Mathematics Tes...

The value of the sum of the series 3. ⁿC₀ - 8 . ⁿC₁ + 13 . ⁿC₂ - 18 . ⁿC₃ + ......upto (n + 1) terms where n>2, is

The system x + 4y - 2z = 3, 3x + y + 5z = 7 and 2x + 3y + z = 5 has

Let \(\int \mathrm{e}^{\mathrm{x}}\left\{f(\mathrm{x})-f^{\prime}(\mathrm{x}) \mathrm{d} \mathrm{x}\right\}=\phi(\mathrm{x})+\mathrm{C}\) Then \(\int \mathrm{e}^{\mathrm{x}} f(\mathrm{x}) \mathrm{d} \mathrm{x}\) is equal to

\(\operatorname{Letf}_{(x)}=x^{2}-4 x-3, x>2\)and let g(x) be the inverse of f(x). Find the value of g'(2) where f (x) = 2

\(\int_{0}^{1} \frac{\tan ^{-1} x}{x} d x\).

Let \(f:[a, b] \rightarrow R\) be a function such that for \(c \in(a, b), f^{\prime}+(c)=f(c)=f(c)=f^{i v}(c)=f^{v}(c)=0\), then :

A car  manufacturing company has two plants. Plant P manufactures 70% of cars and plant Q 30%. At plant P 80% of the cars are rated as of standard quality and at plant Q, 90% of the cars are rated as of standard quality. A car is chosen at random and is found to be of standard quality. The chance that it has come from plant P is.

The p^thderivative of a q^thdegree monic polynomial, where p, q are positive integers and 2p⁴+ 3pq3⁄2= 3q^3⁄2+ 2qp³is given by?

The solution of the differential equationis:dy/dx=1+x+y+xy { Where C is an arbitrary constant }

A purse contains 4 copper coins and 3 silver coins the second purse contains 6 copper coins and 2 silver coins. A coin is taken out from any purse. The probability that it is a copper coin is :