RD Sharma solution class 7 chapter 7 Algebraic Expression Objective Type Questions

Objective Type Questions

Page-7.21

Question 1:

Mark the correct alternative in the following question:

Which of the following pairs is/are like terms?
(1) x           (2) x²           (3) 3x³           (4) 4x³

(a) 1, 2                               (b) 2, 3                               (c) 3, 4                              (d) None of these

Answer 1:

Since, 3x³ and 4x³ is the pair of like terms.

Hence, the correct option is (c).

Question 2:

Mark the correct alternative in the following question:

Which of the following is not a monomial?

(a) 2x² + 1                           (b) 3x⁴                           (c) ab                           (d) x²y

Answer 2:

Since, 2x² + 1 has two terms 2x² and 1.

So, 2x² + 1 is a binomial.

Hence, the correct alternative is option (a).

Question 3:

Mark the correct alternative in the following question:

The sum of the coefficients in the monomials 3a²b and $-$2ab² is

(a) 5                           (b) $-$1                           (c) 1                           (d) 6

Answer 3:

Since, the coefficient in the monomial 3a²b is 3 and the coefficient in the monomial $-$2ab² is $-$2.

So, the sum of the coefficients in the monomials 3a²b and $-$2ab² = 3 + ($-$2) = 3 $-$ 2 = 1

Hence, the correct alternative is option (c).

Question 4:

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{The} \mathrm{coefficient} \mathrm{of} x^2 \mathrm{in} -\frac{5}{3}{x}^{2}y \mathrm{is} \mathrm{equal} \mathrm{to} \\ \left(\mathrm{a}\right) -\frac{5}{3} \left(\mathrm{b}\right) -\frac{5}{3}y \left(\mathrm{c}\right) \frac{5}{3} \left(\mathrm{d}\right) \frac{5}{3}y \end{gathered}$$

Answer 4:

$\mathrm{Since}, \mathrm{the} \mathrm{coefficient} \mathrm{of} x^2 \mathrm{in} -\frac{5}{3}{x}^{2}y \mathrm{is} \mathrm{equal} \mathrm{to} -\frac{5}{3}y.$

Hence, the correct alternative is option (b).

Question 5:

Mark the correct alternative in the following question:

If a, b and c are respectively the coefficients of x² in $-$x², 2x² + x and 2x $-$ x², respectively, then a + b + c =

(a) 0                                         (b) $-$2                                         (c) 2                                         (d) $-$1

Answer 5:

As, the coefficient x² in $-$x² = $-$1, the coefficient x² in 2x² + x = 2 and the coefficient x² in 2x $-$ x² = $-$1.

Now, a + b + c = ($-$1) + 2 + ($-$1) = $-$2 + 2 = 0

Hence, the correct alternative is option (a).

Question 6:

Mark the correct alternative in the following question:

The sum of the coefficients in the terms of 2x²y $-$ 3xy² + 4xy is

(a) $-$3                                     (b) 3                                     (c) 9                                     (d) 5

Answer 6:

As, the coefficient in the term 2x²y = 2, the coefficient in the term $-$3xy² = $-$3 and the coefficient in the term 4xy = 4.

So, the sum of the coefficients in the terms of 2x²y $-$ 3xy² + 4xy = 2 + ($-$3) + 4 = $-$3 + 6 = 3

Hence, the correct alternative is option (b).

Question 7:

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{The} \mathrm{product} \mathrm{of} \mathrm{the} \mathrm{coefficients} \mathrm{of} \mathrm{terms} \mathrm{in} -\frac{4}{3}a{b}^2+\frac{1}{4}b{c}^2+3c{a}^2 \mathrm{is} \\ \left(\mathrm{a}\right) 1 \left(\mathrm{b}\right) \frac{1}{2} \left(\mathrm{c}\right) -1 \left(\mathrm{d}\right) 3 \end{gathered}$$

Answer 7:

$$\begin{gathered} \mathrm{As}, \mathrm{the} \mathrm{coefficient} \mathrm{of} \mathrm{the} \mathrm{term} -\frac{4}{3}a{b}^2 \mathrm{is} -\frac{4}{3}, \\ \mathrm{the} \mathrm{coefficient} \mathrm{of} \mathrm{the} \mathrm{term} \frac{1}{4}b{c}^2 \mathrm{is} \frac{1}{4} \mathrm{and} \\ \mathrm{the} \mathrm{coefficient} \mathrm{of} \mathrm{the} \mathrm{term} 3c{a}^2 \mathrm{is} 3. \\ \mathrm{So}, \mathrm{the} \mathrm{product} \mathrm{of} \mathrm{the} \mathrm{coefficients} \mathrm{of} \mathrm{the} \mathrm{terms}=-\frac{4}{3}\times \frac{1}{4}\times 3=-1 \end{gathered}$$

Hence, the correct alternative is option (c).

Question 8:

Mark the correct alternative in the following question:

If a and b are respectively the sum and product of coefficients of terms in the expression x² + y² + z² $-$ xy $-$ yz $-$ zx, then a + 2b =

(a) 0                                             (b) 2                                             (c) $-$2                                             (d) $-$1

Answer 8:

We have,
The expression x² + y² + z² $-$ xy $-$ yz $-$ zx,
 

Terms	Coefficients
x2	1
y2	1
z2	1
$-$xy	$-$1
$-$yz	$-$1
$-$zx	$-$1
Sum, a	0
Product, b	$-$1

So, a + 2b = 0 + 2($-$1) = $-$2

Hence, the correct alternative is option (c).

Question 9:

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If} P=3x^3+3x^2+3x+3 \mathrm{and} Q=3x^2-3x+3, \mathrm{then} P-Q= \\ \left(\mathrm{a}\right) 3x^3 \left(\mathrm{b}\right) 3x^3+6x^2+6x+6 \left(\mathrm{c}\right) 6x^2+6x+6 \left(\mathrm{d}\right) 3x^3+6x \end{gathered}$$

Answer 9:

$$\begin{gathered} \mathrm{We} \mathrm{have}, \\ P=3x^3+3x^2+3x+3 \mathrm{and} Q=3x^2-3x+3 \\ \mathrm{Now}, \\ P-Q=\left(3x^3+3x^2+3x+3\right)-\left(3x^2-3x+3\right) \\ =3x^3+3x^2+3x+3-3x^2+3x-3 \\ =3x^3+6x \end{gathered}$$

Hence, the correct alternative is option (d).

Question 10:

Mark the correct alternative in the following question:

The sum of the values of the expression 2x² + 2x + 2 when x = $-$1 and x = 1 is
​
(a) 6                                         (b) 8                                         (c) 4                                         (d) 2

Answer 10:

Since, when x = $-$1, the value of the expression 2x² + 2x + 2 = 2($-$1)² + 2($-$1) + 2 = 2 $-$ 2 + 2 = 2

And, when x = 1, the value of the expression 2x² + 2x + 2 = 2(1)² + 2(1) + 2 = 2 + 2 + 2 = 6

So, the sum of the values of the expression 2x² + 2x + 2 when x = $-$1 and x = 1 = 2 + 6 = 8

Hence, the correct alternative is option (b).

Question 11:

Mark the correct alternative in the following question:

What should be added to 3x² + 4 to get 9x² $-$ 7?
​
(a) 6x² $-$ 11                               (b) 6x² + 11                               (c) 12x² $-$ 11                               (d) 12x² + 11

Answer 11:

Since, (9x² $-$ 7) $-$ (3x² + 4) = 9x² $-$ 7 $-$ ​3x² $-$ 4 = 6x² $-$ 11

 So, 6x² $-$ 11 should added to 3x² + 4 to get 9x² $-$ 7.

Hence, the correct alternative is option (a).

Question 12:

Mark the correct alternative in the following question:

How much is a² $-$ 3a greater than 2a² + 4a?

(a) a² $-$ 7a                                (b) a² + 7a                                (c) $-$a² $-$ 7a ​                               (d) $-$a² + 7a

Answer 12:

Since, (a² $-$ 3a) $-$ (2a² + 4a) = a² $-$ 3a $-$ 2a² $-$ 4a = $-$ a² $-$​7a

So, a² $-$ 3a is greater than 2a² + 4a by $-$ a² $-$​7a.

Hence, the correct alternative is option (c).

Question 13:

Mark the correct alternative in the following question:

How much is $-$2x² + x + 1 less than x² + 2x $-$ 3?

(a) $-$x² + 3x $-$ 2                      (b) 3x² + x $-$ 4                      (c) $-$3x² $-$ x + 4                       (d) 3x² + 3x $-$ 4

Answer 13:

Since, (x² + 2x $-$ 3) $-$ ($-$2x² + x + 1) = x² + 2x $-$ 3 + 2x² $-$ x $-$ 1 = 3x² + x $-$ 4

So, $-$2x² + x + 1 is less than x² + 2x $-$ 3 by 3x² + x $-$ 4.

Hence, the correct alternative is option (b).

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Question 14:

Mark the correct alternative in the following question:

​What should be added to xy + yz + zx to get $-$xy $-$ yz $-$ zx?

(a) $-$2xy $-$ 2yz $-$ 2zx                       (b) $-$3xy $-$ yz $-$ zx                       (c) $-$3xy $-$ 3yz $-$ 3zx ​                      (d) 2xy + 2yz + 2zx

Answer 14:

Since, ($-$xy $-$ yz $-$ zx) $-$ (xy + yz + zx) = $-$xy $-$ yz $-$ zx $-$ xy $-$ yz $-$ zx = $-$2xy $-$ 2yz $-$ 2zx

So, $-$2xy $-$ 2yz $-$ 2zx should be added to xy + yz + zx to get $-$xy $-$ yz $-$ zx.

Hence, the correct alternative is option (a).