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GATE ME Algebra — practice questions

Explore 3 free Algebra questions in GATE ME Engineering Materials. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra questions and exercises with answers

Showing questions 1–3 of 3.

A BASIC requirement for a matrix material in FRP is:Read the answer and worked solution →Of these common FRP reinforcing fibers — Glass, Carbon, Kevlar (Aramid), Boron — which has the HIGHEST SPECIFIC STIFFNESS (E/ρ)?Read the answer and worked solution →Modulus of typical CARBON fibers is approximately:Read the answer and worked solution →

Worked practice questions

A BASIC requirement for a matrix material in FRP is:

  1. Lower elastic modulus than fibers
  2. STRAIN AT BREAK must be LARGER than the strain at break of the fibers it holds
  3. Higher density
  4. Higher tensile strength than the fibers
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Correct answer: B. STRAIN AT BREAK must be LARGER than the strain at break of the fibers it holds

If the matrix were to fail at lower strain than fibers, the composite would fail at matrix failure — fibers never reach their capacity. Matrix strain-at-break > fiber strain-at-break ensures fibers carry load until their own failure.

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Of these common FRP reinforcing fibers — Glass, Carbon, Kevlar (Aramid), Boron — which has the HIGHEST SPECIFIC STIFFNESS (E/ρ)?

  1. Boron
  2. Kevlar
  3. Carbon (Graphite)
  4. Glass
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Correct answer: C. Carbon (Graphite)

**Carbon fiber:** E ≈ 230-700 GPa, ρ ≈ 1.8 g/cm³ → highest specific stiffness in common composites. Glass E ≈ 70 GPa (lower stiffness, denser). Kevlar excels in toughness, not stiffness. Boron is stiff but very dense.

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Modulus of typical CARBON fibers is approximately:

  1. 0.1-1 GPa
  2. 230-700 GPa (range depending on PAN-based standard vs ultra-high-modulus pitch)
  3. 3000 GPa
  4. 10-20 GPa
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Correct answer: B. 230-700 GPa (range depending on PAN-based standard vs ultra-high-modulus pitch)

Carbon fibers span a huge property range. **Standard-modulus PAN-based:** ~230 GPa. Intermediate: ~290 GPa. **High-modulus pitch:** 500-700 GPa. Strength typically decreases as modulus increases. Compare to E-glass (~70 GPa).

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More Engineering Materials topics

CarbonCompositesFibersGlassKevlarLimits and ContinuityLinear ProgrammingMathematics