MCQ

MCQ 11 Mark

The coefficient of $x^2$ in $-\frac{5}{3} x^2 y$ is equal to:

A
$-\frac53$
✓
$-\frac53\text{y}$
C
$\frac{5}{3}$
D
$\frac{5}{3} y$

Answer

Correct option: B.

$-\frac53\text{y}$

Since, the coefficient of $x^2$ in $-\frac{5}{3} x^2 y$ is equal to $-\frac{5}{3} y$
Hence, the correct alternative is option $(b).$

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MCQ 21 Mark

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

✓
$0$
B
$-2$
C
$2$
D
$-1$

Answer

Correct option: A.

$0$

As, the coefficient $x^2$ in $-x^2=-1$, the coefficient $x^2$ in $2 x^2+x=2$ and the coefficient $x^2$ in $2 x-x^2=-1$.
Now, $a + b + c =(-1)+2+(-1)=-2+2=0$
Hence, the correct alternative is option $(a).$

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MCQ 31 Mark

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

A
$-x^2+3 x-2$
✓
$3 x^2+x-4$
C
$-3 x^2-x+4$
D
$3 x^2+3 x-4$

Answer

Correct option: B.

$3 x^2+x-4$

Since, $\left(x^2+2 x-3\right)-\left(-2 x^2+x+1\right)$
$=x^2+2 x-3+2 x^2-x-1$
$=3 x^2+x-4$
So, $-2 x^2+x+1$ is less than $x^2+2 x-3$ by $3 x^2+x-4$.
Hence, the correct alternative is option $(b).$

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MCQ 41 Mark

What should be added to $3 x^2+4$ to get $9 x^2-7$ ?

✓
$6 x^2-11$
B
$6 x^2+11$
C
$12 x^2-11$
D
$12 x^2+11$

Answer

Correct option: A.

$6 x^2-11$

Since, $\left(9 x^2-7\right)-\left(3 x^2+4\right)=9 x^2-7-3 x^2-4=6 x^2-11$
So, $6 x^2-11$ should added to $3 x^2+4$ to get $9 x^2-7$.
Hence, the correct alternative is option $(a).$

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MCQ 51 Mark

Which of the following is not a monomial?

✓
$2 x^2+1$
B
$3 x^4$
C
$a b$
D
$x^2 y$

Answer

Correct option: A.

$2 x^2+1$

Since, $2 x^2+1$ has two terms $2 x^2$ and $1 $.
So, $2 x^2+1$ is a binomial.
Hence, the correct alternative is option $(a).$

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MCQ 61 Mark

The sum of the values of the expression $2 x^2+2 x+2$ when $x=-1$ and $x=1$ is:

A
$6$
✓
$8$
C
$4$
D
$2$

Answer

Correct option: B.

$8$

Since, when $x=-1$, the value of the expression $2 x^2+2 x+2$
$=2(-1)^2+2(-1)+2$
$=2-2+2$
$=2$
And, when $x=1$, the value of the expression $2 x^2+2 x+2$
$=2(1)^2+2(1)+2$
$=2+2+2$
$=6$
So, the sum of the values of the expression $2 x^2+2 x+2$ when $x=-1$ and $x=1=2+6=8$
Hence, the correct alternative is option $(b).$

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MCQ 71 Mark

Which of the following pairs is/ are like terms?
$i. x$
$ii. x^2$
$iii. 3 x^3$
$iv.4 x^3$

A
$(i), (ii)$
B
$(ii), (iii)$
✓
$(iii), (iv)$
D
None of these.

Answer

Correct option: C.

$(iii), (iv)$

Since, $3 x^3$ and $4 x^3$ is the pair of like terms.
Hence, the correct alternative option is $(c).$

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MCQ 81 Mark

If $P=3 x^3+3 x^2+3 x+3$ and $Q=3 x^2-3 x+3$, then $P-Q=$

A
$3 x^3$
B
$3 x^3+6 x^2+6 x+6$
C
$6 x^2+6 x+6$
✓
$3 x^3+6 x$

Answer

Correct option: D.

$3 x^3+6 x$

We have,
$P=3 x^3+3 x^2+3 x+3 \text { and } Q=3 x^2-3 x+3$
Now,
$P-Q\left(3 x^3+3 x^2+3 x+3\right)-\left(3 x^2-3 x+3\right)$
$=3 x^3+3 x^2+3 x+3-3 x^2+3 x-3$
$=3 x^3+6 x$
Hence, the correct alternative is option $(d).$

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MCQ 91 Mark

The sum of the coefficients in the terms of $2 x^2 y-3 x y^2+4 x y$ is:

A
$-3$
✓
$3$
C
$9$
D
$5$

Answer

Correct option: B.

$3$

As, the coefficient in the term $2 x^2 y=2$, the coefficient in the term $-3 x y^2=-3$ and the coefficient in the term $4 x y=4$.
So, the sum of the coefficients in the terms of $2 x^2 y-3 x y^2+4 x y$
$=2+(-3)+4$
$=-3+6$
$=3$
Hence, the correct alternative is option $(b).$

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MCQ 101 Mark

The Peoduct of the coeffiecients of terms in $-\frac{4}{3}\text{ab}^2+\frac14\text{bc}^2+3\text{ca}^2$ is

A
$1$
B
$\frac{1}{2}$
✓
$ -1$
D
$3$

Answer

Correct option: C.

$ -1$

As, the coefficient of the term $-\frac{4}{3} ab ^2$ is $-\frac{4}{3}$, the coefficient of the term $\frac{1}{4} bc ^2$ is $\frac{1}{4}$ and the coefficient of the term $3 ca ^2$ is $3$.
So, the product of the coefficients of the terms $=-\frac{4}{3} \times 14 \times 3=-1$
Hence, the correct alternative is option $(c).$

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MCQ 111 Mark

If $a$ and $b$ are respectively the sum and product of coefficients of terms in the expression $x^2+y^2+z^2-x y-y z-z x$, then $a+2 b=$

A
$0$
B
$2$
✓
$-2$
D
$-1$

Answer

Correct option: C.

$-2$

We have,
The expression $x^2+y^2+z^2-x y-y z-z x$,

Terms	Coefficients
$x^2$	$1$
$y^2$	$1$
$z^2$
-$xy$	$-1$
$-yz$	$-1$
$-zx$	$-1$
Sum, $a$	$0$
Product,$b$	$-1$

So, $a + 2b$
$= 0 + 2(-1)$
$= -2$
Hence, the correct alternative is option $(c).$

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