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  • Question 1
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    If \(\frac{x}{\alpha}+\frac{y}{\beta}=1\) touches the circle \(x^{2}+y^{2}=a^{2},\) then the point \((1 / \alpha, 1 / \beta)\) lies on a/an :

  • Question 2
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    The horizontal distance between two towers is 60 m and the angles of depression of the top of the first tower as seen from the top of the second is 30o. If the height of the second tower is 150 m, then the height of the first tower is :

  • Question 3
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    If f(x) = ax2 + bx + c and g(x) = px2 + qx with g(1) = f(1), g(2) - f(2) = 1 and g(3) - f(3) = 4, then g(4) - f(4) is equal to :

  • Question 4
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    \(\int \frac{e^{x}(1+\sin x)}{1+\cos x} d x\) is equal to :

  • Question 5
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    For hyperbola \(\frac{x^{2}}{\cos ^{2} \alpha}-\frac{y^{2}}{\sin ^{2} \alpha}=1,\) which of the following remains constant with change in \({ }^{\prime} \alpha^{\prime} ?\)

  • Question 6
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    The number of common tangents to the circles x2 + y2 + 2x + 8y - 23 = 0 and x2 + y2 - 4x - 10y + 9 = 0, is :

  • Question 7
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    If \(0<\alpha<\beta<\gamma<\frac{\pi}{2}\), then the equation \(\frac{1}{x-\sin \alpha}+\frac{1}{x-\sin \beta}+\frac{1}{x-\sin \gamma}=0\) has :

  • Question 8
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    Find all the values of the parameter a for which both roots of the quadratic equation x2−ax+2=0 belong to the interval (0,3).

  • Question 9
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    Number of integer values of k for which the quadratic equation 2x2+kx−4=0 will have two rational solutions is :

  • Question 10
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    Let α,β be the roots of the equation ax2+bx+c=0 and α4+β4 be the roots of the equation px2+qx+r=0, then the roots of the equation a2px2−4acpx+2c2p+a2q=0 are:

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