MCQ - Maths STD 7 Questions - Vidyadip

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20 questions · auto-graded multiple-choice test.

MCQ 11 Mark

If $a = (-1) \times (-1) \times (-1) ..... 100$ times and $b = (-1) \times (-1) \times (-1) ..... 95$ times, then $a + b =$

A
$-1$
B
$-2$
✓
$0$
D
$1$

Answer

Correct option: C.

$0$

$a = (-1) \times (-1) \times (-1) \times ...... 100$ times
Here, the number of integers in the product is even.
$\therefore\ a = (-1) \times (-1) \times (-1) \times ...... 100$ times
$= 1 \times 1 \times 1 \times ...... 100$ times
$= 1$
$b = (-1) \times (-1) \times (-1) \times ..... 95$ times
Here, the number of integers in the product is odd.
$\therefore\ b = (-1) \times (-1) \times (-1) \times ... 95$ times
$= − (1 \times 1 \times 1 \times ... 95$ times$)$
$= −1$
So,
$a + b = 1 + (-1) = 0$

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MCQ 21 Mark

$||3 - 2| - 4| =$

A
$-5$
✓
$5$
C
$7$
D
$-7$

Answer

Correct option: B.

$5$

$||3 - 12| - 4|$
$= ||3 + (-12)| - 4|$
$= ||-9| - 4|$
$= |9 - 4| ($Absolute value of an integer is its numerical value regardless of its sign$)$
$= |5|$
$= 5$

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MCQ 31 Mark

If $x = (-10) + (-10) + ..... 15$ times and $y = (-2) \times (-2) \times (-2) \times (-2) \times (-2)$ then $x - y =$

A
$118$
✓
$-118$
C
$-182$
D
$182$

Answer

Correct option: B.

$-118$

$x = (-10) + (-10) + ..... 15$ times
$= - (10 + 10 + .... 15$ times$)$
$= -150$
$y = (-2) × (-2) × (-2) × (-2) × (-2)$
$= -(2 × 2 × 2 × 2 × 2) ($When the number of negative integers in a product is odd, the product is negative$)$
$= -32$
$\therefore x - y = -150 - (-32)$
$= -150 + 32$
$= -118$

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MCQ 41 Mark

$(-35) \times 2 + (-35) \times 8 =$

✓
$-350$
B
$-70$
C
$-280$
D
$350$

Answer

Correct option: A.

$-350$

$(-35) \times 2 + (-35) \times 8$
$= (-35) \times (2 + 8) [a \times b + a \times c = a \times (b + c)]$
$= (-35) \times 10$
$= -350$

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MCQ 51 Mark

What should be divided by $6$ to get $-18?$

A
$-3$
B
$3$
✓
$-108$
D
$108$

Answer

Correct option: C.

$-108$

$\therefore\ \text{x}\div6=-18$
$\Rightarrow\frac{\text{x}}{6}=-18$
Putting $x = -108$, we get
$\text{L.H.S}=\frac{-108}{6}=-\frac{|-108|}{6}$
$=-\frac{108}{6}=-18=\text{R.H.S}$
Thus, $-108$ should be divided by $6$ to get $-18$

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MCQ 61 Mark

$(-1) + (-1) + (-1) + (-1) + .......... 500$ times $=$

A
$500$
B
$1$
C
$-1$
✓
$-500$

Answer

Correct option: D.

$-500$

$(-1) + (-1) + (-1) + (-1) + .......... 500$ times
$= -(1 + 1 + 1 + 1 + ..... 500$ times$)$
$= -500$

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MCQ 71 Mark

If the difference of an integer a and $(-9)$ is $5$, then:

A
$4$
B
$5$
✓
$-4$
D
$-9$

Answer

Correct option: C.

$-4$

$a - (-9) = 5 ($Given$)$
$\Rightarrow a + 9 = 5$
Putting $a = -4$, we get
$\text{L.H.S} = -4 + 9$
$= 5 = \text{R.H.S}$
$a = -4$

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MCQ 81 Mark

Which of the following is correct?

A
$-12 > -9$
✓
$-12 < -9$
C
$(-12) + 9 > 0$
D
$(-12) × 9 > 0$

Answer

Correct option: B.

$-12 < -9$

We know that if $a$ and $b$ are two negative integers, then the integer with greater absolute value is less than the integer with smaller absolute value.
Absolute value of $-12 = |-12| = 12$
Absolute value of $-9 = |-9| = 9$
$\therefore -12 < -9$
Also,
$(-12) + 9 = -3 < 0$
and $(-12) \times 9 = -(12 \times 9) = -108 < 0$

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MCQ 91 Mark

$(-1) \times (-1) \times (-1) \times (-1) \times .......... 500$ times $=$

A
$-1$
✓
$1$
C
$500$
D
$-500$

Answer

Correct option: B.

$1$

The number of integers in the given product is even.
$\therefore (-1) \times (-1) \times (-1) \times (-1) \times ........ 500$ times
$= 1 \times 1 \times 1 \times 1 \times ..... 500$ times
$= 1$

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MCQ 101 Mark

The sum of two integers is $10$. If one of them is negative, then the other has to be:

A
Negative.
✓
Positive.
C
May be positive or negative.
D
None of these.

Answer

Correct option: B.

Positive.

It is given that the sum of two integers is $10$, which is a positive integer.
But, we know that the sum of two negative integers is always a negative integer.
So, if the sum of two integers is positive and one of them is negative, then the other has to be positive.
For example,
$\Rightarrow -2 + 12 = 10$
$\Rightarrow -5 + 15 = 10$
Thus, the other integer has to be positive.

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MCQ 111 Mark

The modulus of an integer $x$ is $9$, then:

A
$x = 9$ only.
B
$x = -9$ only.
✓
$\text{x}=\pm9$
D
None of these.

Answer

Correct option: C.

$\text{x}=\pm9$

The modulus $($or absolute value$)$ of an integer is its numerical value regardless of its sign.
The absolute value of an integer is always non$-$negative.
It is given that,
Modulus of $x = |x| = 9$
Now, $|-9| = 9$ and $|9| = 9$
$\therefore x = -9$ or $x = 9$
$\text{x}=\pm9$

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MCQ 121 Mark

By how much does $5$ exceed $-4?$

A
$1$
B
$-1$
✓
$9$
D
$-9$

Answer

Correct option: C.

$9$

Difference between $5$ and $-4 = 5 - (-4)$
$= 5 + 4 = 9$
Thus, $5$ exceed $-4$ by $9$

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MCQ 131 Mark

If $x = (-1) \times (-1) \times (-1) \times (-1) \times ...... 25$ times, $y = (-3) \times (-3) \times (-3)$, then $xy =$

A
$-27$
✓
$27$
C
$26$
D
$-26$

Answer

Correct option: B.

$27$

$x = (-1) \times (-1) \times (-1) \times (-1) \times ..... 25$ times
The number of integers in the given product is odd.
$x = (-1) \times (-1) \times (-1) \times (-1) \times ...... 25$ times
$= -(1 \times 1 \times 1 \times ...... 25$ times$)$
$= -1$
$y = (-3) \times (-3) \times (-3)$
The number of integers in the given product is odd.
$y = (-3) \times (-3) \times (-3)$
$= -(3 \times 3 \times 3)$
$= -27$
So,
$xy = (-1) \times (-27) = 27 ($Product of two negative integers is always positive$)$

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MCQ 141 Mark

The sum of two integers is $24$. is one them is $-9$, then the other is:

✓
$43$
B
$-43$
C
$5$
D
$-5$

Answer

Correct option: A.

$43$

Sum of two integers $= 24$
One of the integers $= -19$
$\therefore$ Other integer $=$ Sum of two integers $-$ One of the integers$= 24 - (-19)$
$= 24 + 19$
$= 43$

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MCQ 151 Mark

What must be subtracted from $-6$ to obtain $-14?$

✓
$8$
B
$20$
C
$-20$
D
$-8$

Answer

Correct option: A.

$8$

Let $x$ be subtracted from $-6$ to obtain $-14.$
$\therefore -6 - x = -14$
Putting $x = 8$, we get
$\text{L.H.S} = -6 - 8$
$= -6 + (-8)$
$= 14 = \text{R.H.S}$
Thus, $8$ must be subtracted from $-6$ to obtain $-14$

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MCQ 161 Mark

If $\text{x}\div29=0,$ then $x =$

A
$29$
B
$-29$
✓
$0$
D
None of these.

Answer

Correct option: C.

$0$

We know that if a is a non$-$zero integer, then $0\div\text{a}=0$
$\therefore\ \text{x}\div29=0$
$\text{x}=0$

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MCQ 171 Mark

The additive inverse of $-7$ is:

A
$-7$
B
$-\frac{1}{7}$
✓
$7$
D
$\frac{1}{7}$

Answer

Correct option: C.

$7$

We know that, for every integer a, there exists integer $-a$ such that
$a + (-a) = 0 = -a + a$
Here, $-a$ is the additive inverse of a and a is the additive inverse of $-a.$
Now, $7 + (-7) = 0 = -7 + 7$
$\therefore\ 7$ is the additive inverse of $-7$

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MCQ 181 Mark

The Sum of two integers is $-8$. If one of the integers is $2$, then the other is:

A
$20$
B
$4$
C
$-4$
✓
$-20$

Answer

Correct option: D.

$-20$

Sum of two integers $= -8$
One of the integers $= 12$
$\therefore$ Other integer $=$ Sum of two integers $-$ One of the integers
$= -8 - 12$
$= -8 + (-12)$
$= -20$

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MCQ 191 Mark

On subtracting $-14$ from $-18$, we get:

A
$4$
✓
$-4$
C
$-32$
D
$32$

Answer

Correct option: B.

$-4$

$-14$ subtracted from $-18$
$= -18 - (-14)$
$= -18 + 14$
$= -4$

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MCQ 201 Mark

By how much less than $-3$ is $-7?$

✓
$4$
B
$-4$
C
$10$
D
$-10$

Answer

Correct option: A.

$4$

Difference between $-3$ and $-7 = (-3) - (-7)$
$= -3 + 7 = 4$
Thus, $-7$ is less than $-3$ by $4$

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