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Yukti Vault

JEE Mathematics / Practice

Question Bank

Showing 361-365 of 408 questions.

IIT-JEE 2003Question 361
Using the relation $2(1-\cos x)<x^2$, $x\neq0$ or otherwise, prove that $\sin(\tan x)\ge x$, $\forall x\in\left[0,\dfrac{\pi}{4}\right]$.
Differentiation and its Application

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IIT-JEE 2002Question 362
Prove that, in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.
Ellipse

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IIT-JEE 2004Question 363
If $a,b,c$ are positive real numbers, then prove that $(a+1)^{7}(b+1)^{7}(c+1)^{7}>7^{7}a^{4}b^{4}c^{4}$.
Sequence and Series · Means and Inequalities (AM, GM, HM)

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IIT-JEE 2004Question 364
Prove that for $x\in\left[0,\dfrac{\pi}{2}\right]$, $\sin x+2x\ge\dfrac{3x(x+1)}{\pi}$. Explain the identity, if any, used in the proof.
Differentiation and its Application

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IIT-JEE 1981Question 365
For all $x$ in $[0,1]$, let the second derivative $f''(x)$ of a function $f(x)$ exist and satisfy $|f''(x)|<1$. If $f(0)=f(1)$, then show that $|f'(x)|<1$ for all $x$ in $[0,1]$.
Differentiation and its Application

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