Q: Solve −722+(12−3)=

−722+(12−3)=−722−123Take L.C.M of 7,12=7×12=84=84−22×12−7×3=−84285

Q: 81−42x+1=0, Find the value of ′x′

Given that 81−42x+1=081+1=42x81+11=2x Take L.C.M of 8 and 1=8×1=881×1+1×8=2x81+8=2x89=2xCross multiply, 9×2=x×818=8x x=818=49

Q: Express 81−2 in the powers of 3

Given that:81 can be written in powers of 3true81=3×3×3×381−2=(3×3×3×3)−2=(34)−2=3−8=(31)8

Question 1

If Ramesh buys five apples at a cost of Rs. 10 each and he sells all apples to Ganesh at a profit of 10%. Find the selling price of each apple.

Accepted Answer

Given that
Ramesh buys five apples at a cost of Rs. 10 each
The cost price of 5 apples  Rs. 50
He sells all apples to Ganesh at a profit of 10% = 110% of  Rs. 55
Therefore, selling price of each apple = 55/11 = Rs 11.

Question 2

Find the volume of the rectangular box whose length (l)=mn, breadth (b)= m2p, depth (d)=pmn2.

Accepted Answer

Given that length (l)=mn, breadth (b)=m2p,Depth(d)=pmn2Volume of the rectangular box =l×b×d=mn×m2p×pmn2=(m×m2×m)×(n×n2)×(p×p)​ If bases are equal then their powers are to be added, am×an=am+n=(m1+2+1)×(n1+2)×(p1+1)=m4n3p2​

Question 3

What is the Euler's formula for a Polyhedron?

Accepted Answer

F+V-E=2Where ' F ' stands for number of faces,'V' stands for number of vertices and' E ' stands for number of edges.This relationship is called Euler's formula.

Question 4

In a 5-match test series, Indian team won 60 percentage of matches. Find how many matches lost by Indian team?

Accepted Answer

Given that,Number of matches in a series (N)=5Matches won by the India =60% of N=60% of 5=10060​×5=3No of matches lost by India =N - (Matches won by India) =5−3=2

Question 5

If p=2q+6, then what is the value of p3−8q3−36pq−216?

Accepted Answer

Rewrite p=2q+6 as p−2q=6,Taking the cube on both sides of p−2q=6, we get(p−2q)3=63Using the algebraic identity​(x±y)3=x3±y3±3xy(x±y)p3−(2q)3−3(p)(2q)(p−2q)=216p3−8q3−6pq(6)=216[ Since given that (p−2q)=6]p3−8q3−36pq−216=0​ So the value of p3−8q3−36pq−216 is 0

Question 6

Solve −722​+(12−3​)=

Accepted Answer

−722​+(12−3​)=−722​−123​Take L.C.M of 7,12=7×12=84=84−22×12−7×3​=−84285​

Question 7

81​−42​x+1=0, Find the value of ′x′

Accepted Answer

Given that 81​−42​x+1=0​81​+1=42x​81​+11​=2x​​ Take L.C.M of 8 and 1=8×1=8​81×1+1×8​=2x​81+8​=2x​89​=2x​​Cross multiply, 9×2=x×818=8x x=818​=49​

Question 8

What values of (x,y) satisfy the given equation x3−2x2y+2xy2−y2=0

Accepted Answer

Given that equation x3−2x2y+2xy2−y2=0Substitute the options in the given equation and check whether it is satisfied(1,1)​x=1,y=1x3−2x2y+2xy2−y2=0⇒13−2×12×1+2×1×12−12=0​ Therefore, it satisfies the equation

Question 9

Express 81−2 in the powers of 3

Accepted Answer

Given that:81 can be written in powers of 3true​81=3×3×3×381−2=(3×3×3×3)−2=(34)−2=3−8=(31​)8​

Question 10

Waheeda bought an air cooler for ₹ 3300 including a tax of 10%. What is the price of the air cooler before VAT was added?

Accepted Answer

The price includes the VAT, i.e., the value added tax. Thus, a 10% VAT means if the price without VAT is ₹ 100 then price including VAT is ₹ 110 .Now, when price including VAT is ₹110, original price is ₹100.Hence when price including tax is ₹3300, the original price =₹110100​×3300=₹3000.

Question 11

Simplify the expression, (a22×a−12)×(b−10×b20)

Accepted Answer

Given: (a22×a−12)×(b−10×b20)
If bases are equal then their powers are to be added, am×an=am+n =(a22−12)×(b−10+20)
=a10×b10
 Since, am×bn=(ab)m
Since, am×bn=(ab)mn=(ab)10

Question 12

If square root of 25x is 16 what is the value of ?

Accepted Answer

We have,25x​=16To find, the value of x= ?∴25x​=16Squaring both sides, we get​25x​2=162⇒25x=16×16⇒25x=256​ Comparing both sides, we getx=6∴ The value of x=6Thus, the value of x is equal to 6 .

Question 13

The value of x for which −3x+6=0, is :

Accepted Answer

​3x−6=03x=6x=6/3x=2​

Question 14

If 82×2n24×4×162​=1, find the value of n

Accepted Answer

82×2n24×4×162​=1⇒(23)2×2n24×22×(24)2​=1
⇒(26×2n)24×22×28​=1⇒24+2+8−6−n=1
⇒28−n=1⇒28−n=20
⇒8−n=0⇒n=8

Question 15

Find the number of sides of a regular polygon whose each exterior angle measures 18∘.

Accepted Answer

Sum of all the exterior angles of a regular polygon =360∘Measure of each exterior angle =18∘Number of sides = Measure of one exterior angle  Sum of all exterior angles ​=18∘360∘​=20

Question 16

In case of reproduction in Frogs, the eggs are hold together by

Accepted Answer

The female frogs lay hundreds of shell less eggs which are hold together by a jelly like substance.

Question 17

Which of the following gives the step wise method of reproduction?

Accepted Answer

The first step in reproduction is fertilization leading to the formation of zygote. The later development of zygote is called as embryo which leads to the formation of foetus.

Question 18

The development of shell in hen's egg takes places during

Accepted Answer

After fertilisation, the zygote divides repeatedly and travels down the oviduct, during which the shell of the egg is formed.

Question 19

In case of multicellular organisms, a group of specialized cells form,

Accepted Answer

In multicellular organisms, a group of specialized cells form tissues which in turn form organs to perform functions.

Question 20

Which of the following components of plant cells permits to and fro movement of particles?

Accepted Answer

The plasma membrane in a cell is porous which allows the movement of substance both inwards and outwards.

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