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All questions of Indices & Surds for RRB NTPC/ASM/CA/TA Exam

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(256)0.16 x (256)0.09 = ?
  • a)
    4
  • b)
    16
  • c)
    64
  • d)
    256.25
Correct answer is option 'A'. Can you explain this answer?

Naroj Boda answered
⇒  (256)0.16 x (256)0.09 = (256)(0.16 + 0.09)
= (256)0.25
= (256)(25 / 100)
= (256)(1 / 4)
= (44)(1 / 4)
= 44(1 / 4)
= 41
= 4

If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to:
  • a)
    0
  • b)
    2
  • c)
    4
  • d)
    6
Correct answer is option 'C'. Can you explain this answer?

Yash Patel answered
⇒  3x - y = 27 = 33    ⇔    x - y = 3 ....(i)
⇒ 3x + y = 243 = 35    ⇔    x + y = 5 ....(ii)
On solving (i) and (ii), we get x = 4.

(6)6.5 × (36)4.5 ÷ (216)4.5 = (6)?
  • a)
    1
  • b)
    2
  • c)
    4
  • d)
    6
Correct answer is option 'B'. Can you explain this answer?

Uday Nambiar answered
(6)6.5 × (36)4.5 ÷ (216)4.5

= (6)6.5 × [(6)2]4.5 ÷ [(6)3]4.5

= (6)6.5 × (6)9 ÷ (6)13.5

= (6)(6.5 + 9 - 13.5) 

= (6)2

1/(1 + x(b - a) + x(c - a)) + 1/(1 + x(a - b) + x(c - b)) + 1/(1 + x(b - c) +x(a - c) ) = ?
  • a)
    0
  • b)
    1
  • c)
    xa - b - c
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Rhea Reddy answered
Given Exp: 
1/(1 + xb / xa + xc / xa) + 1/(1 + xa / xb + xc / xb) + 1/(1 + xb / xc +xa / xc)
= xa/(xa + xb + xc ) + xb/(xa + xb + xc ) + xc/(xa + xb + xc )
= (xa + xb + xc ) / (xa + xb + xc )
= 1.

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?
  • a)
    8.5
  • b)
    13
  • c)
    16
  • d)
    17.5
Correct answer is option 'B'. Can you explain this answer?

Alok Verma answered
Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x.
Then, (52)7.5 x 52.5 / (53) 1.5 = 5x
⇒ (52)7.5 x 52.5 / (5)3 x 1.5 = 5x
⇒ 515 x 52.5 / 54.5 = 5x
⇒ 5x = 5(15 + 2.5 - 4.5)
⇒ 5x = 513
∴ x = 13.

  • a)
  • b)
    1
  • c)
    2
  • d)
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
To solve the equation (a / b)x - 1 = (b / a)x - 3, we can start by simplifying both sides of the equation.

Step 1: Simplify the left side of the equation
(a / b)x - 1 = (b / a)x - 3
Multiply both sides of the equation by b to eliminate the fraction:
a^x - b = (b^2 / a)x - 3b

Step 2: Simplify the right side of the equation
(b / a)x - 3 = (b^2 / a)x - 3
Multiply both sides of the equation by a to eliminate the fraction:
ab^x - 3a = b^2x - 3a

Step 3: Combine like terms
a^x - b = ab^x - 3a
Rearrange the terms:
a^x - ab^x = b - 3a

Step 4: Factor out common terms
a^x(1 - b) = b - 3a

Step 5: Divide both sides of the equation by (1 - b)
a^x = (b - 3a) / (1 - b)

Step 6: Simplify the right side of the equation
a^x = (-3a + b) / (b - 1)

Step 7: Take the logarithm of both sides of the equation
log(a^x) = log((-3a + b) / (b - 1))

Step 8: Apply logarithmic properties
x log(a) = log((-3a + b) / (b - 1))

Step 9: Divide both sides of the equation by log(a)
x = log((-3a + b) / (b - 1)) / log(a)

At this point, we have obtained an expression for x in terms of a and b. To determine the specific value of x, we need to know the values of a and b. Without this information, we cannot calculate the exact value of x.

However, if we are given values for a and b, we can substitute them into the equation to find the value of x. In this case, the correct answer is option C, but we need to know the specific values of a and b to confirm this.

if 6m = 46656, What is the value of 6m-2
  • a)
    36
  • b)
    7776
  • c)
    216
  • d)
    1296
Correct answer is option 'D'. Can you explain this answer?

Sagar Sharma answered
Given: 6m = 46656

To find: The value of 6m - 2a

Solution:
We are given that 6m = 46656. We can solve this equation to find the value of m.

Dividing both sides of the equation by 6:
6m/6 = 46656/6
m = 7776

Now, we need to find the value of 6m - 2a.

Substituting the value of m in the equation:
6m - 2a = 6(7776) - 2a

Simplifying the equation:
6(7776) - 2a = 46656 - 2a
46656 - 2a = 46656 - 2a
46656 - 2a = 46656 - 2a

We can see that the equation is balanced on both sides and there are no variables left.

The value of 6m - 2a is equal to 46656.

Therefore, the correct answer is option D) 1296.

Chapter doubts & questions for Indices & Surds - Mathematics for RRB NTPC / ASM 2025 is part of RRB NTPC/ASM/CA/TA exam preparation. The chapters have been prepared according to the RRB NTPC/ASM/CA/TA exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for RRB NTPC/ASM/CA/TA 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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