Other Maths · JEE Main previous year questions

2004 5 questions

1. Q62004 · 24 Apr 2004 · Shift 1

   If $|z^2-1|=|z{|}^2+1$, then z lies on :

   1. A.an ellipse
   2. B.the imaginary axis
   3. C.a circle
   4. D.the real axis
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   Answer: B

2. Q292004 · 24 Apr 2004 · Shift 1

   The value of ${\int }_{-2}^3|1-x^2|dx$ is

   1. A.$\frac{1}{3}$
   2. B.$\frac{14}{3}$
   3. C.$\frac{7}{3}$
   4. D.$\frac{28}{3}$
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   Answer: D

3. Q362004 · 24 Apr 2004 · Shift 1

   A particle acted on by constant forces $4\hat{i}+\hat{j}-3\hat{k}$ and $3\hat{i}+\hat{j}-\hat{k}$ is displaced from the point $\hat{i}+2\hat{j}+3\hat{k}$ to the point $5\hat{i}+4\hat{j}+\hat{k}$. The total work done by the forces is :

   1. A.$50$ units
   2. B.$20$ units
   3. C.$30$ units
   4. D.$40$ units
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   Answer: D

4. Q512004 · 24 Apr 2004 · Shift 1

   Let $S(K)=1+3+5\dots +(2K-1)=3+K^2$. Then which of the following is true

   1. A.Principle of mathematical induction can be used to prove the formula
   2. B.$S(K)\Rightarrow S(K+1)$
   3. C.$S(K)\ne S(K+1)$
   4. D.$S(1)$ is correct
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   Answer: B

5. Q522004 · 24 Apr 2004 · Shift 1

   If $S_n={\sum }_{r=0}^n\frac{1}{{}^n{C}_r}$ and $t_n={\sum }_{r=0}^n\frac{r}{{}^n{C}_r}$, then $\frac{t_n}{S_n}$ is equal to

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