If a+4&3b 8&-6 = 2a+2&b+2 8&a-8b , write the value of a - 2b.

Integrate the following functions w. r. t. x

$\int \frac{1}{3+2 \sin x-\cos x} \cdot d x$

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$\int\limits^{1}_0\{\text{x}\}\text{dx},$ where {x} denotes the fractional part of x.

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Evaluate :

$\int_{-1}^1 \frac{1}{a^2 e^x+b^2 e^{-x}} \cdot d x$

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If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.

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Write the dual of each of the following statements :
(a) $\sim p \wedge( q \vee c )$
(b) "Shweta is a doctor or Seema is a teacher."

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Find the Cartesian co-ordinates of the point whose polar co-ordinates are :

$\left(\sqrt{2}, \frac{\pi}{4}\right)$

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Construct the truth table for each of the following : (~p ∨ ~q) ↔ [~(p ∧ q)]

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If $\begin{bmatrix}1&0\\\text{y}&5\end{bmatrix}+2\begin{bmatrix}\text{x}&0\\1&-2\end{bmatrix}=\text{I},$ where I is 2×2 unit matrix. Find x and y.

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Solve the differentlal equation $x^2 \frac{d y}{d x}=x^2+x y+y^2$

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Differentiate the following w. r. t. x.$\sin ^{-1}\left(\frac{2 \cos x+3 \sin x}{\sqrt{13}}\right)$

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Answer