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Mathematics Tes...

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  • Question 1
    3 / -1

    If A=[aij]3×3 is a square matrix so that

    aij=i2−j2, then A is a

  • Question 2
    3 / -1

    Directions: The following question has four choices, out of which ONE or MORE can be correct.

    For \(0<\theta<\frac{\pi}{2},\) the solution \((s)\) of \(\sum_{m=1}^{6} \operatorname{cosec}\left(\theta+\frac{(m-1) \pi}{4}\right) \operatorname{cosec}\left(\theta+\frac{m \pi}{4}\right)=4 \sqrt{2}\) is / are

  • Question 3
    3 / -1

    If \(A=\left[\begin{array}{cc}2 & 2 \\ -3 & 2\end{array}\right], B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]\) then \(\left(B^{-1} A^{-1}\right)^{-1}=\)

  • Question 4
    3 / -1

    If \(0 \leq x \leq 2 \pi\) and \(|\cos x| \leq \sin x,\) then

  • Question 5
    3 / -1

    Directions: The following question has four choices, out of which one or more is/are correct.

    For any two events A and B in a sample space

  • Question 6
    3 / -1

    \(A=\left|\begin{array}{cc}1 & 1 \\ 2 & 2 \\ 3 & -1\end{array}\right|\) and \(B=\left|\begin{array}{cc}2 & 1 \\ 1 & 2 \\ -1 & 0\end{array}\right|,\) then find matrix \(C\) if \(A+2 B+C=0\)

  • Question 7
    3 / -1

    If \(A=[x, y], B=\left[\begin{array}{ll}a & h \\ h & b\end{array}\right], C=\left[\begin{array}{l}x \\ y\end{array}\right]\)
    then \(A B C=\)

  • Question 8
    3 / -1

    Directions: The following question has four choices, out of which ONE or MORE can be correct.

    Let z1 and z2 be complex numbers such that z1 ≠ z2 and | z1 | = | z2 |, If z1 has positive real part and z2 has negative imaginary part, then (z1+z2)/(z1-z2) may be

  • Question 9
    3 / -1

    Using elementary transformations, find the inverse of matrix, \(A=\left[\begin{array}{ll}1 & 3 \\ 2 & 7\end{array}\right]\)

  • Question 10
    3 / -1

    Directions: The following question has four choices out of which ONE or MORE can be correct.

    The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has a 75% chance of passing in at least one, 50% chance of passing in at least two, and 40% chance of passing in exactly two. Which of the following relations is/are true?

  • Question 11
    3 / -1

    Directions: The following question has four choices, out of which ONE or MORE can be correct.

    If \(I_{n}=\int_{-\pi}^{\pi} \frac{\sin n x}{\left(1+\pi^{x}\right) \sin x} d x, n=0,1,2, \ldots,\) then

  • Question 12
    3 / -1

    If A, B are two idempotent matrices and

    AB = BA = 0, then A + B is

  • Question 13
    3 / -1

    If \(\left[\begin{array}{ll}x+3 & 2 y+x \\ z-1 & 4 a-z\end{array}\right]=\left[\begin{array}{ll}0 & -7 \\ 3 & 2 a\end{array}\right]\), then
    \((x+y+z+a) i s\)

  • Question 14
    3 / -1

    Find the inverse of \(A=\left|\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right|\) if
    \(A^{-1}=\left[\begin{array}{ccc}1 / 2 & -1 / 2 & 1 / 2 \\ a & 3 & b \\ c & -3 / 2 & 1 / 2\end{array}\right]\)
    \(|a b c| ?\)

  • Question 15
    3 / -1

    If \(A=\left[\begin{array}{ll}2 & 5 \\ 4 & 4\end{array}\right], \quad B=\left[\begin{array}{ll}0 & 5 \\ 1 & 6\end{array}\right],\) find \(5 A^{\prime}+3 B^{\prime}\)

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