Fundamental Concepts Test

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Fundamental Concepts Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

$F i n d (m + n) (m - n) (m^{2} + n^{2}) (m^{4} + n^{4})$

A
$m^{2} - n^{2}$

B
$m^{2} + n^{2}$

C
$m^{4} + n^{4}$

D
$m^{8} - n^{8}$

Solution

$(m^{2} - n^{2}) (m^{2} + n^{2}) (m^{4} + n^{4})$
$[u s i n g t h e f o r m u l a (a + b) (a - b) = a^{2} - b^{2}]$
$= [(m^{2})^{2} - (n^{2})^{2}] (m^{4} + n^{4})$
$= [m^{4} - n^{4}] [m^{4} + n^{4}]$
$= m^{8} - n^{8}$
Question 2
1 / -0

Howmuch more than $2 x^{2} + 4 x y + 2 y^{2} i s 5 x^{2} + 10 x y - y^{2}$

A
$3 x^{2} - 6 x y - 3 y^{2}$

B
$3 x + 6 x^{2} y + 3 y$

C
$3 x^{2} - 6 x y^{2} + 3 y^{2}$

D
None of these

Solution

$\begin{matrix} 5 x^{2} + 10 x y - y^{2} \\ + 2 x^{2} + 4 x y + 2 y^{2} \end{matrix}$
$3 x^{2} - 6 x y - 3 y^{2}$
Question 3
1 / -0

Find $2 [97 \times 103]$ using suitable identity

A
40000

B
39964

C
38784

D
40340

Solution

$2 [97 \times 103] = 194 \times 206$
194=(200-6) and 206=(200+6)
$∴ 194 \times 206 = (200 - 6) (200 + 6)$
$U \sin g i d e n t i t y$ $(a - b) (a + b) = a^{2} - b^{2}$
$= (200)^{2} - (6)^{2}$
= 40000-36
= 39964
Question 4
1 / -0

The statement form of the equation 5p = 20 is

A
5 when added to p gives 20

B
Five times a number p is 20

C
Twenty times a number p is 20

D
None of these

Solution

Twenty times a number p is 20
Question 5
1 / -0

Whatmust be added $x^{4} - x^{3} + x^{2} + x + 3$ to obtain $x^{4} + x^{2} - 1 ?$

A
$x^{3} + x - 4$

B
$x^{2} - x + 4$

C
$x + x^{2} - 4$

D
None of these

Solution

$\begin{matrix} x^{4} + x^{2} \\ + x^{4} - x^{3} + x^{2} + x + 3 \end{matrix}$
$- + 1 -$
$x 3 - x - 4$
Question 6
1 / -0

Amit is 6 years older thanJitendra. Six years ago Amit was twice old as Jitendra. Write down thesituation in algebraic expression and find how old is each now?

A
Jitendra12, Amit 18

B
Jitendra10, Amit 16

C
Jitendra14, Amit 20

D
Cannot be determined

Solution

Let x= Jitendra present age
x+6= Amit age now
x-6= Jitendra age 6 yearsago
(a+6)-6 = Amit age 6 years ago
Since six years ago Amit was twice as oldas he is now
(x+6)-6=2(x-6)
x+6-6=2x-12
-x= -12
x= 12: Jitendra present age
x+6=18: Amit present age.
Question 7
1 / -0

From the sum of $o f 3 a - b + 9 a n d - b - 9$ , substract 3a-b-9

A
b+9

B
b-9

C
-b+9

D
-b-9

Solution

$[(3 a - b + 9) + (- b - 9)] - (3 a - b - 9)$
$[3 a - b + 9 - b - 9] - 3 a + b + 9$
$3 a - 2 b - 3 a + b + 9$
$= - b + 9$
Question 8
1 / -0

$S u b s t r a c t 4 x y^{2} f r o m 3 x y^{2}$

A
xy

B
xy²

C
$- x y^{2}$

D
$N o n e o f t h e s e$

Solution

$3 x y^{2} - 4 x y^{2} = - x y^{2}$
Question 9
1 / -0

Writethe degree of polynomial given below:
$X^{2} - 6 x^{3} + 8 y$

A
3

B
4

C
2

D
1

Solution

For polynomials in two or more variables,the degree of a term is the sum of the exponents of thevariables in the term; the degree (sometimes called thetotal degree) of the polynomial is again themaximum of the degrees of all terms in the polynomial.
Here the answer is 3
Question 10
1 / -0

Subtract $3 x^{3} + 4 x^{2} - 5 x + 6 f r o m 3 x - 4 x^{2} + 5 x - 6 .$

A
$6 x + 8 x^{2} - 10 x + 10$

B
$6 x^{3} - 8 x^{2} + 10 x - 12$

C
$6 x^{2} - 8 x - 10 x^{2} + 12$

D
None of these

Solution

$3 x^{3} - 4 x^{2} + 5 x - 6$
$- 3 x^{3} + 4 x^{2} - 5 x + 6$
$+ - + -$
$6 x^{3} - 8 x^{2} + 10 x - 12$
Question 11
1 / -0

Howmuch less $2 a^{2} + 1 is than 3 a^{2} - 6 ?$

A
a-7

B
a3+7

C
a²-7

D
non of these

Solution

$\begin{matrix} \begin{matrix} 3 a^{2} - 6 \\ 2 a^{2} + 1 \end{matrix} \end{matrix}$
$a^{2} - 7$
Question 12
1 / -0

If $x + \frac{1}{x} = 9,$ find the value of $(x^{2} + \frac{1}{x^{2}})$

A
77

B
76

C
78

D
79

Solution

Squaring on both sides
${(x + \frac{1}{x})}^{2} = (9)^{2} = 81$
$U \sin g f o r m u l a (a + b)^{2} = a^{2} + b^{2} + 2 a b$
$\begin{array}{r} \Rightarrow {(x + \frac{1}{x})}^{2} = x^{2} + {(\frac{1}{x})}^{2} + 2 x \times \frac{1}{x} \\ \Rightarrow {(x + \frac{1}{x})}^{2} = x^{2} + \frac{1}{x^{2}} + 2 \\ \Rightarrow 81 = x^{2} + \frac{1}{x^{2}} + 2 \\ \Rightarrow x^{2} + \frac{1}{x^{2}} = 81 - 2 \\ x^{2} + \frac{1}{x^{2}} = 79 \end{array}$
Question 13
1 / -0

Writethe number of terms in the following polynomials.
$5 j^{2} + 3 j a j 5 j^{2} + 3 \times a j = 5 j^{2} + 3 a j$

A
1

B
3

C
2

D
4

Solution

The number of terms in this Polynomial =2 a and j.
Question 14
1 / -0

Find the total savings of a boy who saves£ (4x-6y); £ (6x+2y); £ (4y-x)and £ (y-2x)for four consecutive weeks.

A
x+4y

B
7x+y

C
X+7y

D
Cannot be determined

Solution

$4 x - 6 y + 6 x + 2 y + (- x + 4 y) + (- 2 x + y)$
$\Rightarrow 4 x - 6 y + 6 x + 2 y - x + 4 y - 2 x + y$
Adding the same variables,
$\Rightarrow 4 x + 6 x - x - 2 x + (- 6 y + 2 y + 4 y + y)$
$= 7 x + y ∴ T o t a l s a v i n g s = 7 x + y$
Question 15
1 / -0

Find the product of $(a - 3 b) (a + 3 b) (a^{2} + 9 b^{2})$

A
$a^{2} - 9 b^{2}$

B
$a^{4} - 81 b^{2}$

C
$a^{4} - 81 b^{4}$

D
None of these

Solution

$= [(a)^{2} - (3 b)^{2}] (a^{2} + 9 b^{2}) [∴ (a - b) (a + b) = a^{2} - b^{2}]$

$= (a^{2} - 9 b^{2}) (a^{2} + 9 b^{2})$

$= (a^{2})^{2} - (9 b^{2})^{2}$

$= a^{4} - 81 b^{4}$

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Re-Attempt Weekly Quiz Competition

Fundamental Concepts Test - 8

Result

Fundamental Concepts Test - 8

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SHARING IS CARING

Question 1

m2-n2

m2+n2

m4+n4

m8-n8

Solution

Question 2

3x2-6xy-3y2

3x+6x2y+3y

3x2-6xy2+3y2

None of these

Solution

Question 3

40000

39964

38784

40340

Solution

Question 4

5 when added to p gives 20

Five times a number p is 20

Twenty times a number p is 20

None of these

Solution

Question 5

x3+x-4

x2-x+4

x+x2-4

None of these

Solution

Question 6

Jitendra12, Amit 18

Jitendra10, Amit 16

Jitendra14, Amit 20

Cannot be determined

Solution

Question 7

b+9

b-9

-b+9

-b-9

Solution

Question 8

xy

xy2

-xy2

None of these

Solution

Question 9

3

4

2

1

Solution

Question 10

6x+8x2-10x+10

6x3-8x2+10x-12

6x2-8x-10x2+12

None of these

Solution

Question 11

a-7

a3+7

a2-7

non of these

Solution

Question 12

77

76

78

79

Solution

$m^{2} - n^{2}$

$m^{2} + n^{2}$

$m^{4} + n^{4}$

$m^{8} - n^{8}$

$3 x^{2} - 6 x y - 3 y^{2}$

$3 x + 6 x^{2} y + 3 y$

$3 x^{2} - 6 x y^{2} + 3 y^{2}$

$x^{3} + x - 4$

$x^{2} - x + 4$

$x + x^{2} - 4$

xy²

$- x y^{2}$

$N o n e o f t h e s e$

$6 x + 8 x^{2} - 10 x + 10$

$6 x^{3} - 8 x^{2} + 10 x - 12$

$6 x^{2} - 8 x - 10 x^{2} + 12$

a²-7

$a^{2} - 9 b^{2}$

$a^{4} - 81 b^{2}$

$a^{4} - 81 b^{4}$