JEE (Advanced) 2017 Paper-2
For the following questions answer them individually
How many $$3\times3$$ matrices M with entries from {0,1,2} are there, for which the sum of the diagonal entries of $$M^{T}M$$ is 5?
Lat S={1,2,3,...,9}. For = 1, 2, … ,5, let $$N_{k}$$ be the number of subsets of S, each containing five elements out of which exactly k are odd, Then $$N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=$$
Three randomly chosen nonnegative integers x,y and z are found to satisfy the equation $$x+y+z=10$$. Then the probability that z is even, is
Let $$\alpha$$ and $$\beta$$ be nonzero real numbers such that $$2(\cos\beta-\cos\alpha)+\cos\alpha\cos\beta=1$$. Then which of the following is/are true?
If $$f:R\rightarrow R$$ is a differentiable function such that $$f'(x)>2f(x)$$ for all $$x\epsilon R$$, and $$f(0)=1$$, then
Let $$f(x)=\frac{1-x(1+\mid1-x\mid)}{\mid1-x\mid}Cos(\frac{1}{1-x})$$ for $$x\neq1$$. Then
If the line $$x=\alpha$$ divides the area of region $$R={(x,y)\epsilon R^{2}:x^{3}\leq y\leq x},0\leq x\leq1$$ into two equal parts, then
