MCA Entrance Previous Year Question Bank

If 49𝑛+16𝑛+𝜆 is divisible by 64 for all 𝑛∈𝑁, then the least negative value of 𝜆 is

The value of ${\int }_0^{\pi }x({\sin }^{4}x{\cos }^{4}x)dx$ is

Let the equation of a curve passing through point $(0,1)$ be given by $y=\int x^2{e}^{x^3}dx$. If the equation of curve is written in the form $x=f(y)$, then $f(y)$ is

${\int }_0^{1000}{e}^{x-[x]}dx$ is

The point of inflection for 𝑓(𝑥)=3𝑥⁴−4𝑥³ are

Z=7x+y, subject to constraints: 5𝑥+𝑦≥5, 𝑥+𝑦≥3 𝑥≥0,𝑦≥0,𝑦 Then minimum value of Z occurs at:

Every gram of wheat provides 0.1 gram of proteins and 0.25 gram of carbohydrates. The responding values of rice are 0.05 gram and 0.5 gram respectively. The minimum daily requirements of proteins & carbohydrates for an average child are 50 gram & 200 gram respectively. Then in what quantities wheat & rice be mixed in daily diet to provide minimum daily requirement of proteins & carbohydrates at minimum cost?

A pair of fair dice is thrown independently 3 times. The probability of getting a score of exactly 9 twice is

The general solution of the differential equation $({\tan }^{-1}y-x)dy=(1+y^2)dx$ is

Solution of the differential equation $\frac{dx}{dy}-\frac{x\log x}{1+\log x}=\frac{e^y}{1+\log x}$, if $y(1)=0$, is