Other Maths · JEE Main previous year questions

2014 4 questions

1. Q102014 · 6 Apr 2014 · Shift 1

   If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x$ then

   1. A.$\alpha =2,\beta =-\frac{1}{2}$
   2. B.$\alpha =2,\beta =\frac{1}{2}$
   3. C.$\alpha =-6,\beta =\frac{1}{2}$
   4. D.$\alpha =-6,\beta =-\frac{1}{2}$
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   Answer: A

2. Q112014 · 6 Apr 2014 · Shift 1

   If $\alpha ,\beta \ne 0$, and $f(n)={\alpha }^n+{\beta }^n$ and $$\left|\begin{array}{ccc}3& 1+f(1)& 1+f(2)\\ 1+f(1)& 1+f(2)& 1+f(3)\\ 1+f(2)& 1+f(3)& 1+f(4)\end{array}\right|=K(1-\alpha {)}^2(1-\beta {)}^2(\alpha -\beta {)}^2,$$ then $K$ is equal to :

   1. A.1
   2. B.$-1$
   3. C.$\alpha \beta$
   4. D.$\frac{1}{\alpha \beta }$
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   Answer: A

3. Q232014 · 6 Apr 2014 · Shift 1

   If $(10{)}^9+2(11{)}^1(10{)}^8+3(11{)}^2(10{)}^7+\cdots +10(11{)}^9=k(10{)}^9$, then k is equal to :

   1. A.100
   2. B.110
   3. C.$\frac{121}{10}$
   4. D.$\frac{441}{100}$
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   Answer: A

4. Q292014 · 6 Apr 2014 · Shift 1

   If $\left[\vec{a}\times \vec{b}\vec{b}\times \vec{c}\vec{c}\times \vec{a}\right]=\lambda {\left[\vec{a}\vec{b}\vec{c}\right]}^2$ then $\lambda$ is equal to :

   1. A.$0$
   2. B.$1$
   3. C.$2$
   4. D.$3$
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   Answer: B