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  • Question 1
    4 / -1

    If \(\lim _{x \rightarrow \infty}\left(\frac{x^{2}+1}{x+1}-a x-b\right)=0,\) then

  • Question 2
    4 / -1

    If A and B are two matrices such that AB = B and BA = A, then A2 + B2 is equal to

  • Question 3
    4 / -1

    The locus of the point of intersection of the lines x sinθ + (1 – cos θ) y = a sinθ and x sin – (1 + cosθ ) y + a sinθ = 0 is

  • Question 4
    4 / -1

    If pth, qth and rth terms of an AP, respectively are a, b and c, then a(q - r) + b(r - p) + c(p - q) is equal to

  • Question 5
    4 / -1

    If \(A=\left[\begin{array}{lll}1 & 0 & 2 \\ 5 & 1 & x \\ 1 & 1 & 1\end{array}\right]\) is a singular matrix, then \(x\) is equal to

  • Question 6
    4 / -1

    The sides of the rectangle of the greatest area, that can be inscribed in the ellipse x2 + 2y2 = 8, are given by

  • Question 7
    4 / -1

    Let \(f(x)=g(x) \frac{e^{1 / x}-e^{-1 / x}}{e^{1 / x}+e^{-1 / x}},\) where \(g\) is a continuous function. Then, \(\lim _{x \rightarrow 0} f(x)\) exists if

  • Question 8
    4 / -1

    If \(1+\omega+\omega^{2}=0\) and \(\omega^{3}=1,\) find the value of \(\left[\begin{array}{cc}\omega & \omega+1 \\ \omega+1 & 1\end{array}\right]\left[\begin{array}{cc}-1 & -1 \\ 1+\omega & \omega-1\end{array}\right]\)

  • Question 9
    4 / -1

    \(\mathrm{n} \in \mathrm{N}\) satisfies the inequality \(\left.\mathrm{n}-1 \mathrm{C}_{3}+\mathrm{n}-1 \mathrm{C}_{4}\right\rangle \mathrm{n}_{\mathrm{C}_{3}}\) and \(\mathrm{E}=\left(\mathrm{x}^{2}-\frac{1}{2 \mathrm{x}}\right)^{\mathrm{n}}\)

    The terms independent of x in the expansion of E are in

  • Question 10
    4 / -1

    Let S = (x – 1)10 + (x – 1)9 (x + 1) + (x – 1)8 (x + 1)2 + ……. + (x + 1)10

    If O is the sum of coefficients of odd powers of x and E is the sum of the coefficients of even powers of x, which of the following statements is correct?

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