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Maths M.C.Q. [1 Marks Each]

Integers · Jharkhand Board (JAC) STD 7 (Jharkhand - English Medium). 50 questions.

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M.C.Q. [1 Marks Each]

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50 questions · auto-graded multiple-choice test.

MCQ 11 Mark
If $a = (-1) × (-1) × (-1) ..... 100$ times and $b = (-1) × (-1) × (-1) ..... 95$ 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 $y = (-2) × (-2) × (-2) × (-2) × (-2)$ 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
$L.H.S = -4 + 9$
$= 5 = R.H.S$
$a = -4$
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MCQ 81 Mark
Which of the following is correct?
  • A
    $-12 > -9$
  • ✓
    $-12 < -9$
  • C
    $(-12) + 9 > 0$
  • D
    $(-12) \times 9 > 0$
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 $x = (-1) × (-1) × (-1) × (-1) × ...... 25$ times, $y = (-3) × (-3) × (-3),$ 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
$L.H.S = -6 - 8$
$= -6 + (-8)$
$= 14 = R.H.S$
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.
$-20$
$-20$
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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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MCQ 221 Mark
The product of two integers is 105. If one integer 3 more than - 10, then the other integer is
  • A
    -7
  • B
    15
  • ✓
    -15
  • D
    7
Answer
Correct option: C.
-15
C
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MCQ 231 Mark
Which of the following integers is closest to zero on the number line?
  • A
    -10
  • B
    7
  • C
    3
  • ✓
    -2
Answer
Correct option: D.
-2
D
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MCQ 251 Mark
Pair of positive and negative integers whose sum is - 5, is
  • A
    2,3
  • B
    -9,2
  • ✓
    -9,4
  • D
    -2,-3
Answer
Correct option: C.
-9,4
C
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MCQ 281 Mark
The sum of two integers is – 5. If one of them is 6, then the other one is
  • ✓
    -11
  • B
    11
  • C
    1
  • D
    -1
Answer
Correct option: A.
-11
A
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MCQ 301 Mark
The sum of two integers is – 4. If one of them is 5, then the other is
  • A
    4
  • B
    -5
  • ✓
    -9
  • D
    9
Answer
Correct option: C.
-9
C
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MCQ 311 Mark
If $x=(-1) \times(-1) \times(-1) \times(-1) \ 25$ times, $y=(-3) \times(-3) \times(-3)$, then $x y=$
  • A
    -27
  • ✓
    27
  • C
    26
  • D
    -26
Answer
Correct option: B.
27
B
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MCQ 321 Mark
The sum of two integers is 10. If one of them is negative, then other has to be
  • A
    negative
  • ✓
    positive
  • C
    may be positive or negative
  • D
    none of these
Answer
Correct option: B.
positive
B
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MCQ 351 Mark
If a = (-1) x (-1) x (-1) ...100 times and b = (-1) x (-1) x (-1) __________95 times, then a + b =
  • A
    -1
  • B
    -2
  • ✓
    0
  • D
    1
Answer
Correct option: C.
0
C
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MCQ 361 Mark
If x = (-10) + (–10) + __________15 times and y = (-2) x (-2) x (-2) x (-2) x (-2), then x - y =
  • A
    118
  • ✓
    -118
  • C
    -182
  • D
    182
Answer
Correct option: B.
-118
B
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MCQ 401 Mark
The sum of two integers is - 8. If one of the integers is 12, then the other is
  • A
    20
  • B
    4
  • C
    -4
  • ✓
    -20
Answer
Correct option: D.
-20
D
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MCQ 441 Mark
The sum of two integers is 24. If one of them is - 19, then the other is
  • ✓
    43
  • B
    -43
  • C
    5
  • D
    -5
Answer
Correct option: A.
43
A
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MCQ 471 Mark
The modulus of an integer x is 9, then
  • A
    x = 9 only
  • B
    x = -9 only
  • ✓
    x= ±9
  • D
    none of these
Answer
Correct option: C.
x= ±9
C
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