of a table is trapezium. Its parallel sides are 1 m and 1.4 m and the perpendicular distance between them is 0.9 m. Find its area. Solution: Area of a trapezium $=\frac{1}{2} \times($ Sum of parallel sides $) \times($ Distance between them $)$ $=\left\{\frac{1}{2} \times(1+1.4) \times 0.9\right\} \mathrm{m}^{2}$ $=\left(\frac{1}{2} \times 2.4 \times 0.9\right) \mathrm{m}^{2}$ $=(1.2 \times 0.9) \mathrm{m}^{2}$ $=1.08 \mathrm{~m}^{2}$ Hence, the area of the ...
Read More →Find the area of a trapezium whose parallel sides are 38.7 cm
Question: Find the area of a trapezium whose parallel sides are 38.7 cm and 22.3 cm, and the distance between them is 16 cm. Solution: Area of a trapezium $=\frac{1}{2} \times($ Sum of parallel sides $) \times($ Distance between them $)$ $=\left\{\frac{1}{2} \times(38.7+22.3) \times 16\right\} \mathrm{cm}^{2}$ $=\left(\frac{1}{2} \times 61 \times 16\right) \mathrm{cm}^{2}$ $=(61 \times 8) \mathrm{cm}^{2}$ $=488 \mathrm{~cm}^{2}$ Hence, the area of the trapezium is $488 \mathrm{~cm}^{2}$....
Read More →Find five rational numbers between 0 and 1.
Question: Find five rational numbers between 0 and 1. Solution: The five rational numbers between 0 and 1 are, 1/6, 2/6, 3/6, 4/6, 5/6....
Read More →Find the area of a trapezium whose parallel sides are 24 cm
Question: Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm. Solution: Area of a trapezium $=\frac{1}{2} \times($ Sum of parallel sides $) \times($ Distance between them $)$ $=\left\{\frac{1}{2} \times(24+20) \times 15\right\} \mathrm{cm}^{2}$ $=\left(\frac{1}{2} \times 44 \times 15\right) \mathrm{cm}^{2}$ $=(22 \times 15) \mathrm{cm}^{2}$ $=330 \mathrm{~cm}^{2}$ Hence, the area of the trapezium is $330 \mathrm{~cm}^{2}$....
Read More →Can you find a rational number
Question: Can you find a rational number whose multiplicative inverse is 1? Solution: No, we cannot find a rational number whose multiplicative inverse is 1....
Read More →Find the real values of x and y for which
Question: Find the real values of $x$ and $y$ for which $(x-i y)(3+5 i)$ is the conjugate of $(-6-$ 24i). Solution: Given: $(x-i y)(3+5 i)$ is the conjugate of $(-6-24 i)$ We know that, Conjugate of $-6-24 i=-6+24 i$ According to the given condition, $(x-i y)(3+5 i)=-6+24 i$ $\Rightarrow x(3+5 i)-i y(3+5 i)=-6+24 i$ $\Rightarrow 3 x+5 i x-3 i y-5 i^{2} y=-6+24 i$ $\Rightarrow 3 x+i(5 x-3 y)-5(-1) y=-6+24 i\left[\because i^{2}=-1\right]$ $\Rightarrow 3 x+i(5 x-3 y)+5 y=-6+24 i$ $\Rightarrow(3 x+5...
Read More →The product of two rational numbers is –7.
Question: The product of two rational numbers is 7. If one of the number is 5, find the other? Solution: Let us assume the other number be y. Given, product of two rational number = -7 One number = -5 Then, = y (-5) = -7 = y = -7/ (-5) = y = 7/5 So, the other number is 7/5...
Read More →By what number should we multiply -8/13
Question: By what number should we multiply -8/13 so that the product may be 24? Solution: Let us assume the other number be y. Given, product of two rational number = 24 One number = -8/13 Then, = y (-8/13) = 24 = y = 24/ (-8/13) = y = (24/1) (-13/8) = y = (3/1) (-13/1) = y = -39 So, the other number is -39...
Read More →By what numbers should we multiply
Question: By what numbers should we multiply -15/20 so that the product may be -5/7? Solution: Let us assume the other number be y. Given, product of two rational number = -5/7 One number = -15/20 Then, = y (-15/20) = -5/7 = y = (-5/7)/ (-15/20) = y = (-5/7) (-20/15) = y = (-1/7) (-20/3) = y = -20/21 So, the other number is -20/21...
Read More →The product of two rational numbers is -14/27.
Question: The product of two rational numbers is -14/27. If one of the numbers be 7/9, find the other. Solution: Let us assume the other number be y. Given, product of two rational number = -14/27 One number = 7/9 Then, = y (7/9) = -14/27 = y = (-14/27)/ (7/9) = y = (-14/27) (9/7) = y = (-2/3) (1/1) = y = -2/3 So, the other number is -2/3...
Read More →Find the real values of x and y for which:
Question: Find the real values of x and y for which: $\frac{(1+i) x-2 i}{(3+i)}+\frac{(2-3 i) y+i}{(3-i)}=i$ Solution: Consider, $\frac{(1+i) x-2 i}{3+i}+\frac{(2-3 i) y+i}{3-i}=i$ $=\frac{x+x i-2 i}{3+i}+\frac{2 y-3 i y+i}{3-i}=i$ Taking LCM $\Rightarrow \frac{(x+x i-2 i)(3-i)+(2 y-3 i y+i)(3+i)}{(3+i)(3-i)}=i$ $\Rightarrow \frac{3 x+3 x i-6 i-x i-x i^{2}+2 i^{2}+6 y-9 i y+3 i+2 i y-3 i^{2} y+i^{2}}{(3)^{2}-(i)^{2}}=i$ Putting $i^{2}=-1$ $\Rightarrow \frac{3 x+2 x i-6 i-x(-1)+2(-1)+6 y-7 i y+3 ...
Read More →Arrange the numbers ¼,
Question: Arrange the numbers , 13/16, 5/8 in the descending order. Solution: The LCM of the denominators 4, 16 and 8 is 16 = [(14)/ (44)] = (4/16) (13/16) = [(131)/ (161)] = (13/16) (5/8) = [(52)/ (82)] = (10/16) Now, 13 10 4 ⇒ (13/16) (10/16) (4/16) Hence, (13/16) (5/8) () Descending order 13/16, 5/8, 1/4...
Read More →Find the multiplicative inverse of
Question: Find the multiplicative inverse of (i) $-1 \frac{1}{8}$ (ii) $3 \frac{1}{3}$ Solution: (i) The given numbercan be written as = -9/8 The multiplicative inverse = -8/9 (ii) The given numbercan be written as = 10/3 The multiplicative inverse = 3/10...
Read More →Construct a quadrilateral PQRS in which PQ = 4.2 cm,
Question: Construct a quadrilateralPQRSin whichPQ= 4.2 cm,PQR= 60,QPS= 120,QR= 5 cm andPS= 6 cm. Solution: Steps of construction: Step 1: Take $P Q=4.2 \mathrm{~cm}$ Step 2: Make $\angle X P Q=120^{\circ}, \angle Y Q P=60^{\circ}$ Step 3: Cut an arc of length 5 cm from pointQ. Name that point asR. Step 4: FromP,make an arc of length 6 cm. Name that point as S. Step 5: JoinPandS. Thus,PQRSis a quadrilateral....
Read More →Write 'T' for true and 'F' for false for each of the following:
Question: Write 'T' for true and 'F' for false for each of the following: (i) The diagonals of a parallelogram are equal. (ii) The diagonals of a rectangle are perpendicular to each other. (iii) The diagonals of a rhombus bisect each other at right angles. (iv) Every rhombus is a kite. Solution: (i) FThe diagonals of a parallelogram need not be equal in length.(ii) FThe diagonals of a rectangle are not perpendicular to each other.(iii) T(iv) TAdjacent sides of a kite are equal and this is also t...
Read More →Name the property used in each of the following.
Question: Name the property used in each of the following. (i) (-7/4) (-3/4) = (-3/5) (-7/11) (ii) (-2/3) [(3/4) + (-)] = [(-2/3) (3/4)] + [(-2/3) ()] (iii) (1/3) + [(4/9) + (-4/3)] = [(1/3) + (4/9)] + [-4/3] (iv) (-2/7) + 0 = 0 + (-2/7) = (-2/7) (v) (3/8) 1 = 1 (3/8) = (3/8) Solution: (i) (-7/4) (-3/4) = (-3/5) (-7/11) The above rational number is in the form of Commutative property over multiplication. (ii) (-2/3) [(3/4) + (-)] = [(-2/3) (3/4)] + [(-2/3) ()] The above rational number is in the...
Read More →Fill in the blanks.
Question: Fill in the blanks. (i) Each interior angle of a regular octagon is (.........). (ii) The sum of all interior angles of a regular hexagon is (.........). (iii) Each exterior angle of a regular polygon is 60. This polygon is a ......... (iv) Each interior angle of a regular polygon is 108. This polygon is a ......... (v) A pentagon has ......... diagonals. Solution: (i) Octagon has 8 sides. $\therefore$ Interior angle $=\frac{180^{\circ} n-360^{\circ}}{n}$ Int erior angle $=\frac{\left(...
Read More →Find the real values of x and y for which:
Question: Find the real values of x and y for which: $\frac{(x+3 i)}{(2+i y)}=(1-i)$ Solution: Given: $\frac{x+3 i}{2+i y}=(1-i)$ $\Rightarrow x+3 i=(1-i)(2+i y)$ $\Rightarrow x+3 i=1(2+i y)-i(2+i y)$ $\Rightarrow x+3 i=2+i y-2 i-i^{2} y$ $\Rightarrow x+3 i=2+i(y-2)-(-1) y\left[i^{2}=-1\right]$ $\Rightarrow x+3 i=2+i(y-2)+y$ $\Rightarrow x+3 i=(2+y)+i(y-2)$ Comparing the real parts, we get $x=2+y$ $\Rightarrow x-y=2 \ldots$ (i) Comparing the imaginary parts, we get $3=y-2$ $\Rightarrow y=3+2$ $\...
Read More →Tell which property allows you to compare
Question: Tell which property allows you to compare (2/3) [ (5/7)] and [(2/3) (5/7)] Solution: (2/3) [ (5/7)] and [(2/3) (5/7)] this can be compared with associative property and commutative property....
Read More →Fill in the blanks.
Question: Fill in the blanks. For a regular polygon ofnsides, we have: (i) Sum of all exterior angles = ......... (ii) Sum of all interior angles = ......... Solution: (i) Sum of all exterior angles of a regular polygon is $360^{\circ}$. (ii) Sum of all interior angles of a polygon is $(n-2) \times 180^{\circ}$, where $n$ is the number of sides....
Read More →Find the real values of x and y for which:
Question: Find the real values of x and y for which: $(1+i) y^{2}+(6+i)=(2+i) x$ Solution: Given: $(1+i) y^{2}+(6+i)=(2+i) x$ Consider, $(1+i) y^{2}+(6+i)=(2+i) x$ $\Rightarrow y^{2}+i y^{2}+6+i=2 x+i x$ $\Rightarrow\left(y^{2}+6\right)+i\left(y^{2}+1\right)=2 x+i x$ Comparing the real parts, we get $y^{2}+6=2 x$ $\Rightarrow 2 x-y^{2}-6=0 \ldots(i)$ Subtracting the eq. (ii) from (i), we get $2 x-y^{2}-6-\left(x-y^{2}-1\right)=0$ $\Rightarrow 2 x-y^{2}-6-x+y^{2}+1=0$ $\Rightarrow x-5=0$ $\Righta...
Read More →A mother and her two daughters got a room constructed for ₹ 62,000.
Question: A mother and her two daughters got a room constructed for ₹ 62,000. The elder daughter contributes 3/8 of her mothers contribution while the younger daughter contributes of her mothers share. How much do the three contribute individually? Solution: From the question it is given that, A mother and her two daughters got a room constructed for = ₹ 62,000 Let us assume mothers share be x, Then, The elder daughters contribute = 3/8 of her mothers share = 3/8 x The younger daughters contribu...
Read More →Fill in the blanks.
Question: Fill in the blanks. For a convex polygon ofnsides, we have: (i) Sum of all exterior angles = ......... (ii) Sum of all interior angles = ......... (iii) Number of diagonals = ......... Solution: (i) Sum of all exterior angles $=360^{\circ}$ (ii) Sum of all interior angles $=(n-2) \times 180^{\circ}$ (iii) Number of diagonals $=\frac{n(n-3)}{2}$...
Read More →Huma, Hubna and Seema received a total of ₹ 2,016
Question: Huma, Hubna and Seema received a total of ₹ 2,016 as monthly allowance from their mother such that Seema gets of what Huma gets and Hubna getstimes Seemas share. How much money do the three sisters get individually? Solution: From the question it is given that, Total monthly allowance received by Huma, Hubna and Seem = ₹ 2,016 from their mother Seema gets allowance = of Humas share Hubna gets allowance =of Seemas share = 5/3 of Seemas share = 5/3 of of Humas share [∵ given] = 5/3 of Hu...
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: Each interior angle of a polygon is 135. How many sides does it have?(a) 10 (b) 8 (c) 6 (d) 5 Solution: (b) 8 Interior angle $=\frac{180(n-2)}{n}$ $\Rightarrow 135=\frac{180(n-2)}{n}$ $\Rightarrow 135 n=180 n-360$ $\Rightarrow 360=180 n-135 n$ $\Rightarrow n=8$ It has 8 sides....
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