GRE Subject 2026 Practice Test Maths Real Analysis Free Quiz 1

1. What does real analysis study?

A. Real numbers, sequences, continuity, differentiation, integration B. Complex numbers C. Abstract algebra D. Topology

2. What happens to a convergent sequence?

A. Diverges B. Oscillates C. Converges D. Constant

3. What condition defines continuity of a function?

A. Differentiable B. Integrable C. Bounded D. Continuous

4. What does the epsilon-delta definition formalize?

A. Derivative B. Limit C. Integral D. Sequence

5. What theorem states there exists c such that f'(c) = (f(b)-f(a))/(b-a)?

A. Intermediate Value B. Bolzano-Weierstrass C. Rolle's D. Mean Value

6. What theorem states if f(a)=f(b), then f'(c)=0?

A. Mean Value B. Rolle's C. Intermediate Value D. Bolzano

7. What is a Cauchy sequence?

A. Cauchy B. Convergent C. Divergent D. Bounded

8. Is every convergent sequence Cauchy?

A. Not B. Sometimes C. Always D. Never

9. What defines an open set?

A. Closed B. Open C. Compact D. Bounded

10. What defines a closed set?

A. Closed B. Open C. Compact D. Bounded