Fundamental Concepts Test

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Fundamental Concepts Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

Carry out the multiplication of expressions ineach of the following pairs. az, a−z

A
$a^{2} z^{2} - a z^{2}$

B
$a^{2} z^{2} - a z$

C
$a z - a z^{2}$

D
$a^{2} z - a z^{2}$

Solution

$a z \times (a - z)$
$= (a z \times a) + (a z \times (- z))$
$a^{2} z^{2} - a z^{2}$
Question 2
1 / -0

Simplify: $(1.5 x - 4 a) (1.5 x + 4 a + 3) - 4.5 x + 12$

A
$1.5 x + 4 a$

B
$2.25 x^{2} - 16 a^{2}$

C
$4.5 x + 12 a$

D
0

Solution

$(1.5 x - 4 a) (1.5 x + 4 a + 3) - 4.5 x + 12 a$
$\Rightarrow (1.5 x - 4 a) (1.5 x + 4 a + 3) - 3 (1.5 x - 4 a)$
$⟹ (1.5 x - 4 a) [(1.5 x + 4 a) + (4 a) + 3 - 3]$
$⟹ (1.5 x - 4 a) (1.5 x + 4 a)$
$⟹ (1.5 x)^{2} - (4 a)^{2} ⟹ 2.25 x^{2} - 16 a^{2} .$
Question 3
1 / -0

Find the product $(x + 7 a) (7 x - a)$

A
$7 x^{2} - 7 a^{2} + 48 x a$

B
$7 x - 7 a + 48 x a$

C
$7 x^{2} - 7 a^{2} + 40 x a$

D
$7 x - 7 a^{2} + 48 x a$

Solution

$x (7 x - a) + 7 a (7 x - a)$
$7 x^{2} - x a + 49 x a - 7 a^{2}$
$= 7 x^{2} - 7 a^{2} + 48 x a$
Question 4
1 / -0

Simplify $(m^{2} + 5) (b^{3} + 3) + 5$

A
$m^{2} b^{3} + 3 m^{2} + 5 b^{3} + 20$

B
$m^{2} b^{3} + 3 m^{2} + 5 b^{2}$

C
$m^{2} b^{3} + 3 m^{2} + 5 b^{2}$

D
$m^{2} b^{3} + 3 m^{2} + 5 b^{3} + 15$

Solution

multiplying both thebrackets with get $m^{2} b^{3} + 3 m^{2} + 5 b^{3} + 15 + 5$
$m^{2} b^{3} + 3 m^{2} + 5 b^{3} + 20$
Question 5
1 / -0

Add: $2 j^{2} - 4 k^{2} - l^{2}, 8 j^{2} + 5 k^{2} + 4 j^{2}, 5 j - 5 k^{2} + 2 l^{2}$

A
$16 j + 4 k^{2} - 5 l$

B
$15 j^{2} + 4 k + 5 l$

C
$15 j^{2} - 4 k^{2} + 5 l^{2}$

D
$15 j^{2} + 4 k^{2} - 5 l$

Solution

say A=
$2 j^{2} - 4 k^{2} - l^{2}$
$B = 8 j^{2} + 5 k^{2} + 4 l^{2}$
$C = 5 j^{2} - 5 k^{2} + 2 l^{2}$
Now same variables with same exponents will be added so,
$= 2 j^{2} + 8 j^{2} + 5 j^{2} = 15 j^{2},$
$= - 4 k^{2} + 5 k^{2} + (- 5 k^{2}) = - 4 k^{2},$
$= - l^{2} + 4 l^{2} + 2 l^{2} = 5 l^{2}$
$∴ A + B + C = 15 j^{2} - 4 k^{2} + 5 l^{2}$
Question 6
1 / -0

Add all of them x−8a,3xa−ax−8a,3xa−a and a+1

A
$x + 3 x a - 8 a + 1$

B
$x + 3 x a + 8 a$

C
$x + 2 x a - 6 a + 1$

D
$2 x + x a - 8 a + 1$

Solution

we have,
$x - 8 a, 3 x a - a a n d a + 1$
On adding,
$(x - 8 a) + (3 x a - a) + (a + 1)$
$x - 8 a + 3 x a - a + a + 1$
$x + 3 x a - 8 a + 1$
Question 7
1 / -0

What is the addition of the given variables : p(p−q),q(q−r)p(p−q),q(q−r) & r(r−p)

A
$p + q^{2} + r - p q - q r$

B
$p^{2} + q^{2} + r^{2} - p q - q r - r p$

C
$p^{2} + q + r^{2} + p q + r p - q r$

D
$p^{2} + r^{2} + p q + r p - q r$

Solution

$p (p - q) + q (q - r) + r (r - p)$
$p^{2} - p q + q^{2} - q r + r^{2} - p r$
$= p^{2} + q^{2} + r^{2} - p q - q r - r p$
Question 8
1 / -0

$S o l v e : - x r + y r + x t + y t$

A
$(x + t) (y + r)$

B
$(x + y) (r + t)$

C
$(x + y)$

D
(r+t)

Solution

xr+yr+xt+yt
= r(x+y) + t(x+y)
= (x+y) (r+t)
Hence this is the correct answer.
Question 9
1 / -0

Divide $9 h^{4} b y 3 h^{2}$

A
$3 h^{2}$

B
$4 h^{2}$

C
$3 h$

D
4h

Solution

Let a = $9 h^{4} a n d b = 3 h^{2}$
According to the question,
$\frac{a}{b} = \frac{9 h^{4}}{3 h^{2}}$
$\frac{a}{b} = \frac{3 h^{2} \times 3 h^{2}}{3 h^{2}}$
$\frac{a}{b} = 3 h^{2}$
Hence this is the answer.
Question 10
1 / -0

If a polynomial f(x) isdivided by $c^{2} - 16$ then the remainder is $5 c + 3$ , what will be the remainder when the same polynomial is divided by (c+4)?

A
-17

B
16

C
-15

D
-16

Solution

Let the quotient be q(x)then,
$f (c) = (c^{2} - 16) + (5 c + 3)$
$\frac{f (c)}{(c + 4)} = \frac{(c + 4) (c - 4)}{c + 4} q (c) + \frac{5 c + 3}{c + 4}$
Remainder when 5c+3 is divided by c+4 =5(-4)+3= -17
Question 11
1 / -0

Substract $x + 2 b - c f r o m 3 x - b + 2 c$

A
2x+3b+4c

B
5x+b-6c

C
2x-3b+3c

D
2x+3b-3c

Solution

$= 3 x - b + 2 c - x - 2 b + c$
$= 3 x - b + 2 c - x - 2 b + c$
$= 3 x - x - b - 2 b + 2 c + c$
$2 x - 3 b + 3 c .$
Question 12
1 / -0

Find the product $w^{2} \times (2 w^{2} 2) \times (4 w^{2} 6)$

A
$8 w^{5}$

B
$8 w^{5} 0$

C
$8 w^{5} 5$

D
$8 w^{5} 2$

Solution

All the terms have samebase, so we can add the powers $∴ 8 w^{(} 2 + 22 + 26) = 8 w^{5} 0$
Question 13
1 / -0

Add $2 d^{2} + 7 d + 5; 3 d + 9; 3 d^{2} - 4 d - 3$

A
$5 d^{2} + 6 d + 7$

B
$5 d^{2} - 6 d + 10$

C
$5 d^{2} + 6 d + 11$

D
$5 d + 6 d + 11$

Solution

we have,
$2 d^{2} + 7 d + 5$
$3 d + 9$
$3 d^{2} - 4 d - 3$
According to thequestion,
= $2 d^{2} + 7 d + 5 + 3 d + 9 + 3 d^{2} - 4 d - 3$
= $5 d^{2} + 6 d + 11$
Question 14
1 / -0

Add $(x a + a z)^{2} - 2 x^{2} a^{2} z$ Find the value when $x = - 1, a = 1, z = 2$

A
-3

B
4

C
-2

D
1

Solution

$(x a + a z)^{2} - 2 x^{2} a^{2} z$ when $x = - 1, a = 1, z = 2$
$\to [a (x + z)]^{2} - 2 x^{2} a^{2} z$
$\to a^{2} [x^{2} + z^{2} + 2 x z - 2 x^{2} z]$
Now, putting the values inthe expression
$\to (1)^{2} [(- 1)^{2} + 2^{2} + 2 (- 1) (2) - 2 (- 1)^{2} (2)]$
$\to [1 + 4 - 4 - 4] = - 3$
Question 15
1 / -0

Multiply the binomial (f−8)and (3f−4)

A
$3 f - 28 f + 30$

B
$3 f - 28 f^{2} + 32$

C
$3 f^{2} - 28 f + 32$

D
$3 f^{2} - 28 f + 31$

Solution

$f (3 f - 4) - 8 (3 f - 4)$
$3 f^{2} - 28 f + 32$

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Fundamental Concepts Test - 6

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Fundamental Concepts Test - 6

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Question 1

a2z2-az2

a2z2-az

az-az2

a2z-az2

Solution

Question 2

1.5x+4a

2.25x2-16a2

4.5x+12a

0

Solution

Question 3

7x2-7a2+48xa

7x-7a+48xa

7x2-7a2+40xa

7x-7a2+48xa

Solution

Question 4

m2b3+3m2+5b3+20

m2b3+3m2+5b2

m2b3+3m2+5b2

m2b3+3m2+5b3+15

Solution

Question 5

16j+4k2-5l

15j2+4k+5l

15j2-4k2+5l2

15j2+4k2-5l

Solution

Question 6

x+3xa-8a+1

x+3xa+8a

x+2xa-6a+1

2x+xa-8a+1

Solution

Question 7

p+q2+r-pq-qr

p2+q2+r2-pq-qr-rp

p2+q+r2+pq+rp-qr

p2+r2+pq+rp-qr

Solution

Question 8

(x+t) (y+r)

(x+y) (r+t)

(x+y)

(r+t)

Solution

Question 9

3h2

4h2

3h

4h

Solution

Question 10

-17

16

-15

-16

Solution

Question 11

2x+3b+4c

5x+b-6c

2x-3b+3c

2x+3b-3c

Solution

Question 12

8w5

8w50

8w55

8w52

Solution

$a^{2} z^{2} - a z^{2}$

$a^{2} z^{2} - a z$

$a z - a z^{2}$

$a^{2} z - a z^{2}$

$1.5 x + 4 a$

$2.25 x^{2} - 16 a^{2}$

$4.5 x + 12 a$

$7 x^{2} - 7 a^{2} + 48 x a$

$7 x - 7 a + 48 x a$

$7 x^{2} - 7 a^{2} + 40 x a$

$7 x - 7 a^{2} + 48 x a$

$m^{2} b^{3} + 3 m^{2} + 5 b^{3} + 20$

$m^{2} b^{3} + 3 m^{2} + 5 b^{2}$

$m^{2} b^{3} + 3 m^{2} + 5 b^{2}$

$m^{2} b^{3} + 3 m^{2} + 5 b^{3} + 15$

$16 j + 4 k^{2} - 5 l$

$15 j^{2} + 4 k + 5 l$

$15 j^{2} - 4 k^{2} + 5 l^{2}$

$15 j^{2} + 4 k^{2} - 5 l$

$x + 3 x a - 8 a + 1$

$x + 3 x a + 8 a$

$x + 2 x a - 6 a + 1$

$2 x + x a - 8 a + 1$

$p + q^{2} + r - p q - q r$

$p^{2} + q^{2} + r^{2} - p q - q r - r p$

$p^{2} + q + r^{2} + p q + r p - q r$

$p^{2} + r^{2} + p q + r p - q r$

$(x + t) (y + r)$

$(x + y) (r + t)$

$(x + y)$

$3 h^{2}$

$4 h^{2}$

$3 h$

$8 w^{5}$

$8 w^{5} 0$

$8 w^{5} 5$

$8 w^{5} 2$

$5 d^{2} + 6 d + 7$

$5 d^{2} - 6 d + 10$

$5 d^{2} + 6 d + 11$

$5 d + 6 d + 11$

$3 f - 28 f + 30$

$3 f - 28 f^{2} + 32$

$3 f^{2} - 28 f + 32$

$3 f^{2} - 28 f + 31$