Sets, Relations & Functions · JEE Main previous year questions

2015 3 questions

1. Q112015 · 4 Apr 2015 · Shift 1

   The set of all values of $\lambda$ for which the system of linear equations: $$2x_1-2x_2+x_3=\lambda x_1$$ $$2x_1-3x_2+2x_3=\lambda x_2$$ $$-x_1+2x_2=\lambda x_3$$ has a non-trivial solution

   1. A.contains two elements
   2. B.contains more than two elements
   3. C.is an empty set
   4. D.is a singleton
   Show answer

   Answer: A

2. Q192015 · 4 Apr 2015 · Shift 1

   If the function. $$g(x)=\{\begin{array}{ll}k\sqrt{x+1},& 0\le x\le 3\\ mx+2,& 3<x\le 5\end{array}$$ is differentiable, then the value of $k+m$ is :

   1. A.$\frac{10}{3}$
   2. B.$4$
   3. C.$2$
   4. D.$\frac{16}{5}$
   Show answer

   Answer: C

3. Q202015 · 4 Apr 2015 · Shift 1

   Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set $\mathrm{A}\times \mathrm{B}$, each having at least three elements are

   1. A.$219$
   2. B.$256$
   3. C.$275$
   4. D.$510$
   Show answer

   Answer: A