In Indus valley Civilisation
Question: In Indus valley Civilisation (about $3000 \mathrm{BC}$ ), the bricks used for construction work were having dimensions in the ratio (a) $1: 3: 4$ (b) $4: 2: 1$ (c) $4: 4: 1$ (d) $4: 3: 2$ Solution: (b) In Indus valley Civilisation, the bricks used for construction work were having dimensions in the ratio length: breadth : thickness $=4: 2: 1$....
Read More →Boundaries of surfaces are
Question: Boundaries of surfaces are (a) surfaces (b) curves (c) lines (d) points Solution: (b) The boundaries of surfaces are curves....
Read More →Boundaries of solids are
Question: Boundaries of solids are (a) surfaces (b) curves (c) lines (d) points Solution: (b) The boundaries of surfaces are curves....
Read More →Multiply:
Question: Multiply: $\left(\frac{x}{7}+\frac{x^{2}}{2}\right) b y\left(\frac{2}{5}+\frac{9 x}{4}\right)$ Solution: To multiply the expressions, we will use the distributive law in the following way: $\left(\frac{x}{7}+\frac{x^{2}}{2}\right) b y\left(\frac{2}{5}+\frac{9 x}{4}\right)$ $=\frac{x}{7}\left(\frac{2}{5}+\frac{9 x}{4}\right)+\frac{x^{2}}{2}\left(\frac{2}{5}+\frac{9 x}{4}\right)$ $=\frac{2 x}{35}+\frac{9 x^{2}}{28}+\frac{x^{2}}{5}+\frac{9 x^{3}}{8}$ $=\frac{2 x}{35}+\left(\frac{45+28}{14...
Read More →The total number of propositions
Question: The total number of propositions in The Elements are (a)465 (b)460 (c)13 (d)55 Solution: (a)The statements that can be proved are called propositions or theorems. Euclid deduced 465 propositions in a logical chain using his axioms, postulates, definitions and theorems....
Read More →Multiply:
Question: Multiply:(2x2y2 5xy2) by (x2y2) Solution: To multiply, we will use distributive law as follows: (2x2y2 5xy2) by (x2y2) $\left(2 x^{2} y^{2}-5 x y^{2}\right)\left(x^{2}-y^{2}\right)$ $=2 x^{2} y^{2}\left(x^{2}-y^{2}\right)-5 x y^{2}\left(x^{2}-y^{2}\right)$ $=2 x^{4} y^{2}-2 x^{2} y^{4}-5 x^{3} y^{2}+5 x y^{4}$ Thus, the answer is $2 x^{4} y^{2}-2 x^{2} y^{4}-5 x^{3} y^{2}+5 x y^{4}$....
Read More →Euclid divided his famous treatise
Question: Euclid divided his famous treatise The Elements into (a)13 chapters (b)12 chapters (c)11 chapters (d)9 chapters Solution: (a)Euclid divided his famous treatise The Elements into 13 chapters....
Read More →Multiply: (0.8a − 0.5b) by (1.5a − 3b)
Question: Multiply:(0.8a 0.5b) by (1.5a 3b) Solution: To multiply, we will use distributive law as follows: (0.8a 0.5b) by (1.5a 3b) $=0.8 a(1.5 a-3 b)-0.5 b(1.5 a-3 b)$ $=1.2 a^{2}-2.4 a b-0.75 a b+1.5 b^{2}$ $=1.2 a^{2}-3.15 a b+1.5 b^{2}$ Thus, the answer is $1.2 a^{2}-3.15 a b+1.5 b^{2}$....
Read More →The lengths of the two sides of a right triangle containing the right angle differ by 2 cm.
Question: The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the area of the triangle is 24 cm2, find the perimeter of the triangle. Solution: Given: Area of triangle $=24 \mathrm{~cm}^{2}$ Let the sides beaandb, whereais the height andb is the base oftriangle. $a-b=2 \mathrm{~cm}$ $a=2+b \ldots \ldots .(1)$ Area of triangle $=\frac{1}{2} \times b \times h$ $\Rightarrow 24=\frac{1}{2} \times b \times(2+b)$ $\Rightarrow 48=b+\frac{1}{2} b^{2}$ $\Rightar...
Read More →The number of dimensions,
Question: The number of dimensions, a point has (a)0 (b)1 (c)2 (d)3 Solution: (a)A point is that which has no part i.e., no length, no breadth and no height. So, it has no dimension....
Read More →Multiply: [−3d + (−7f)] by (5d + f)
Question: Multiply:[3d+ (7f)] by (5d+f) Solution: To multiply, we will use distributive law as follows: [3d+ (7f)] by (5d+f) $=(-3 d)(5 d+f)+(-7 f)(5 d+f)$ $=\left(-15 d^{2}-3 d f\right)+\left(-35 d f-7 f^{2}\right)$ $=-15 d^{2}-3 d f-35 d f-7 f^{2}$ $=-15 d^{2}-38 d f-7 f^{2}$ Thus, the answer is $-15 d^{2}-38 d f-7 f^{2}$....
Read More →Multiply:
Question: Multiply:(x2+y2) by (3a+ 2b) Solution: To multiply, we will use distributive law as follows: $\left(x^{2}+y^{2}\right)(3 a+2 b)$ $=x^{2}(3 a+2 b)+y^{2}(3 a+2 b)$ $=3 a x^{2}+2 b x^{2}+3 a y^{2}+2 b y^{2}$ Thus, the answer is $3 a x^{2}+2 b x^{2}+3 a y^{2}+2 b y^{2}$....
Read More →The number of dimensions, a surface has
Question: The number of dimensions, a surface has (a) 1 (b) 2 (c) 3 (d) 0 Solution: (b) Boundaries of a solid are called surfaces. A surface (plane) has only length and breadth. So, it has two dimensions....
Read More →Multiply:
Question: Multiply:(x6y6) by (x2+y2) Solution: To multiply, we will use distributive law as follows: $\left(x^{6}-y^{6}\right)\left(x^{2}+y^{2}\right)$ $=x^{6}\left(x^{2}+y^{2}\right)-y^{6}\left(x^{2}+y^{2}\right)$ $=\left(x^{8}+x^{6} y^{2}\right)-\left(y^{6} x^{2}+y^{8}\right)$ $=x^{8}+x^{6} y^{2}-y^{6} x^{2}-y^{8}$ Thus, the answer is $x^{8}+x^{6} y^{2}-y^{6} x^{2}-y^{8}$....
Read More →The number of dimensions,
Question: The number of dimensions, a solid has (a)1 (b)2 (c)3 (d)0 Solution: (c)A solid has shape, size, position and can be moved from one place to another. So, solid has three dimensions, e.g., Cuboid....
Read More →The difference between the sides at right angle in a right-angled triangle is 7 cm.
Question: The difference between the sides at right angle in a right-angled triangle is 7 cm. The area of the triangle is 60 cm2. Find its perimeter. Solution: Given: Area of the triangle $=60 \mathrm{~cm}^{2}$ Let the sides of the triangle bea,bandc,whereais the height,bis the base andcis hypotenuse of the triangle. $a-b=7 \mathrm{~cm}$ $a=7+b \ldots \ldots .(1)$ Area of triangle $=\frac{1}{2} \times b \times h$ $\Rightarrow 60=\frac{1}{2} \times b \times(7+b)$ $\Rightarrow 120=7 b+b^{2}$ $\Rig...
Read More →The three steps from solids to points are
Question: The three steps from solids to points are (a)solids-surfaces-lines-points (b)solids-lines-surfaces-points (c)lines-points-surfaces-solids (d)lines-surfaces-points-solids Solution: (a) The three steps from solids to points are solids-surfaces-lines-points....
Read More →Multiply:
Question: Multiply: $\left(\frac{3}{5} x+\frac{1}{2} y\right)$ by $\left(\frac{5}{6} x+4 y\right)$ Solution: To multiply, we will use distributive law as follows: $\left(\frac{3}{5} x+\frac{1}{2} y\right)\left(\frac{5}{6} x+4 y\right)$ $=\frac{3}{5} x\left(\frac{5}{6} x+4 y\right)+\frac{1}{2} y\left(\frac{5}{6} x+4 y\right)$ $=\frac{1}{2} x^{2}+\frac{12}{5} x y+\frac{5}{12} x y+2 y^{2}$ $=\frac{1}{2} x^{2}+\left(\frac{144+25}{60}\right) x y+2 y^{2}$ $=\frac{1}{2} x^{2}+\frac{169}{60} x y+2 y^{2}...
Read More →The force exerted to pull a cart is directly
Question: The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph, the force required when the acceleration produced is (i)5 ms-2 (ii)6 ms-2 Thinking Process (i)Firstly, make a proportionality equation in terms of force (F) and acceleration (a) i.e., F a. (ii)Secondly, write the proportional equation ...
Read More →The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm.
Question: The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm. Find the area of the triangle. Solution: The perimeter of a right-angled triangle = 40 cmTherefore ,a+b+c= 40 cmHypotenuse= 17 cmTherefore,c= 17 cma+b+c= 40 cm $\Rightarrow a+b+17=40$ $\Rightarrow a+b=23$ $\Rightarrow b=23-a$ ..........(i) Now, using Pythagoras' theorem, we have: $a^{2}+b^{2}=c^{2}$ $\Rightarrow a^{2}+(23-a)^{2}=17^{2}$ $\Rightarrow a^{2}+529-46 a+a^{2}=289$ $\Rightarrow 2 a^{2}-46 a+529-289=...
Read More →Multiply:
Question: Multiply:(3x2+y2) by (2x2+ 3y2) Solution: To multiply, we will use distributive law as follows: $\left(3 x^{2}+y^{2}\right)\left(2 x^{2}+3 y^{2}\right)$ $=3 x^{2}\left(2 x^{2}+3 y^{2}\right)+y^{2}\left(2 x^{2}+3 y^{2}\right)$ $=6 x^{4}+9 x^{2} y^{2}+2 x^{2} y^{2}+3 y^{4}$ $=6 x^{4}+11 x^{2} y^{2}+3 y^{4}$ Thus, the answer is $6 x^{4}+11 x^{2} y^{2}+3 y^{4}$....
Read More →If the temperature of a liquid can be
Question: If the temperature of a liquid can be measured in kelvin units as xK or in fahrenheit units as yF, the relation between the two systems of measurement of temperature is given by the linear equation. $y=\frac{9}{5}(x-273)+32$ (i)find the temperature of the liquid in fahrenheit, if the temperature of the liquid is 313K. (ii)If the temperature is 158F, then find the temperature in kelvin. Solution: Given relation is $y=\frac{9}{5}(x-273)+32$ $\ldots$ (i) (i) Given, $x=313^{\circ} \mathrm{...
Read More →The perimeter of a triangular field is 540 m, and its sides are in the ratio 25:17:12.
Question: The perimeter of a triangular field is 540 m, and its sides are in the ratio25:17:12. Find the area of the field. Also, find the cost of ploughing thefield at₹40 per 100 m2. Solution: Let the sides of the triangular field be $25 x, 17 x$ and $12 x$. As, perimeter $=540 \mathrm{~m}$ $\Rightarrow 25 x+17 x+12 x=540$ $\Rightarrow 54 x=540$ $\Rightarrow x=\frac{540}{54}$ $\Rightarrow x=10$ So, the sides are $250 \mathrm{~m}, 170 \mathrm{~m}$ and $120 \mathrm{~m}$. Now, semi $-$ perimeter, ...
Read More →Multiply: (a − 1) by
Question: Multiply:(a 1) by (0.1a2+ 3) Solution: To multiply, we will use distributive law as follows:b $(a-1)\left(0.1 a^{2}+3\right)$ $=0.1 a^{2}(a-1)+3(a-1)$ $=0.1 a^{3}-0.1 a^{2}+3 a-3$ Thus, the answer is $0.1 a^{3}-0.1 a^{2}+3 a-3$....
Read More →Multiply: (7x + y) by (x + 5y)
Question: Multiply: (7x + y) by (x + 5y) Solution: To multiply, we will use distributive law as follows: $(7 x+y)(x+5 y)$ $=7 x(x+5 y)+y(x+5 y)$ $=7 x^{2}+35 x y+x y+5 y^{2}$ $=7 x^{2}+36 x y+5 y^{2}$ Thus, the answer is $7 x^{2}+36 x y+5 y^{2}$....
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