1
CBSE 12th Mathematics Delhi Set 1 - 2024
Subjective
+2
-0
(a) Verify whether the function $f$ defined by $f(x)=\left\{\begin{array}{cl}x \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$ is continuous at $x=0$ or not.
OR
(b) Check for differentiability of the function $f$ defined by $f(x)=|x-5|$, at the point $x=5$.
2
CBSE 12th Mathematics Delhi Set 1 - 2023
Subjective
+2
-0
(a) If $$f(x)=\left\{\begin{array}{ll}x^2, & \text { if } x \geq 1 \\ x, & \text { if } x<1\end{array}\right.$$, then show that $$f$$ is not differentiable at $$x=1$$.
OR
(b) Find the value(s) of '$$\lambda$$', if the function
$$f(x)=\left\{\begin{array}{cc} \frac{\sin ^2 \lambda x}{x^2}, & \text { if } x \neq 0 \\ 1, & \text { if } x=0 \end{array} \text { is continuous at } x=0 .\right.$$
Questions Asked from Continuity and Differentiability (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
Class 12 Subjects
Physics
Electromagnetism
ElectrostaticsCurrent ElectricityCapacitorMagnetic Effect of CurrentMagnetic Properties of MatterElectromagnetic InductionAlternating CurrentElectromagnetic Waves
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Relations and Functions
Calculus
Continuity and DifferentiabilityApplication of DerivativesIndefinite IntegrationDefinite IntegrationApplication of IntegrationDifferential Equations
Algebra