Function f(x)= c x^2+m, when x 0 -x^2-m, when x=2 ., is continuous at x=0 then find value of m.

Function f(x)= c x^2+m, when x 0 -x^2-m, when x=2 ., is continuou…

Solve the following LPP using graphical method
$
\begin{array}{cc}
\operatorname{minimize} & z=200 x+500 y \\
\text { constraints } & x+2 y \geq 10 \\
& 3 x+4 y \leq 24 \\
& x \geq 0, y \geq 0
\end{array}
$

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Evaluate $\int _ { - 1 } ^ { 2 } \left| x ^ { 3 } - x \right| d x$.

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Solve the following linear programming problem by graphical method.Under the constraints, maximise $Z=60 x+40 y$.
$
\begin{aligned}
x+2 y & \leq 12 \\
2 x+y & \leq 12 \\
x+\frac{5}{4} y & \geq 5 ; x \geq 0, y \geq 0
\end{aligned}
$

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If function $f(x)=\frac{\sqrt{x}-\sqrt{a}}{x-a}$, is continuous at $x=a$, then find value of $f(a)$.

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Find the value of $\int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x$

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If $y=\frac{\sin ^{-1} x}{x}$ then prove that :$
x\left(1-x^2\right) y_2+\left(2-3 x^2\right) y_1-x y=0
$

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One kind of cake requires $200 g$ of flour and $25 g$ of fat, and another kind of cake requires $100 g$ of flour and $50 g$ of fat. Find the maximum number of cakes which can be made from $5 kg$ of flour and $1 kg$ of fat assuming that there is no shortage of the other ingredients used in making of cakes.

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By using the properties of definite integral, evaluate the integral $\int_0^{\frac{\pi}{2}}(2 \log \sin x-\log \sin 2 x) d x$

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By using the properties of definite integrals, evaluate the integral $\int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x$

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Find the value of $\int_0^\pi \frac{\sec x}{\sec x+\tan x} d x$.

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Continuity and Differentiability — MATHS STD 12 Science — Question

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