📘 MTH 165 Mathematics Quiz
50 Multiple Choice Questions
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Unit 1 — Linear Algebra
Q1.What is the order of a matrix having 3 rows and 4 columns?
Q2.Find the determinant of the matrix [[1, 2], [3, 4]].
Q3.What is the rank of a 3 × 3 identity matrix?
Q4.A square matrix is singular if:
Q5.The eigenvalues of the diagonal matrix diag(2, 5) are:
Q6.The sum of eigenvalues of a matrix is equal to its:
Q7.The product of eigenvalues of a square matrix equals its:
Q8.Which equation defines an eigenvector v corresponding to eigenvalue λ?
Q9.The rank of a zero matrix is:
Q10.Cayley-Hamilton theorem states that:
Unit 2 — Differential & Integral Calculus
Q11.Find d/dx (x⁵).
Q12.What is d/dx(sin x)?
Q13.What is d/dx(ln x)?
Q14.If x = t² and y = t³, then dy/dx is:
Q15.Find ∫ x⁴ dx.
Q16.Find ∫(1/x) dx.
Q17.Evaluate ∫₀¹ x dx.
Q18.If f(x) is an odd function, then ∫ from −a to a of f(x) dx is:
Unit 3 — Applications of Derivatives
Q19.One important condition of Rolle’s theorem is:
Q20.According to Rolle’s theorem, there exists c such that:
Q21.Maclaurin series is a Taylor series expanded about:
Q22.The Maclaurin series of eˣ begins with:
Q23.Evaluate lim x→0 (sin x / x).
Q24.L’Hospital’s rule is mainly used for which indeterminate forms?
Q25.If f'(x) > 0 throughout an interval, the function is:
Q26.If f'(c)=0 and f”(c)>0, then c is usually a:
Unit 4 — Multivariable Calculus
Q27.If f(x,y)=x²y+3y, find ∂f/∂x.
Q28.If f(x,y)=x²y+3y, find ∂f/∂y.
Q29.The total differential of z=f(x,y) is:
Q30.For a homogeneous function f(x,y) of degree n, Euler’s theorem is:
Q31.The gradient of f(x,y) consists of:
Q32.For f=x²+y², the gradient ∇f is:
Q33.Lagrange multipliers are mainly used for:
Q34.If D=fxx fyy−(fxy)² < 0 at a stationary point, it is a:
Unit 5 — Multiple Integrals
Q35.The double integral ∬R 1 dA represents:
Q36.Find the area of the rectangle 0≤x≤2, 0≤y≤3.
Q37.In polar coordinates, x equals:
Q38.In polar coordinates, the area element dA becomes:
Q39.The area of a unit circle is:
Q40.The triple integral ∭V 1 dV represents:
Q41.What is the volume of a box of dimensions 2 × 3 × 4?
Q42.For a circular region, which coordinate system is often most convenient?
Unit 6 — Fourier Series