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  • Question 1
    4 / -1

    A line with positive direction cosines passes through the point \(P(2,-1,2)\) and makes equal angles with the coordinate axes. The line meets the plane \(2 x+y+z=9\) at point \(Q\). The length of the line segment \(P Q\) equals:

  • Question 2
    4 / -1

    What is the minimum value of |x - 1|, where x ∈ R?

  • Question 3
    4 / -1

    Find the sum of the series whose nth term is:

    n(n+1)(n+4)

  • Question 4
    4 / -1

    Form the differential equation of \(y=a e^{3 x} \cos (x+b)\) Where \(y^{\prime}=\frac{d y}{d x}\) and \(y^{n}=\frac{d^{2} y}{d x^{2}}\)?

  • Question 5
    4 / -1

    Let \(f(x)=\left\{\begin{array}{cc}\max \left\{|x|, x^{2}\right\}, & |x| \leq 2 \\ 8-2|x|, & 2<|x| \leq 4\end{array}\right.\)
    Let \(S\) be the set of points in the interval \((-4,4)\) at which \(f\) is not differentiable. Then \(S\) :

  • Question 6
    4 / -1

    \(A B\) is a chord of the circle and \(A O C\) is its diameter such that angle \(A C B\) \(=50^{\circ}\). If \(\mathrm{AT}\) is the tangent to the circle at the point \(\mathrm{A}\), then \(\angle \mathrm{BAT}\) is equal to:

  • Question 7
    4 / -1

    If \({ }^{\mathrm{n}} \mathrm{P}_{\mathrm{r}}=720\) and \({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=120\), then the value of \(\mathrm{r}\) is:

  • Question 8
    4 / -1

    The second degree equation \(2 x^{2}+2 y^{2}-5 x-7 y-3=0\) represents:

  • Question 9
    4 / -1

    Find the number of elements in the union of 4 sets A, B, C and D having 150, 180, 210 and 240 elements respectively, given that each pair of sets has 15 elements in common. Each triple of sets has 3 elements in common and A ∩ B ∩ C ∩ D = ϕ.

  • Question 10
    4 / -1

    \(\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-\cot A}\) is equals to:

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