MCQ test, Set 4

Set 4 of 10
25 questions
25 marks
30 minutes

Download the PDF (with key sheet and solutions, 75.1 KB)

Choose one answer for each question, then check your score at the end. Each correct answer carries 1 mark; there is no negative marking.

$7 \times 7 \times 7 = 7^{\square}$ . The number in the box is
A $21$ B $3$ C $2$ D $7$

Answer and solution

Answer: (B) $3$

7 is multiplied by itself 3 times, so the power is 3.

$7 \times 7 \times 7 = 7^3$
In $a^3$ , the power 3 shows that
A 3 is added to $a$ B $a$ is added to itself 3 times C $a$ is multiplied by 3 D $a$ is multiplied by itself 3 times

Answer and solution

Answer: (D) $a$ is multiplied by itself 3 times

$a^3 = a \times a \times a$ : three $a$ 's are multiplied.
$a \times a \times a \times b \times b \times b$ in power form is
A $a^3 \times b^3$ B $3a \times 3b$ C $(a \times b)^6$ D $a^2 \times b^2$

Answer and solution

Answer: (A) $a^3 \times b^3$

$a \times a \times a = a^3$ and $b \times b \times b = b^3$

So it is $a^3 \times b^3$ .
The next number in $1000, 729, 512, 343, \ldots$ is
A $174$ B $125$ C $216$ D $36$

Answer and solution

Answer: (C) $216$

These are $10^3$ , $9^3$ , $8^3$ , $7^3$ .

Next is $6^3 = 216$
100 lies between
A $4^3$ and $5^3$ B $5^3$ and $6^3$ C $3^3$ and $4^3$ D $10^3$ and $11^3$

Answer and solution

Answer: (A) $4^3$ and $5^3$

$4^3 = 64$ and $5^3 = 125$

$64 < 100 < 125$
Which number is NOT the cube of any whole number?
A $64$ B $1000$ C $216$ D $90$

Answer and solution

Answer: (D) $90$

$64 = 4^3$ , $216 = 6^3$ , $1000 = 10^3$ .

90 is not in the table of cubes.
$\square^3 = 729$ . The number in the box is
A $9$ B $243$ C $81$ D $10$

Answer and solution

Answer: (A) $9$

$9 \times 9 \times 9 = 729$

So the box is 9.
$14^3 =$
A $2197$ B $2744$ C $196$ D $42$

Answer and solution

Answer: (B) $2744$

$14 \times 14 = 196$

$196 \times 14 = 2744$
A big cube is built from small cubes, with 20 small cubes along each edge. How many small cubes does it have?
A $400$ B $8000$ C $240$ D $2400$

Answer and solution

Answer: (B) $8000$

Number = $20^3$

$20 \times 20 = 400$ , $400 \times 20 = 8000$
$17^3 = 289 \times \square$ . The number in the box is
A $289$ B $3$ C $2$ D $17$

Answer and solution

Answer: (D) $17$

$17^3 = 17 \times 17 \times 17$ and $17 \times 17 = 289$

$\therefore 17^3 = 289 \times 17$
Which number, multiplied by itself 3 times, gives $-512$ ?
A $-7$ B $-9$ C $-8$ D $-64$

Answer and solution

Answer: (C) $-8$

$(-8)^3 = -8^3 = -512$
$(-9) \times (-9) \times (-9) =$
A $-243$ B $-729$ C $-27$ D $81$

Answer and solution

Answer: (B) $-729$

$(-9) \times (-9) = 81$

$81 \times (-9) = -729$
$(-40)^3 =$
A $1600$ B $-120$ C $-6400$ D $-64000$

Answer and solution

Answer: (D) $-64000$

$(-40) \times (-40) = 1600$

$1600 \times (-40) = -64000$
$2^3 + 3^3 + 4^3 =$
A $729$ B $27$ C $99$ D $29$

Answer and solution

Answer: (C) $99$

$2^3 + 3^3 + 4^3 = 8 + 27 + 64$

$= 99$
$1^3 + 4^3 =$
A $125$ B $15$ C $65$ D $17$

Answer and solution

Answer: (C) $65$

$1^3 + 4^3 = 1 + 64$

$= 65$
Two big cubes are made of small cubes, with 2 and 5 small cubes along each edge. How many small cubes are there in the two cubes together?
A $133$ B $343$ C $174$ D $29$

Answer and solution

Answer: (A) $133$

Total = $2^3 + 5^3$

$2^3 + 5^3 = 8 + 125$

$= 133$
$(-4)^3 + (-5)^3 =$
A $-41$ B $-189$ C $61$ D $-729$

Answer and solution

Answer: (B) $-189$

$(-4)^3 + (-5)^3 = -64 + (-125)$

$= -64 - 125$

$= -189$
$(-3)^3 + 7^3 =$
A $40$ B $370$ C $316$ D $64$

Answer and solution

Answer: (C) $316$

$(-3)^3 + 7^3 = -27 + 343$

$= 316$
$(-3)^3 + 1^3 + (-2)^3 =$
A $-34$ B $36$ C $-64$ D $-18$

Answer and solution

Answer: (A) $-34$

$(-3)^3 + 1^3 + (-2)^3 = -27 + 1 + (-8)$

$= -27 + 1 - 8$

$= -34$
One big cube has 8 small cubes along each edge and another has 3. How many more small cubes does the first one have?
A $55$ B $125$ C $485$ D $539$

Answer and solution

Answer: (C) $485$

More = $8^3 - 3^3$

$8^3 - 3^3 = 512 - 27$

$= 485$
Ravi says $4^3 - 6^3 = 152$ . The correct value is
A $-280$ B $-8$ C $-20$ D $-152$

Answer and solution

Answer: (D) $-152$

$4^3 - 6^3 = 64 - 216$

$= -152$

Ravi took the smaller cube from the bigger one.
$11^3 - 12^3 =$
A $-23$ B $-397$ C $-1$ D $-3059$

Answer and solution

Answer: (B) $-397$

$12^3 = 144 \times 12 = 1728$

$11^3 - 12^3 = 1331 - 1728$

$= -397$
$-11^3 - (-11)^3 =$
A $11^6$ B $-2 \times 11^3$ C $0$ D $-11^3$

Answer and solution

Answer: (C) $0$

$(-11)^3 = -11^3$

$-11^3 - (-11^3) = -11^3 + 11^3 = 0$
$a^3 - (-a)^3 =$
A $a^6$ B $0$ C $2a$ D $2a^3$

Answer and solution

Answer: (D) $2a^3$

$(-a)^3 = -a^3$

$a^3 - (-a^3) = a^3 + a^3 = 2a^3$
If $x = -2$ and $y = -3$ , then $x^3 + y^3 =$
A $-35$ B $-125$ C $13$ D $19$

Answer and solution

Answer: (A) $-35$

$(-2)^3 + (-3)^3 = -8 + (-27)$

$= -8 - 27$

$= -35$

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MCQ test, Set 4