81279 + Interview Questions in Mathematics QA in Mathematics Page 54 InterviewSolution

2651.	1. If HCF (a, b) 12 and a x b 1800, then find LCM (a, b).2. If the roots of th
Answer»

Discussion

2652.	(A) KBirds are flying in the pattern like 1 in the first row, 3 in the eand so on. Making total 20 rows as per the figure given belo itotal number of birds.43.) A student named Akash is observing birds tlying in the sky nate second(B) 400(C) 40(D) 200(A) 39
Answer» This is an APwhere a= 1 d= 2n= 20Sn= n/2(2a+(n-1)d) = 10(2+38) = 400 thanks

2652.

(A) KBirds are flying in the pattern like 1 in the first row, 3 in the eand so on. Making total 20 rows as per the figure given belo itotal number of birds.43.) A student named Akash is observing birds tlying in the sky nate second(B) 400(C) 40(D) 200(A) 39

Answer»

This is an APwhere a= 1 d= 2n= 20Sn= n/2(2a+(n-1)d)

= 10(2+38)

= 400

thanks

Discussion

2653.	ththe same as the Sum otiS Zer0
Answer» m/2 * (2a + (m-1)d) = n/2 * (2a + (n-1)d) we get m(2a + (m-1)d) - n(2a+ (n-1)d) = 0 2am + m^2d - md -2an -n^2d +nd =0 2a(m-n) + (m^2 - n^2)d -(m - n)d =0 2a(m-n) + ( (m + n) (m- n) ) d - (m - n )d = 0 taking (m-n) common 2a + ( m + n -1) d = 0------------ 1 S m+n = m+n/2( 2a + (m+n -1)d we know that 2a + (m+n)d is 0 from eqn. 1 therefore S m+n = 0

2653.

ththe same as the Sum otiS Zer0

Answer»

m/2 * (2a + (m-1)d) = n/2 * (2a + (n-1)d)

we get

m(2a + (m-1)d) - n(2a+ (n-1)d) = 0

2am + m^2d - md -2an -n^2d +nd =0

2a(m-n) + (m^2 - n^2)d -(m - n)d =0

2a(m-n) + ( (m + n) (m- n) ) d - (m - n )d = 0

taking (m-n) common

2a + ( m + n -1) d = 0------------ 1

S m+n = m+n/2( 2a + (m+n -1)d

we know that 2a + (m+n)d is 0 from eqn. 1

therefore S m+n = 0

Discussion

2654.	Understanding Square and Cube Roots-Item 6229Which is the best approximation of the yalue ot V730727432.190
Answer» option A because the cube root of 9

Discussion

2655.	the roots of the equation 4x4 - 2x + = = Oby the method of completing the square.16. Find the roots of th
Answer» 4x^2 - 2x + 1/4 = 0 16x^2 - 8x + 1 = 0 (4x)^2 + (1)^2 - 21(4x) = 0 (4x - 1)^2 = 0 (4x - 1)(4x - 1) = 0 x = 1/4, 1/4 Therefore,Given equation have two equal roots 1/4 and 1/4

2655.

the roots of the equation 4x4 - 2x + = = Oby the method of completing the square.16. Find the roots of th

Answer»

4x^2 - 2x + 1/4 = 0

16x^2 - 8x + 1 = 0

(4x)^2 + (1)^2 - 2*1*(4x) = 0

(4x - 1)^2 = 0

(4x - 1)(4x - 1) = 0

x = 1/4, 1/4

Therefore,Given equation have two equal roots 1/4 and 1/4

Discussion

2656.	c which is thde 8.7: Solve : (x+ y)2 =a2n : Put x + y = z, Different, ot;
Answer» 8.7)1 2 3

2656.

c which is thde 8.7: Solve : (x+ y)2 =a2n : Put x + y = z, Different, ot;

Answer»

8.7)1

2

3

Discussion

2657.	1s. If the mi srn ot an APand the th temithen prove the tswherc
Answer» Given that, mth term=1/n and nth term=1/m.then ,let a and d be the first term and the common difference of the A.P.so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2).subtracting equation (1) by (2) we get,md-d-nd+d=1/n-1/m=>d(m-n)=m-n/mn=>d=1/mn. again if we put this value in equation (1) or (2) we get, a=1/mn.then, let A be the mnth term of the APa+(mn-1)d=1/mn+1+(-1/mn)=1 hence proved.

Discussion

2658.	In the given figure, ABCD is a rhombus. Are Î ADC and Î ABCcongruent? Give reasons.(g)
Answer»

Discussion

2659.	3 if mth and nth terms ot an A.P. be andI respectively, then show that its (mn)th term is 1.
Answer» Given that, mth term=1/n and nth term=1/m. then ,let a and d be the first term and the common difference of the A.P. so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2). subtracting equation (1) by (2) we get,md-d-nd+d=1/n-1/m=>d(m-n)=m-n/mn=>d=1/mn. again if we put this value in equation (1) or (2) we get, a=1/mn. then, let A be the mnth term of the AP a+(mn-1)d=1/mn+1+(-1/mn)=1 hence proved. Like my answer if you find it useful!

2659.

3 if mth and nth terms ot an A.P. be andI respectively, then show that its (mn)th term is 1.

Answer»

Given that, mth term=1/n and nth term=1/m.

then ,let a and d be the first term and the common difference of the A.P.

so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2).

subtracting equation (1) by (2) we get,md-d-nd+d=1/n-1/m=>d(m-n)=m-n/mn=>d=1/mn.

again if we put this value in equation (1) or (2) we get, a=1/mn.

then, let A be the mnth term of the AP

a+(mn-1)d=1/mn+1+(-1/mn)=1

hence proved.

Like my answer if you find it useful!

Discussion

2660.	IfAD = x, DB =x-2, AE = x + 2 and EC = x-1,find the value of Y
Answer»

Discussion

2661.	FIND(K)1äštH E EQUATIONHASEQU ALroots(k+4) x^{2}+(k+1) x+1=0
Answer»

Discussion

2662.	10Prove that in a right triangle, the square of the hypotenuse is equal to sum of squares of other two sidesUsing the above result, prove that, in rhombus ABC25.AB AC2BD
Answer» Here, We see that, AO = 1/2AC BO = 1/2BD In triangle ABO, According to Pythagoras theorem, AO² + BO² = AB² (1/2AC)² + (1/2BD)² = AB² 1/4AC² + 1/4BD² = AB² 1/4 ( AC² + BD²) = AB² (AC² + BD²) = 4AB² [ Hence proved ] Like my answer if you find it useful!

2662.

10Prove that in a right triangle, the square of the hypotenuse is equal to sum of squares of other two sidesUsing the above result, prove that, in rhombus ABC25.AB AC2BD

Answer»

Here, We see that, AO = 1/2AC BO = 1/2BD

In triangle ABO,

According to Pythagoras theorem,

AO² + BO² = AB²

(1/2AC)² + (1/2BD)² = AB²

1/4AC² + 1/4BD² = AB²

1/4 ( AC² + BD²) = AB²

(AC² + BD²) = 4AB²

[ Hence proved ]

Like my answer if you find it useful!

Discussion

2663.	25. If the equation x2 + 5kx + 16 = 0 has no real roots th
Answer»

Discussion

2664.	20. Let z, and z be th roots of unity which aubtend a rightangle at the origin, theri 'n' must be of the form(a) 4k +1 (b) 4k2(c) 4k +3 (d) 4k
Answer» why do u get i in second step?

Discussion

2665.	IUNI UI CUVUUUFind the area of the base of each shape.C.A.12 cm14 cm71cm9 cm3.com4 cm
Answer» A ) area=36cm² B)area=18cm² C) area=88cm²is the best answer A.area=l×b×h =14×4×9 =504sq.cmB.area=l×b×h =12×3×6 =216sq.cmC.area=l×b×h =6×8×11 =528sq.cm

2665.

IUNI UI CUVUUUFind the area of the base of each shape.C.A.12 cm14 cm71cm9 cm3.com4 cm

Answer»

A ) area=36cm² B)area=18cm² C) area=88cm²is the best answer

A.area=l×b×h =14×4×9 =504sq.cmB.area=l×b×h =12×3×6 =216sq.cmC.area=l×b×h =6×8×11 =528sq.cm

Discussion

2666.	Simplify :\frac{\left(x^{a+b}\right)^{3}\left(x^{b+c}\right)^{3}\left(x^{c+a}\right)^{3}}{\left(x^{a} x^{b} x^{c}\right)^{6}}, x \neq 0
Answer»

Discussion

2667.	\frac{\left(a^{2}-b^{2}\right)^{3}+\left(b^{2}-c^{2}\right)^{3}+\left(c^{2}-a^{2}\right)^{3}}{(a-b)^{3}+(b-c)^{3}+(c-a)^{3}}
Answer»

Discussion

2668.	\frac { \left( b ^ { 2 } - c ^ { 2 } \right) ^ { 3 } + \left( c ^ { 2 } - a ^ { 2 } \right) ^ { 3 } + \left( a ^ { 2 } - b ^ { 2 } \right) ^ { 3 } } { ( b - c ) ^ { 3 } + ( c - a ) ^ { 3 } + ( a + b ) ^ { 3 } }
Answer»

Discussion

2669.	\frac{\left(b^{2}-c^{2}\right)^{3}+\left(c^{2}-a^{2}\right)^{3}+\left(a^{2}-b^{2}\right)^{3}}{(b-c)^{3}+(c-a)^{3}+(a-b)^{3}}
Answer»

Discussion

2670.	\left( \frac { x ^ { a + b } } { x ^ { c } } \right) ^ { a - b } \cdot \left( \frac { x ^ { b + c } } { x ^ { a } } \right) ^ { b - c } \cdot \left( \frac { x ^ { c + a } } { x ^ { b } } \right) ^ { c - a }
Answer»

Discussion

2671.	\left(\frac{x^{a}}{x^{b}}\right)^{a^{2}+a b+b^{2}}\left(\frac{x^{b}}{x^{c}}\right)^{b^{2}+b c+c^{2}}\left(\frac{x^{c}}{x^{a}}\right)^{c^{2}+a c+a^{2}}
Answer»

Discussion

2672.	\left(\frac{x^{a}}{x^{b}}\right)^{a^{2}+a b+b^{2}}\left(\frac{x^{b}}{x^{c}}\right)^{b^{2}+h c+c^{2}}\left(\frac{x^{c}}{x^{a}}\right)^{c^{2}+a c+a^{2}}
Answer» same base so

Discussion

2673.	\begin{array}{l}{\text { Simplify: }} \\ {\left(\frac{X^{4}}{X^{b}}\right)^{a-b}\left(\frac{X^{b}}{X^{-c}}\right)^{b-c}\left(\frac{X^{c}}{X^{-u}}\right)^{c-a}}\end{array}
Answer»

Discussion

2674.	Find the value of a, whichpoints Q(-5.4) and R(-1,0).or which point P(,2) is the mid-point of the line segment joe a
Answer»

Discussion

2675.	6. In Fig 5.10, if AC BD, then prove thut AB CD
Answer» AC = BDdeduct BC from bothso we getAC - BC= BD - BCAB = CD

Discussion

2676.	9. In a AABC, D and E are points on the sides AB and AC respectively, such thattheADx EC AEx DB. Prove that DE \| BC.Jo
Answer»

Discussion

2677.	In a Rhombus ABC shous thetan
Answer»

Discussion

2678.	1) There are forty-five children in the classroom, each student will get twenty-seven pencilsand thirty-seven erasers. How many pencils will the teacher have to give out?
Answer» for one student got pencils=27for 45 children =2745 =12151215 pencils is the correct answer 1 child = 27 pencilsSo,45 children = 27×45 = 1215 one student got on pencils=27; for 45 children = 27×45=1215 2745=1215is the answer

2678.

1) There are forty-five children in the classroom, each student will get twenty-seven pencilsand thirty-seven erasers. How many pencils will the teacher have to give out?

Answer»

for one student got pencils=27for 45 children =27*45 =12151215 pencils is the correct answer

1 child = 27 pencilsSo,45 children = 27×45 = 1215

one student got on pencils=27; for 45 children = 27×45=1215

27*45=1215is the answer

Discussion

2679.	EXERCISE 3.1. Aftab tells his daughter, "Seven years ago, I was seven times as old as youethatAlso, three years from now, I shall be three times as old as you will be equashointeresting?) Represent this situation algebraically and graphicallyget
Answer» sol.let the present age of aftab be 'x' and that of her daughter be 'y' seven years ago age of aftab=x-7 age of his

Discussion

2680.	If three times the larger of two numbers is divided by the smaller one, we get 4 as thqu8.otient and 3 as the remainder. Also, if seven times the smialler number is divided by theget 5 as the quotient and 1 as the renainder Find the numbers.
Answer»

Discussion

2681.	ich we add 8 125 times theswe get thousandOKThere are seven bume membe57L13 itid 23 golangehese brume numbers anthe seven squars so thatthe evous and the dignaagnae
Answer» Send well questions plz send the question again please send the question again please

2681.

ich we add 8 125 times theswe get thousandOKThere are seven bume membe57L13 itid 23 golangehese brume numbers anthe seven squars so thatthe evous and the dignaagnae

Answer»

Send well questions plz

send the question again please

Discussion

2682.	If three times the larger of two numbers is divided by the smaller one, we get 4 as thequotient and 3 as the remainder. Also, if seven times the smaller number is divided by thelarger one, we get 5 as the quotient and 1 as the renainder: Find the numbers.8.
Answer»

Discussion

2683.	10. Seven friends bought 58.8 metres of clothat a sale and shared it equally. How muchdid each get?
Answer» Total length of cloth bought=58.8 metresThis cloth is divided equally between seven friends.∴Length that each did get=58.8/7=8.4 metres 7friends=58.8m 1friend=58.8÷7m 1friend=8.4m

2683.

10. Seven friends bought 58.8 metres of clothat a sale and shared it equally. How muchdid each get?

Answer»

Total length of cloth bought=58.8 metresThis cloth is divided equally between seven friends.∴Length that each did get=58.8/7=8.4 metres

7friends=58.8m

1friend=58.8÷7m

1friend=8.4m

Discussion

2684.	2.The breadth of a rectangle is 3 less than the length. If both length and breadth are reduced by3 units, the area of the rectangle reduces by 176 sq, units. Find the dimensions' of the'origithalrectangle.HOTS
Answer» Thanks

Discussion

2685.	(Idioms & Proverbs)
Answer» Themeaningof anidiomis different from the actualmeaningof the words used. “An apple a day keeps the doctor away” is aproverb.Proverbsare old but familiarsayingsthat usually give advice. Bothidioms and proverbsare part of our daily speech.

Discussion

2686.	Jo
Answer» 14=(7x/10)-7(7x/10)=14+7(7x/10)=217x=210x=30

Discussion

2687.	19-79sinÂŽ _Jo
Answer» Sinx/√xHencesinx√x/xnow lim x--->0 sinx/x√x=1*0=0by sandwich theorem

Discussion

2688.	Jo+J6+6+..
Answer» thanks

Discussion

2689.	= ० Jo onea [एपीणएएत 7
Answer»

Discussion

2690.	eBle Jo-i2 2B
Answer» 3V2/V3+ V6 - 4V3/ V6+ V2 + V6/ V2+V3= 3V2 × V3- V6/ V+ V6 - 4V3/ V6+ V2 x V6- V2/ V6-V2 + V6/V2+V3 x V2-V3/V2-V3 = 3V2×V3-V6/3-6 - 4V3( V6-V2)/6-3 +V6( V2-V3)/2-3=3V6-V6/-3 -4V3(V6-V2)/6-2 + V6( V2-V3)/2-3=3/3-4( V18-V6)/4+V6(V2-V3)/-1= 1 -4( V18-V6)/4+2V3+V18=1-(V12)+V12+V18=1+V18=1+3V2 G.A.A. 16 and Multiplication 3072 If you have L.A.A.Find out 3V2/V3+V6=3V2(V3-V6)/ ( V3-V6)^2=3V2( V3-V6)/3-6=3V6-3V12/-3=3V6/ -3=V6________(1), 4V3/ V6+ V2=4V3(V6-V2)/6-2=4(V18-V6)/4=V18-V6=3V2-V6/4_____(2), V6/ V2+V3= V6(V2-V3)/-1=V12-V18/-1=2V3-3V2/-1=3V2-2V3_____(3); V6-3V2/4+V6/4-3V2+2V3=V6+6/4+2V3=4V6

2690.

eBle Jo-i2 2B

Answer»

3V2/V3+ V6 - 4V3/ V6+ V2 + V6/ V2+V3= 3V2 × V3- V6/ V+ V6 - 4V3/ V6+ V2 x V6- V2/ V6-V2 + V6/V2+V3 x V2-V3/V2-V3 = 3V2×V3-V6/3-6 - 4V3( V6-V2)/6-3 +V6( V2-V3)/2-3=3V6-V6/-3 -4V3(V6-V2)/6-2 + V6( V2-V3)/2-3=3/3-4( V18-V6)/4+V6(V2-V3)/-1= 1 -4( V18-V6)/4+2V3+V18=1-(V12)+V12+V18=1+V18=1+3V2

G.A.A. 16 and Multiplication 3072 If you have L.A.A.Find out

3V2/V3+V6=3V2(V3-V6)/ ( V3-V6)^2=3V2( V3-V6)/3-6=3V6-3V12/-3=3V6/ -3=V6________(1), 4V3/ V6+ V2=4V3(V6-V2)/6-2=4(V18-V6)/4=V18-V6=3V2-V6/4_____(2), V6/ V2+V3= V6(V2-V3)/-1=V12-V18/-1=2V3-3V2/-1=3V2-2V3_____(3); V6-3V2/4+V6/4-3V2+2V3=V6+6/4+2V3=4V6

Discussion

2691.	Find the volume of a cuboid Whose lenoti10 m width4mand heigh200 m
Answer»

Discussion

2692.	Ir a+bi 4 and abthen the vetue of a h
Answer» ab=-12a+b=4take square both the sidesa^2+2ab+b^2=16so a^2+b^2=16-2ab=16+24=40a^-2ab+b^2=(a-b)^240-2(-12)=40+24=64=8^2so a-b=8

Discussion

2693.	plastic box 1.5 m long. 1.25 m wide and 6S cm deep is to be made. It Is opened atbe made. It is opened at theIgnoring the thickness of the plastic sheet, determine0The arca of the sheet required for making the box.The cost of sheet for it, if a sheet measuring Im costs Rs11g l㎡ costs Rs 20.
Answer»

Discussion

2694.	(iii) (4x3)2-2(x+3)=0
Answer»

Discussion

2695.	ARRAS AND VoLUMiS2i3EXERCISE 13.1L. Aplastic box 1.5 m long, 1.25 m wide and 65 em decgethe top. Ignoring the thickness of the plastic sheet, determine(0 The area of the sheet required for making the box.( The cost of sheet for it, if a sheet measuring Im' coss Rs 20.
Answer»

Discussion

2696.	19. If 4 cubes with dimensions 3 Units3 UnitsHOTS \|x 3 units are kept one on top of another, whatwill be the dimensions of the cuboid formed?
Answer» breadth will be 3cmlength will be 12cmheight will be 12 cm

Discussion

2697.	If the area of triangle with vertices (x, 3), (4, 4) and (3, 5) is 4square units, find x.
Answer»

Discussion

2698.	A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the7top. Ignoring the thickness of the plastic sheet, determine:0 The area of the sheet required for making the box.(ii) The cost of sheet for it, if a sheet measuring Im costs Rs 201.
Answer»

Discussion

2699.	1.The dimensions of a cuboid are in the ratio 3:2:2 and the lateral surface area of cuboid is 2000m2·The outersurface of the cuboid is painted with coloured enamel at the rate of RS 8 per m2. Find the total cost of paintingthe outer surface of the cuboid.
Answer»

Discussion

2700.	, A plastic box 1 5 m long. 1.25 m wide and 65 cm deep is to be made Itis opened at thetop. Ignoring the thickness of the plastic sheet, determine0 The area of the sheet required for making the bo(ii) The cost of sheet for it if a sheet measuring Ind costs Rs 20.
Answer»

Discussion

Explore topic-wise InterviewSolutions in .

1. If HCF (a, b) 12 and a x b 1800, then find LCM (a, b).2. If the roots of th

(A) KBirds are flying in the pattern like 1 in the first row, 3 in the eand so on. Making total 20 rows as per the figure given belo itotal number of birds.43.) A student named Akash is observing birds tlying in the sky nate second(B) 400(C) 40(D) 200(A) 39

ththe same as the Sum otiS Zer0

Understanding Square and Cube Roots-Item 6229Which is the best approximation of the yalue ot V730727432.190

the roots of the equation 4x4 - 2x + = = Oby the method of completing the square.16. Find the roots of th

c which is thde 8.7: Solve : (x+ y)2 =a2n : Put x + y = z, Different, ot;

1s. If the mi srn ot an APand the th temithen prove the tswherc

In the given figure, ABCD is a rhombus. Are Î ADC and Î ABCcongruent? Give reasons.(g)

3 if mth and nth terms ot an A.P. be andI respectively, then show that its (mn)th term is 1.

IfAD = x, DB =x-2, AE = x + 2 and EC = x-1,find the value of Y

FIND(K)1äštH E EQUATIONHASEQU ALroots(k+4) x^{2}+(k+1) x+1=0

10Prove that in a right triangle, the square of the hypotenuse is equal to sum of squares of other two sidesUsing the above result, prove that, in rhombus ABC25.AB AC2BD

25. If the equation x2 + 5kx + 16 = 0 has no real roots th

20. Let z, and z be th roots of unity which aubtend a rightangle at the origin, theri 'n' must be of the form(a) 4k +1 (b) 4k2(c) 4k +3 (d) 4k

IUNI UI CUVUUUFind the area of the base of each shape.C.A.12 cm14 cm71cm9 cm3.com4 cm

Simplify :\frac{\left(x^{a+b}\right)^{3}\left(x^{b+c}\right)^{3}\left(x^{c+a}\right)^{3}}{\left(x^{a} x^{b} x^{c}\right)^{6}}, x \neq 0

\frac{\left(a^{2}-b^{2}\right)^{3}+\left(b^{2}-c^{2}\right)^{3}+\left(c^{2}-a^{2}\right)^{3}}{(a-b)^{3}+(b-c)^{3}+(c-a)^{3}}

\frac { \left( b ^ { 2 } - c ^ { 2 } \right) ^ { 3 } + \left( c ^ { 2 } - a ^ { 2 } \right) ^ { 3 } + \left( a ^ { 2 } - b ^ { 2 } \right) ^ { 3 } } { ( b - c ) ^ { 3 } + ( c - a ) ^ { 3 } + ( a + b ) ^ { 3 } }

\frac{\left(b^{2}-c^{2}\right)^{3}+\left(c^{2}-a^{2}\right)^{3}+\left(a^{2}-b^{2}\right)^{3}}{(b-c)^{3}+(c-a)^{3}+(a-b)^{3}}

\left( \frac { x ^ { a + b } } { x ^ { c } } \right) ^ { a - b } \cdot \left( \frac { x ^ { b + c } } { x ^ { a } } \right) ^ { b - c } \cdot \left( \frac { x ^ { c + a } } { x ^ { b } } \right) ^ { c - a }

\left(\frac{x^{a}}{x^{b}}\right)^{a^{2}+a b+b^{2}}\left(\frac{x^{b}}{x^{c}}\right)^{b^{2}+b c+c^{2}}\left(\frac{x^{c}}{x^{a}}\right)^{c^{2}+a c+a^{2}}

\left(\frac{x^{a}}{x^{b}}\right)^{a^{2}+a b+b^{2}}\left(\frac{x^{b}}{x^{c}}\right)^{b^{2}+h c+c^{2}}\left(\frac{x^{c}}{x^{a}}\right)^{c^{2}+a c+a^{2}}

\begin{array}{l}{\text { Simplify: }} \\ {\left(\frac{X^{4}}{X^{b}}\right)^{a-b}\left(\frac{X^{b}}{X^{-c}}\right)^{b-c}\left(\frac{X^{c}}{X^{-u}}\right)^{c-a}}\end{array}

Find the value of a, whichpoints Q(-5.4) and R(-1,0).or which point P(,2) is the mid-point of the line segment joe a

6. In Fig 5.10, if AC BD, then prove thut AB CD

9. In a AABC, D and E are points on the sides AB and AC respectively, such thattheADx EC AEx DB. Prove that DE | BC.Jo

In a Rhombus ABC shous thetan

1) There are forty-five children in the classroom, each student will get twenty-seven pencilsand thirty-seven erasers. How many pencils will the teacher have to give out?

EXERCISE 3.1. Aftab tells his daughter, "Seven years ago, I was seven times as old as youethatAlso, three years from now, I shall be three times as old as you will be equashointeresting?) Represent this situation algebraically and graphicallyget

If three times the larger of two numbers is divided by the smaller one, we get 4 as thqu8.otient and 3 as the remainder. Also, if seven times the smialler number is divided by theget 5 as the quotient and 1 as the renainder Find the numbers.

ich we add 8 125 times theswe get thousandOKThere are seven bume membe57L13 itid 23 golangehese brume numbers anthe seven squars so thatthe evous and the dignaagnae

If three times the larger of two numbers is divided by the smaller one, we get 4 as thequotient and 3 as the remainder. Also, if seven times the smaller number is divided by thelarger one, we get 5 as the quotient and 1 as the renainder: Find the numbers.8.

10. Seven friends bought 58.8 metres of clothat a sale and shared it equally. How muchdid each get?

2.The breadth of a rectangle is 3 less than the length. If both length and breadth are reduced by3 units, the area of the rectangle reduces by 176 sq, units. Find the dimensions' of the'origithalrectangle.HOTS

(Idioms &amp; Proverbs)

Jo

19-79sinÂŽ _Jo

Jo+J6+6+..

= ० Jo onea [एपीणएएत 7

eBle Jo-i2 2B

Find the volume of a cuboid Whose lenoti10 m width4mand heigh200 m

Ir a+bi 4 and abthen the vetue of a h

plastic box 1.5 m long. 1.25 m wide and 6S cm deep is to be made. It Is opened atbe made. It is opened at theIgnoring the thickness of the plastic sheet, determine0The arca of the sheet required for making the box.The cost of sheet for it, if a sheet measuring Im costs Rs11g l㎡ costs Rs 20.

(iii) (4x3)2-2(x+3)=0

ARRAS AND VoLUMiS2i3EXERCISE 13.1L. Aplastic box 1.5 m long, 1.25 m wide and 65 em decgethe top. Ignoring the thickness of the plastic sheet, determine(0 The area of the sheet required for making the box.( The cost of sheet for it, if a sheet measuring Im' coss Rs 20.

19. If 4 cubes with dimensions 3 Units3 UnitsHOTS |x 3 units are kept one on top of another, whatwill be the dimensions of the cuboid formed?

If the area of triangle with vertices (x, 3), (4, 4) and (3, 5) is 4square units, find x.

A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the7top. Ignoring the thickness of the plastic sheet, determine:0 The area of the sheet required for making the box.(ii) The cost of sheet for it, if a sheet measuring Im costs Rs 201.

1.The dimensions of a cuboid are in the ratio 3:2:2 and the lateral surface area of cuboid is 2000m2·The outersurface of the cuboid is painted with coloured enamel at the rate of RS 8 per m2. Find the total cost of paintingthe outer surface of the cuboid.

, A plastic box 1 5 m long. 1.25 m wide and 65 cm deep is to be made Itis opened at thetop. Ignoring the thickness of the plastic sheet, determine0 The area of the sheet required for making the bo(ii) The cost of sheet for it if a sheet measuring Ind costs Rs 20.

In the given figure, ABCD is a rhombus. Are Î ADC and Î ABCcongruent? Give reasons.(g)

FIND(K)1äštH E EQUATIONHASEQU ALroots(k+4) x^{2}+(k+1) x+1=0

(Idioms & Proverbs)