For the following questions answer them individually
Let a function $$f:\left[-\pi, \pi\right] \rightarrow $$ be expressed as $$f(x) : \sum_{j=1}^k a_{j} \cos(jx) + \sin x + 2 \sin 3x + 4 \sin 8x$$. f(-x) = -f(x), then
If h(x) = |x+3| — |x— 3| for all real x, then for how many integer values of x is the inequality |h(x)| < 6 satisfied?
If b is the largest natural number that divides $$8^{8}$$ and $$b = a^{3}$$ for some $$a \epsilon N$$, then what s the value of a?
The ratio of the incomes of P and Q is 16 : 9 and the ratio of their expenditures is 8 : 5.
The saving of P is 220% more than that of Q.R earns 25% less than P and spends 20% more than Q. What is the ratio of P's income to R's savings?
Let a, b be nonzero real numbers. Choose the correct statement.
On the number line, what is the distance of any given number from the double of the same number?
If $$x_{1}, x_{2}$$ are the roots of the equation, $$2x^{2} — 4x + 5 = 0$$, then the equation whose roots are $$x_{1} + \frac{1}{x_{1}}$$ and $$x_{2} + \frac{1}{x_{2}}$$ is:
\What is the sum of the following series?
$$2.12 + 1.0012 + 0.000012 + 0.00000012 + 0.0000000012 +....\infty$$
$$\sqrt{10 + 4\sqrt{3 -2\sqrt{2}}} = a + \sqrt{2}b$$, then what is the value of $$\sqrt{a^{3} + b^{3} + 4a^{2}b}$$?
In still water, a boat can cover a distance of 10 km at the speed of 5 km/h in certain time interval and during the same time interval it can cover a distance of 8 km while moving upstream in a river. What is the speed of the river (in km/h)?
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