CBSE Class 8 Mathematics Exponents and Powers Assignments Set 02

Question. The value of 2²⁰⁰¹ + 2¹⁹⁹⁹ / 2²⁰⁰⁰ - 2¹⁹⁹⁸, is ____.
(A) 2
(B) 10/3
(C) 2¹⁰⁰⁰ + 1
(D) 10
Answer : B

Question. When simplified, (x –1 + y –1)–1 is equal to ____.
(A) x + y
(B) xy/x + y
(C) x y
(D) 1/x y
Answer : B

Question. The value of x + x (xx) at x = 2 is ____.
(A) 10
(B) 16
(C) 18
(D) 36
Answer : A

Question. If ax = by = c^z and b² = ac, then y equals
(A) 2xz/x + z
(B) xz/2(x − z)
(C) xz/2(z − x)
(D) 2xz/(x − z)
Answer : A

Question. Find x, if (5/11)^-3 x (5/11)⁵ = (5/11)^x.
(A) 3
(B) 4
(C) 8
(D) 2
Answer : D

Question. The size of a red blood cell is 0.000007 m and the size of a plant cell is 0.00001275 m.
Find the ratio of the size of red blood cell to that of plant cell.
(A) 13 : 56
(B) 28 : 51
(C) 31 : 39
(D) 22 : 31
Answer : B

Question. Pluto is 5913000000 km away from the Sun.
Express this distance in standard form.
(A) 5.913 × 10^–11
(B) 5.913 × 10^–9
(C) 5.913 × 10⁶
(D) 5.913 × 10⁹
Answer : D

Question. Solve for y, if

(A) 1/2
(B) −19/18
(C) 3/10
(D) 12/17
Answer : B

Question. Simplify :

(A) 1
(B) (a + b + c)³
(C) a² + b² + c²
(D) 0
Answer : A

Question. If (6x)⁶ = 62³ = then find the value of x.
(A) 1
(B) √6
(C) 3√6
(D) 6√6
Answer : C

Question. Find the value of (0.000064)^5/6 ÷ (0.00032)^6/5 .
(A) 0.2
(B) 0.4
(C) 5
(D) 2.5
Answer : C

Question. The value of (7^–1 – 8^–1)–1 – (3^–1 – 4^–1)^–1 is 
(A) 56
(B) 12
(C) 68
(D) 44
Answer : C

Question. When 5 × 10^–3 – 2000 × 10^–6 is expressed in standard form, we will get
(A) 3 × 10^–2
(B) 3 × 10^–3
(C) 3 × 10³
(D) 3 × 10²
Answer : B

Question. If 3^{(x – y)} = 27 and 3^{(x + y)} = 243, then x is equal to _______.
(A) 0
(B) 2
(C) 4
(D) 6
Answer : C

Question. Number of prime factors in (216)^3/5 x (2500)^2/5 x (300)^1/5 is _______.
(A) 6
(B) 9
(C) 8
(D) None of these
Answer : D

Question. Match the following.

(A) (P) → (iii); (Q) → (i); (R) → (iv); (S) → (ii)
(B) (P) → (iv); (Q) → (i); (R) → (ii); (S) → (iii)
(C) (P) → (ii); (Q) → (iii); (R) → (iv); (S) → (i)
(D) (P) → (iii); (Q) → (i); (R) → (ii); (S) → (iv)
Answer : A

Question. If x = (3/2)² x (2/3)^-4, find the value of x^–2.
(A) (4/3)¹² 
(B) (2/3)¹² 
(C) (3/2)¹² 
(D) (3/4)¹² 
Answer : B

Question. Fill in the blanks.
(i) If m² = 27^2/3 × 16^–3/2, then m = P 
(ii) If ab = 1, then 1/1+1a^-1 + 1/1 + b^-1 = Q 
(iii) If x = (8^2/3 · 32^–2/5), then x^–5 = R 
        P          Q           R
(A) 5/4         0         10/7
(B) 1            1         5/16
(C) 3/8         1         1
(D) 7/8         0         7/8
Answer : C

Question. If  10/3 × 3^x – 3^{x – 1} = 81, then the value of x is ____.
(A) 2
(B) 1
(C) 3
(D) 0
Answer : C

Question. Which of the following values are equal ?
P. 14     Q. 40
R. 04     S. 41
(A) P and Q
(B) Q and R
(C) P and R
(D) P and S
Answer : A

Question. The cell of bacteria doubles itself after every 1 hour. How many cells will there be after 8 hours?
(A) 200 times of the original
(B) 2¹⁰ times of the original
(C) 2⁸ times of the original
(D) 2⁶ times of the original
Answer : C

19. At the end of the 20^th century, the world’s population was approximately 6.125 × 10⁹.
Express this population in usual form.
(A) 6.125 × 10¹⁰
(B) 6125000000
(C) 6125 × 10⁵
(D) 61250000
Answer : B

Question. Weight of moon is (7.346 × 10²²) kg and weight of Earth is (5.9724 × 10²⁴) kg. What is the total weight of both in standard form?
(A) 6.04 × 10²⁴ kg
(B) 7.08 × 10²² kg
(C) 5.98 × 10²⁴ kg
(D) 6.44 × 10²⁴ kg
Answer : A

Question. Simplify :

(A) (2/3)^-4
(B) 32/3
(C) 243/16
(D) 243/32
Answer : D

Question. If a = (2^–2 – 2^–3), b = (2^–3 – 2^–4) and c =(2^–4 – 2^–2) then find :
(i) a³ + b³ + c³ (ii) 10 abc
           (i)                      (ii)
(A) 9/2048                 7/2048
(B) 3/1024                 5/2048
(C) –3/1024             –10/2048
(D) –9/2048             –15/1024
Answer : D

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