544 + Interview Questions in ALGEBRA IN GENERAL AWARENESS Page 9 InterviewSolution

401.	Let `n ge 2` be an integer, `A=({:(cos((2pi)/(n)),sin((2pi)/(n)),0),(sin((2pi)/(n)),cos((2pi)/(n)),0),(0,0,1):})` and I is the idnetity matrix of order 3. ThenA. `A^(n)=I " and " A^(n-1) ne I`B. `A^(m) ne I` for any positive integer mC. A is not invertibleD. `A^(m)=0` for a positive integer m
Answer» Correct Answer - A

Discussion

402.	If `P=[{:(2,-2,-4),(-1,3,4),(1,-2,-3):}]`, then `P^(5)` equals-A. PB. 2PC. `-P`D. `-2P`
Answer» Correct Answer - A

Discussion

403.	Consider the system of equations :`{:(x+y+z=0),(alphax+betay+gammaz=0),(alpha^(2)x+beta^(2)y+gamma^(2)z=0):}` Then the system of equation has-A. a unique solution for all values of `alpha, beta, gamma`B. infinite number of solutions if any two of `alpha, beta, gamma` are equalC. a unique solution if `alpha, beta, gamma` are distinctD. more than one, but infinite number of solutions depending on values of `alpha, beta, gamma`.
Answer» Correct Answer - B::C

Discussion

404.	State whether the statement are true or false.t minutes are equal to 60t seconds.
Answer» True Since, 1 minute = 60 seconds ∴ t minutes = 60 × t seconds = 60t seconds

404.

State whether the statement are true or false.t minutes are equal to 60t seconds.

Answer»

True

Since, 1 minute = 60 seconds

∴ t minutes = 60 × t seconds = 60t seconds

Discussion

405.	State whether the statement are true or false.x = 5 is the solution of the equation 3x + 2 = 20
Answer» False We have, 3x + 2 = 20 ⇒ 3x + 2 – 2 = 20 – 2 [Subtracting 2 from both sides] ⇒ 3x = 18 ⇒ 3x/3 = 18/3 [Dividing both sides by 3] ⇒ x = 6, which is the solution of the given equation.

405.

State whether the statement are true or false.x = 5 is the solution of the equation 3x + 2 = 20

Answer»

False

We have, 3x + 2 = 20

⇒ 3x + 2 – 2 = 20 – 2 [Subtracting 2 from both sides]

⇒ 3x = 18

⇒ 3x/3 = 18/3 [Dividing both sides by 3]

⇒ x = 6, which is the solution of the given equation.

Discussion

406.	State whether the statement are true or false.One third of a number added to itself gives 8′, can be expressed as x/3 +8 = x.
Answer» False Let the number be x. One third of the number = x/3. According to the given question, x/3 + x = 8

406.

State whether the statement are true or false.One third of a number added to itself gives 8′, can be expressed as x/3 +8 = x.

Answer»

False

Let the number be x.

One third of the number = x/3.

According to the given question,

x/3 + x = 8

Discussion

407.	Say True or False.(i) The shifting of a number from one side of an equation to other is called transposition.(ii) Linear equation in one variable has only one variable with power 2.
Answer» (i) True (ii) False [Linear equation in one variable has only one variable with power one – correct statement]

407.

Say True or False.(i) The shifting of a number from one side of an equation to other is called transposition.(ii) Linear equation in one variable has only one variable with power 2.

Answer»

(i) True

(ii) False

[Linear equation in one variable has only one variable with power one – correct statement]

Discussion

408.	Factorise : x6 – 64y3
Answer» x⁶ – 64y³ = (x²)³ – 4³y³ = (x²)³ – (4y)³ This is of the form a³ – b³ with a = x², b = 4y a³ – b³ = (a – b)(a² + ab + b²) (x²)³ – (4y)³ = (x² – 4y) [(x²)² + (x²)(4y) + (4y)²] = (x² – 4y) [x⁴ + 4x²y + 16y²] ∴ x⁶ – 64y³ = (x² – 4y) [x⁴ + 4x²y + 16y²]

408.

Factorise : x6 – 64y3

Answer»

x⁶ – 64y³

= (x²)³ – 4³y³

= (x²)³ – (4y)³

This is of the form a³ – b³ with a = x², b = 4y

a³ – b³ = (a – b)(a² + ab + b²)

(x²)³ – (4y)³

= (x² – 4y) [(x²)² + (x²)(4y) + (4y)²]

= (x² – 4y) [x⁴ + 4x²y + 16y²]

∴ x⁶ – 64y³ = (x² – 4y) [x⁴ + 4x²y + 16y²]

Discussion

409.	Find x:2x/3 – 4 = 10/3
Answer» Transposing -4 to other side, it becomes +4 ∴ 2x/3 = 10/3 + 4 Taking LCM & adding, 2x/3 = 10/3 + 4/1 = (10+12)/3 = 22/3 2x/3 = 22/3 Multiplying by 3 on both sides 2x/3 x 3 = 22/3 x 3 ⇒ 2x = 22 dividing by 2 on both sides, We get 2x/2 = 22/2 ∴ x = 11

409.

Find x:2x/3 – 4 = 10/3

Answer»

Transposing -4 to other side, it becomes +4

∴ 2x/3 = 10/3 + 4

Taking LCM & adding,

2x/3 = 10/3 + 4/1 = (10+12)/3 = 22/3

2x/3 = 22/3

Multiplying by 3 on both sides

2x/3 x 3 = 22/3 x 3

⇒ 2x = 22

dividing by 2 on both sides,

We get 2x/2 = 22/2

∴ x = 11

Discussion

410.	331 students went on a field trip. Six buses were filled to capacity and 7 students had to travel in a van. How many students were there in each bus?
Answer» Let the number of students in each bus be ‘x’ number of students in 6 buses = 6 × x = 6x Apart from 6 buses, 7 students went in van A total number of students is 331 ∴ 6x + 7 = 331 ∴ 6x = 331 – 7 = 324 ∴ x = 324/6 = 54 ∴ There are 54 students in each bus.

410.

331 students went on a field trip. Six buses were filled to capacity and 7 students had to travel in a van. How many students were there in each bus?

Answer»

Let the number of students in each bus be ‘x’
number of students in 6 buses = 6 × x = 6x

Apart from 6 buses, 7 students went in van

A total number of students is 331

∴ 6x + 7 = 331

∴ 6x = 331 – 7 = 324

∴ x = 324/6 = 54

∴ There are 54 students in each bus.

Discussion

411.	Find the valuesLet y = x + 3(i) If x = 0, find y.(ii) If y = 0, find x.(iii) If x = -2, find y.(iv) If y = -3, find x.Let 2x + y - 6 = 0(i) If x = 0, find y.(ii) If y = 0, find x.(iii) If x = -2, find y.(iv) If y = -3, find x.
Answer» Let y = x + 3 (i) if x = 0 y = 0 + 3 = 3 ∴ y = 3 (ii) y = 0 0 = x + 3 ∴ x = – 3 (iii) x = – 2 y = – 2 + 3 ∴ y = 1 (iv) y = -3 -3 = x + 3 ∴ x = -6 Let 2x + 7 – 6 = 0 (i) x = 0 2 x 0 + y – 6 = 0 ∴ 7 = 6 (ii) y = 0 2x + 0 – 6 = 0 2x = 6 x = 3 (iii) x = – 2 2 x (- 2) + y – 6 = 0 y – 10 = 0 y = 10 (iv) y = -3 2x – 3 – 6 = 0 2x = 9 x = 9/2

411.

Find the valuesLet y = x + 3(i) If x = 0, find y.(ii) If y = 0, find x.(iii) If x = -2, find y.(iv) If y = -3, find x.Let 2x + y - 6 = 0(i) If x = 0, find y.(ii) If y = 0, find x.(iii) If x = -2, find y.(iv) If y = -3, find x.

Answer»

Let y = x + 3

(i) if x = 0

y = 0 + 3 = 3

∴ y = 3

(ii) y = 0

0 = x + 3

∴ x = – 3

(iii) x = – 2

y = – 2 + 3

∴ y = 1

(iv) y = -3

-3 = x + 3

∴ x = -6

Let 2x + 7 – 6 = 0

(i) x = 0

2 x 0 + y – 6 = 0

∴ 7 = 6

(ii) y = 0

2x + 0 – 6 = 0

2x = 6

x = 3

(iii) x = – 2

2 x (- 2) + y – 6 = 0

y – 10 = 0

y = 10

(iv) y = -3

2x – 3 – 6 = 0

2x = 9

x = 9/2

Discussion

412.	The sum of three numbers is 58. The second number is three times of two-fifth of the first number and the third number is 6 less than the first number. Find the three numbers.
Answer» Here what we know a + b + c = 58 (sum of three numbers is 58) Let the first number be ‘x’ b = a + 3 (the second number is three times of 12 of the first number) b = 3 x 2/5x = 6/5x Third number = x – 6 Sum of the numbers is given as 58. ∴ x + 6/5x + (x – 6) = 58 Multiplying by 5 throughout, we get 5 × x + 6x + 5 × (x – 6) = 58 x 5 5x + 6x + 5x – 30 = 290 ∴ 16x = 290 + 30 ∴ 16x = 320 ∴ x = 320/16x = 20 Answer: 1st number =20 2nd number = 3 x 25 x 20 = 24 3rd number = 24 – 6 = 14

412.

The sum of three numbers is 58. The second number is three times of two-fifth of the first number and the third number is 6 less than the first number. Find the three numbers.

Answer»

Here what we know

a + b + c = 58 (sum of three numbers is 58)

Let the first number be ‘x’

b = a + 3 (the second number is three times of 12 of the first number)

b = 3 x 2/5x = 6/5x

Third number = x – 6

Sum of the numbers is given as 58.

∴ x + 6/5x + (x – 6) = 58

Multiplying by 5 throughout, we get

5 × x + 6x + 5 × (x – 6) = 58 x 5

5x + 6x + 5x – 30 = 290

∴ 16x = 290 + 30

∴ 16x = 320

∴ x = 320/16x = 20

Answer:

1st number =20

2nd number = 3 x 25 x 20 = 24

3rd number = 24 – 6 = 14

Discussion

413.	The number of real values of `alpha` for which the system of equations : `{:(x+3y+5z=ax),(5x+y+3z=ay),(3x+5y+z=az):}` has infinite number of solutions is-A. 1B. 2C. 4D. 6
Answer» Correct Answer - A

Discussion

414.	For `3xx3`matrices `Ma n dN ,`which of the following statement (s) is (are) NOT correct ?`N^T M N`is symmetricor skew-symmetric,according as `m`is symmetric or skew-symmetric.`M N-N M`is skew-symmetric for allsymmetric matrices `Ma n dNdot``M N`is symmetric for all symmetricmatrices `M a n dN``(a d jM)(a d jN)=a d j(M N)`for all invertible matrices `Ma n dNdot`A. `N^(T)MN` is symmetric or skew symmetric, according as M is symmetric or skew symmetric.B. MN-NM is skew symmetric for all symmetric matrices M and N.C. MN is symmetric for all symmetric matrices M and N.D. (Adj M) (Adj N)=Adj(MN) for all invertible matrices M and N.
Answer» Correct Answer - C::D

Discussion

415.	Let `p=[(3,-1,-2),(2,0,alpha),(3,-5,0)],` where `alpha in RR.` Suppose `Q=[q_(ij)]` is a matrix such that `PQ=kl,` where `k in RR, k != 0 and l` is the identity matrix of order 3. If `q_23=-k/8 and det(Q)=k^2/2,` thenA. `alpha=0`, k=8B. `4alpha-k+8=0`C. det(Padj(Q))=`2^(9)`D. det(Qadj(P))=`2^(13)`
Answer» Correct Answer - B::C

Discussion

416.	If `P= [[sqrt(3)/2, 1/2],[-1/2 , sqrt(3)/ 2]], A = [[1,1],[0,1]]and Q= PAP^(T)` , the ltbr. `P(Q^(2005)) P^(T)` equal toA. `[{:(0,2015),(0,0):}]`B. `[{:(2015,1),(0,2015):}]`C. `[{:(2015,0),(1,2015):}]`D. `[{:(1,2015),(0,1):}]`
Answer» Correct Answer - D

Discussion

417.	The system of linear equations `x+lambday-z=0` `lambdax-y-z=0` `x+y-lambdaz=0` has a non-trivial solution forA. infinitely many values of `lambda`B. exactly one value of `lambda`C. exactly two values of `lambda`D. exactly three values of `lambda`
Answer» Correct Answer - D

Discussion

418.	The term containing x3 in the expansion of (x – 2y)7 is: (a) 3rd (b) 4th (c) 5th(d) 6th
Answer» (c) 5^th First-term contains x⁷. The second term contains x⁶. The fifth term contains x³.

418.

The term containing x3 in the expansion of (x – 2y)7 is: (a) 3rd (b) 4th (c) 5th(d) 6th

Answer»

(c) 5^th

First-term contains x⁷.

The second term contains x⁶.

The fifth term contains x³.

Discussion

419.	Let m and N be two 3x3 matrices such that MN=NM. Further if `M!=N^2` and `M^2=N^4` then which of the following are correct.A. determinant of `(M^(2)+MN^(2))` is 0.B. there is a `3 times 3` non-zero matrix U such that `(M^(2)+MN^(2))U` is the zero matrix.C. determinant of `(M^(2)+MN^(2)) ge 1`D. for a `3 times 3` matrix U, if `(M^(2)+MN^(2))U` equals the zero matrix then U is the zero matrix.
Answer» Correct Answer - A::B

Discussion

420.	The equation 4x = 16 is satisfied by the following value of x(A) 4 (B) 2 (C) 12 (D) –12
Answer» (A) 4 Consider the given equation 4x = 16 Then, value of x is, x = 16/4 … [divide both numerator and denominator by 4] x = 4

420.

The equation 4x = 16 is satisfied by the following value of x(A) 4 (B) 2 (C) 12 (D) –12

Answer»

(A) 4

Consider the given equation 4x = 16

Then, value of x is,

x = 16/4 … [divide both numerator and denominator by 4]

x = 4

Discussion

421.	Which of the following equations has x=2 as a solution?A. x+2=5B. x-2=0C. 2x+1=0D. x+3=6
Answer» Correct Answer - B

Discussion

422.	The equation 4x=16 is satisfied by the following value of xA. `4`B. `2`C. `12`D. `-12`
Answer» Correct Answer - A

Discussion

423.	In algebra, a × b means ab, but in arithmetic 3 × 5 is(A) 35 (B) 53 (C) 15 (D) 8
Answer» (C) 15 3 × 5 means 15.

423.

In algebra, a × b means ab, but in arithmetic 3 × 5 is(A) 35 (B) 53 (C) 15 (D) 8

Answer»

(C) 15

3 × 5 means 15.

Discussion

424.	In algebra, a × b means ab, but in arithmetic 3 × 5 is (A) 35 (B) 53 (C) 15 (D) 8
Answer» The correct option is (C) 15.

Discussion

425.	In algebra if axb=ab but in arithmetic 3x5=A. `35`B. `53`C. `15`D. `8`
Answer» Correct Answer - A

Discussion

426.	The length of a reactanle is 5 cm more than its bredth. If the perimeter of the rectangle is 42, cm , then find the length of the reactangle.
Answer» Correct Answer - 13 cm Let the breadth of the reactangle be x cm. Length of the reactanle =(x+5) cm Perimeter of the reactangle `=2(l+b)=42 cm` `2(x+5+x)=42 rArr 2x+5=(42)/(2)` `2x+5=21rArr2x=21-5` `x=(16)/(2)rArrx=8cm` `:.` Length of the rectangel =x+5=8+5=13 cm

Discussion

427.	If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 – 2x + a leave the same remainder when divided by (x – 3), find the value of a. and also find the remainder.
Answer» Let f(x) = 2x³ + ax² + 4x – 12 and g(x) = x³ + x² – 2x + a When f(x) is divided by x – 3, the remainder is f(3). Now f(3) = 2(3)³ + a(3)² + 4(3) – 12 = 54 + 9a + 12 – 12 f(3) = 9a + 54 … (1) When g(x) is divided by x – 3, the remainder is g(3). Now g(3) = 3³ + 3² – 2(3) + a = 27 + 9 – 6 + a g(3) = a + 30 … (2) Since, the remainder’s are same (1) = (2) Given that f(3) = g(3) That is 9a + 54 = a + 30 9a – a = 30 – 54 ⇒ 8a = -24 ∴ a = -3 Substituting a = -3 in f(3), we get f(3) = 9(-3) + 54 = -27 + 54 f(3) = 27 ∴ The remainder is 27

427.

If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 – 2x + a leave the same remainder when divided by (x – 3), find the value of a. and also find the remainder.

Answer»

Let f(x) = 2x³ + ax² + 4x – 12 and g(x) = x³ + x² – 2x + a

When f(x) is divided by x – 3, the remainder is f(3).

Now f(3) = 2(3)³ + a(3)² + 4(3) – 12 = 54 + 9a + 12 – 12

f(3) = 9a + 54 … (1)

When g(x) is divided by x – 3, the remainder is g(3).

Now g(3) = 3³ + 3² – 2(3) + a = 27 + 9 – 6 + a

g(3) = a + 30 … (2)

Since, the remainder’s are same (1) = (2)

Given that f(3) = g(3)

That is 9a + 54 = a + 30

9a – a = 30 – 54 ⇒ 8a = -24 ∴ a = -3

Substituting a = -3 in f(3), we get

f(3) = 9(-3) + 54 = -27 + 54

f(3) = 27

∴ The remainder is 27

Discussion

428.	Solve `x: (x)/(4)=6x-(5)/(4)`
Answer» Correct Answer - `(5)/(23)` `(x)/(4)=6x-(5)/(4)rArr(5)/(4)=6x-(x)/(4)` `(5)/(4)=(24x-x)/(4)rArr(5)/(4)=(23x)/()rArr23x=5` `x=(5)/(23)`

Discussion

429.	Solve for x : 3x+7=18x
Answer» Correct Answer - `(7)/(15)` `3x+7=18xrArr7=18x-3x` `7=15xrArrx=(7)/(15)`

Discussion

430.	Simplify : `(15)/(2)xx(4)/(3)[6x^(2)-9x(x-bar(3-2x))]`
Answer» Correct Answer - `28x^(2) - (57)/(2) x` `(15)/(2)x-(4)/(3)[6x^(2)-9x(x-bar(3-2x))]` `(15)/(2)x-(4)/(3)[6x^(2)-9x(x-3+2x)]` `=(15)/(2)x-(4)/(3)[6x^(2)-27x^(2)+27x]` `=(15)/(2)x-(4)/(3)[6x^(2)-27x^(2)+27x]` `=(15)/(2)x-(4)/(3)xx21x^(2)-(4)/(3)xx27x` `(15)/(2)x+28x^(2)-36x=28x^(2)+(15)/(2)x-36x` `=28x^(2)+((15)/(2)-36)x=28x^(2)+((15-72)/(2))x` `28x^(2)-(15)/(2)x`

Discussion

431.	What should be subtracted from `2x^(2)-3x+14`, that the difference is `5x^(2)+7x-5`?
Answer» Correct Answer - ` 19 - 10 x - 3x^(2)` Let f(x) be subtracted from `2x^(2)-3x+14` to get `5x^(2)+7x-5` `(2x^(2)-3x+14)=-(5x^(2)+7x-5)=f(x)` `2x^(2)-3x+14-5x^(2)-7x+5=f(x)` `(2z^(2)-5x^(2))+(-3x-7x)+(14+5)=f(x)` `-3x^(2)-10+19=f(x)` `:. 19-10x-3x^(2)` should be substracte from `2x^(2)-3x+14`, so that the difference is `5x^(2)+7x-5`

Discussion

432.	Simplify and find the degree of 6x2 + 1 – [8x – {3x2 – 7 – (4x2 – 2x + 5x + 9)}]
Answer» 6x² + 1 – [8x – {3x²– 7 – (4x²– 2x + 5x + 9)}] = 6x² + 1 – [8x – {3x² – 7 – 4x²– 2x + 5x + 9}] = 6x² + 1 – [8x – 3x² + 7 + 4x² – 2x + 5x + 9] = 6x² – 1 – [8x + 3x² – 7 – 4x² + 2x – 5x – 9] = 6x² + 3x² – 4x² – 8x + 2x – 5x – 1 – 7 – 9 = x²(6 + 3 – 4) + x(8 + 2 – 5) – 15 = 5x² – 11x – 15 Degree of the expression is 2.

432.

Simplify and find the degree of 6x2 + 1 – [8x – {3x2 – 7 – (4x2 – 2x + 5x + 9)}]

Answer»

6x² + 1 – [8x – {3x²– 7 – (4x²– 2x + 5x + 9)}]

= 6x² + 1 – [8x – {3x² – 7 – 4x²– 2x + 5x + 9}]

= 6x² + 1 – [8x – 3x² + 7 + 4x² – 2x + 5x + 9]

= 6x² – 1 – [8x + 3x² – 7 – 4x² + 2x – 5x – 9]

= 6x² + 3x² – 4x² – 8x + 2x – 5x – 1 – 7 – 9

= x²(6 + 3 – 4) + x(8 + 2 – 5) – 15

= 5x² – 11x – 15

Degree of the expression is 2.

Discussion

433.	`3x^(2)y+7x^(2)y` = _____
Answer» Correct Answer - `10x^(2)y` `3x^(2)y+7x^(2)y=(3+7)x^(2)y=10x^(2)y`

Discussion

434.	The number of second degree terms in the expression `2x^(3)-3x^(2)y+5x^(2)-6xy^(2)+8x^(2)y-4x^(2)y^(2)` is _____A. 3B. 2C. 1D. 4
Answer» Correct Answer - C Only `5x^(2)` is the second degree term. Hence, the correct option is (c)

Discussion

435.	Say True or False:(i) The length of part B in the pencil shown is ‘a – 6’.(ii) If the cost of an apple is ‘x’ and cost of banana is ₹ 5, then the total cost of fruits is ₹ ‘x + 5′(iii) If there are 11 players in a team, then there will be ’11 + q’ players in ‘q’ teams.
Answer» (i) False Length of B is 6 – a (ii) True (iii) False There will be 11q players.

435.

Say True or False:(i) The length of part B in the pencil shown is ‘a – 6’.(ii) If the cost of an apple is ‘x’ and cost of banana is ₹ 5, then the total cost of fruits is ₹ ‘x + 5′(iii) If there are 11 players in a team, then there will be ’11 + q’ players in ‘q’ teams.

Answer»

(i) False

Length of B is 6 – a

(ii) True

(iii) False

There will be 11q players.

Discussion

436.	Fill in the blanks:(i) The letters a, b, c, .., x, y, z are used to represent _____(ii) A quantity that takes _____ values is called a variable.(iii) If there are 5 students on a bench, then the number of students in ‘n’ benches is ‘5 × n’. Here _____ is a variable.
Answer» (i) Variables (ii) Different (iii) n

436.

Fill in the blanks:(i) The letters a, b, c, .., x, y, z are used to represent ___(ii) A quantity that takes _ values is called a variable.(iii) If there are 5 students on a bench, then the number of students in ‘n’ benches is ‘5 × n’. Here ___ is a variable.

Answer»

(i) Variables

(ii) Different

(iii) n

Discussion

437.	Complete the table and find the solution of the equation z/3 = 4 using the table.
Answer» 13/3, 14/3, 5 and z/3 = 4 when z = 12.

Discussion

438.	Nine added to two times x gives 301. Find the value of x.
Answer» x = 146 2x + 9 = 301 2x = 301 - 9 2x = 292 x = 292/2 x = 146

438.

Nine added to two times x gives 301. Find the value of x.

Answer»

x = 146

2x + 9 = 301

2x = 301 - 9

2x = 292

x = 292/2

x = 146

Discussion

439.	Price of oil per litre is ₹ 5 more than three times the price of cool drinks ₹ ‘p’ Express algebraically.
Answer» Price of cool drinks per kg = ₹ p Three times = 3p 5 Rs. more = 3p + 5 Price of oil per kg = ₹ (3p + 5)

439.

Price of oil per litre is ₹ 5 more than three times the price of cool drinks ₹ ‘p’ Express algebraically.

Answer»

Price of cool drinks per kg = ₹ p

Three times = 3p

5 Rs. more = 3p + 5

Price of oil per kg = ₹ (3p + 5)

Discussion

440.	The value of y in 7y – 20 = 99.
Answer» y = 17 7y - 20 = 99 7y = 99 + 20 7y = 119 y = 119/7 y = 17

440.

The value of y in 7y – 20 = 99.

Answer»

y = 17

7y - 20 = 99

7y = 99 + 20

7y = 119

y = 119/7

y = 17

Discussion

441.	A tap is to be pasted along the edges of a square shaped gift box. Its length is 4 cm. What is the length of tap needed for one side.
Answer» The length of tap needed for one side = \(\frac{4p}{4} = p\)

Discussion

442.	Prepare a table for 3x + 10. From the table find the value of x when 3x + 10 = 25.
Answer» 5 3x + 10 = 25 3x = 25 - 10 3x = 15 x = 15/3 x = 5

442.

Prepare a table for 3x + 10. From the table find the value of x when 3x + 10 = 25.

Answer»

5

3x + 10 = 25

3x = 25 - 10

3x = 15

x = 15/3

x = 5

Discussion

443.	Form the expression for which Ramu is 3 years younger than Mathu.
Answer» Ramu is 3 years younger than Mathu. m – 3

443.

Form the expression for which Ramu is 3 years younger than Mathu.

Answer»

Ramu is 3 years younger than Mathu.

m – 3

Discussion

444.	1. Additive identity ____2. Multiplicative identity ____
Answer» 1. Additive identity 0 2. Multiplicative identity 1

444.

1. Additive identity 2. Multiplicative identity

Answer»

1. Additive identity 0

2. Multiplicative identity 1

Discussion

445.	How old was Suja 6 years from now?
Answer» Let Suja’s present age be ‘a’ years. 6 years from now Suja will be (a + 6) years old.

445.

How old was Suja 6 years from now?

Answer»

Let Suja’s present age be ‘a’ years.

6 years from now Suja will be (a + 6) years old.

Discussion

446.	Arivazhagan is 30 years younger to his father. Write Arivazhagan’s age in terms of his father’s age.
Answer» Let Arivazhagan’s father’s age be x years According to the problem, Arivazhagan’s age = (x – 30) years

446.

Arivazhagan is 30 years younger to his father. Write Arivazhagan’s age in terms of his father’s age.

Answer»

Let Arivazhagan’s father’s age be x years

According to the problem,

Arivazhagan’s age = (x – 30) years

Discussion

447.	Rajini’s Father’s age is 5 years more than 3 times Rajini’s age. What is her father’s age?
Answer» Father’s age = 3x + 5

Discussion

448.	Express to an algebraic statement.(i) ‘t’ is added to 100(ii) 4 less to 9 times of y.
Answer» (i) t + 100 (ii) 9y – 4

448.

Express to an algebraic statement.(i) ‘t’ is added to 100(ii) 4 less to 9 times of y.

Answer»

(i) t + 100

(ii) 9y – 4

Discussion

449.	Give verbal expression of(a) 7x + 18(b) 4x/3
Answer» (a) 18 added to 7 times x (b) 4 times x divided by 3.

449.

Give verbal expression of(a) 7x + 18(b) 4x/3

Answer»

(a) 18 added to 7 times x

(b) 4 times x divided by 3.

Discussion

450.	The number of days in ‘w’ weeks is(a) 30 + w(b) 30w(c) 7 + w(d) 7w
Answer» (d) 7w The number of days in ‘w’ weeks is 7w.

450.

The number of days in ‘w’ weeks is(a) 30 + w(b) 30w(c) 7 + w(d) 7w

Answer»

(d) 7w

The number of days in ‘w’ weeks is 7w.

Discussion

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