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  • Question 1
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    The equation of the ellipse whose centre is at origin \((0,0),\) foci (±1,0) and eccentricity \(\frac{1}{2}\), is

  • Question 2
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    If in the triangle ABC, we have cotA + cotB = 2 cotC then,

  • Question 3
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    The coefficient of \(x^{53}\) in the following expansion \(\sum_{m=0}^{100} 100 C_{m}(x-3)^{100-m} .2^{m}\) is

  • Question 4
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    From a group of 7 men & 4 women a committee of 6 persons is formed. What will be the probability that the committee will consist of exactly two women?

  • Question 5
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    The value of x for which \(\left[\begin{array}{lll}1 & 1 & x\end{array}\right]\left[\begin{array}{lll}1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 1 & 0\end{array}\right]\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=0\) is

  • Question 6
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    If \(\mathrm{x}=\mathrm{k}(\theta+\sin \theta)\) and \(\mathrm{y}=\mathrm{k}(1+\cos \theta),\) then what is the derivative of \(\mathrm{y}\) w.r.t \(\mathrm{x}\) at \(\theta=\pi / 2 ?\)

  • Question 7
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    What is the area of a triangle whose vertices are at (3, –1, 2), (1, –1, –3) and (4, –3, 1) ?

  • Question 8
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    If P ,q and r are in AP as well as in GP, then which one of the following is correct?

  • Question 9
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    Equation of circle which passes through the points (1, –2) and (3, –4) and touch the x axis is

  • Question 10
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    In the mean value Theorem \(\frac{f(b)-f(a)}{b-a}=f^{\prime}(c), i f a=0, b=\frac{1}{2}\) and \(f(x)=x(x-1)(x-2),\) the value of \(C\) is

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