MCQ
$\vec{a}=-3 \hat{i}+\hat{j}$ નો $\vec{b}=\hat{i}-\hat{j}-\hat{k}$ પરનો પ્રક્ષેપ _____________ .
- A$\frac{-4}{\sqrt{10}}$
- ✓$\frac{-4}{\sqrt{3}}$
- C$\frac{4}{\sqrt{3}}$
- D$\frac{4}{\sqrt{10}}$
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$f\left( x \right)\left\{ \begin{array}{l}
\frac{{2{x^2}}}{a}\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,\,0 \le x < 1\,\,\,\\
a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,\,1 \le x < \sqrt 2 \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\
\frac{{2{b^2} - 4b}}{{{x^3}}}\,\,\,,\,\,\,\,\,\sqrt 2 \le x < \infty
\end{array} \right.\,\,\,\,$ એ $\left[ {0,\infty } \right)$ પર સતત હોય તો $(a, b)$ જોડ મેળવો.
વિધાન $II:$ દરેક $x \in R ,$ માટે ${\sin ^{ - 1}}\,x + {\cos ^{ - 1}}\,x = \frac{\pi }{2}$ અને $0 \le {\left( {{{\sin }^{ - 1}}\,x - \frac{\pi }{4}} \right)^2} \le \frac{{9{\pi ^2}}}{{16}}$ થાય.