RRB NTPC CBT 1 2016 Mathematics Questions with Solutions

Questions from every shift of the year, grouped by section. Questions 251–252 of 252, each with the correct answer and a step-by-step explanation.

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251Mathematics

If a = 2i + 3j - k and b = i - 2j + 3k, then the projection of a on b is:

A(-7)/(√(14))B(7)/(√(14))C(-7)/(√(11))D(7)/(√(11))

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Answer: (A) (-7)/(√(14))

The scalar projection of vector a on vector b is given by the formula (a · b) / |b|.

Calculating the dot product a · b: a · b = (2 × 1) + (3 × -2) + (-1 × 3) = 2 - 6 - 3 = -7

Calculating the magnitude of vector b: |b| = √(1² + (-2)² + 3²) = √(1 + 4 + 9) = √14

Substituting these values into the formula yields: Projection = -7 / √14

252Mathematics

If Tan A = ¹⁵⁄₈ and Tan B = ⁷⁄₂₄ , then Tan (A + B) = ?

A⁴¹⁶⁄₈₇B⁸⁷⁄₄₁₆C³⁰⁴⁄₂₉₇D²⁹⁷⁄₃₀₄

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Answer: (A) ⁴¹⁶⁄₈₇

Using the tangent addition formula:

tan(A + B) = (tan A + tan B) / (1 - tan A × tan B)

Substitute the given values tan A = 15/8 and tan B = 7/24:

tan A + tan B = 15/8 + 7/24 = (45 + 7) / 24 = 52/24

1 - tan A × tan B = 1 - (15/8 × 7/24) = 1 - 105/192 = 87/192

tan(A + B) = (52/24) / (87/192) = (52 × 8) / 87 = 416/87

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