Other Maths · JEE Main previous year questions

2009 4 questions

1. Q52009 · 27 Apr 2009 · Shift 1

   The remainder left out when $8^{2n}-(62{)}^{2n+1}$ is divided by 9 is :

   1. A.2
   2. B.7
   3. C.8
   4. D.0
   Show answer

   Answer: A

2. Q72009 · 27 Apr 2009 · Shift 1

   The lines $p\left(p^2+1\right)x-y+q=0$ and ${\left(p^2+1\right)}^{2}x+\left(p^2+1\right)y+2q=0$ are perpendicular to a common line for :

   1. A.exactly one values of $p$
   2. B.exactly two values of $p$
   3. C.more than two values of $p$
   4. D.no value of $p$
   Show answer

   Answer: A

3. Q122009 · 27 Apr 2009 · Shift 1

   Given $P(x)=x^4+a{x}^3+b{x}^2+cx+d$ such that $x=0$ is the only real root of $P^{\prime }(x)=0$. If $P(-1)<P(1)$, then in the interval $[-1,1]$ :

   1. A.$P(-1)$ is not minimum but $P(1)$ is the maximum of $P$
   2. B.$P(-1)$ is the minimum but $P(1)$ is not the maximum of $P$
   3. C.Neither $P(-1)$ is the minimum nor $P(1)$ is the maximum of $P$
   4. D.$P(-1)$ is the minimum and $P(1)$ is the maximum of $P$
   Show answer

   Answer: A

4. Q192009 · 27 Apr 2009 · Shift 1

   For real x, let $f(x)=x^3+5x+1$, then

   1. A.f is one-one but not onto R
   2. B.f is onto R but not one-one
   3. C.f is one-one and onto R
   4. D.f is neither one-one nor onto R
   Show answer

   Answer: C