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05 May 2021: PIB Summary & Analysis

May 5th, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. Global Innovation Partnership 2. MoU between India and the UK 3. Social Security... View Article

Read the following information carefully and answer the following request. Let p be an odd prime number and T_p be the following set of 2 x 2 matrices . The number of A in T_p such that A is either symmetric or skew-symmetric or both and det (A) is divisible by p is

1) (p - 1)2 2) 2(p - 1) 3) (p - 1)2/ 4) 2p - 1 Solution: (4) 2p - 1 Tr (A) is not divisible by P. Let (A) be divisible by P. If A is... View Article

If 𝛚 is an imaginary cube root of unity and if [latex]\begin{vmatrix} x+\omega^{2} &\omega &1 \\ \omega& \omega^{2} &1+x \\ 1&x+\omega &\omega^{2} \end{vmatrix}=0[/latex] then one of the value of x is

1) 1 2) 0 3) - 1 4) 2 Solution: (2) 0... View Article

If [latex]\left|\begin{array}{ccc} x^{2}+x & 3 x-1 & -x+3 \\ 2 x+1 & 2+x^{2} & x^{3}-3 \\ x-3 & x^{2}+4 & 3 x \end{array}\right|=a_{0}+a_{1}x+……+a_{7}x^{7}[/latex] then the value of a₀ is

1) 35 2) 24 3) 23 4) 22 5) 21 Solution: (5) 21... View Article

The value of the determinant [latex]\left|\begin{array}{ccc} 15 ! & 16 ! & 17 ! \\ 16 ! & 17 ! & 18 ! \\ 17 ! & 18 ! & 19 ! \end{array}\right|[/latex] =

1) 15 ! + 16 1 2) 2(15!) (16!) (17!) 3) 15! + 161 + 17! 4) 16! + 17! Solution: (2) 2(15!) (16!) (17!)... View Article

If A is a 2 × 2 matrix with non – zero entries let A² = I, where I is 2 × 2 identity matrix. Define tr (A) = Sum of diagonal element of A and |A| = Determinant of matrix A. Statement I tr (A) = 0. Statement II |A| = i

1) Statement I is correct, Statement Ii is correct; Statement Ii is the correct explanation for Statement I 2) Statement I is correct, statement... View Article

The number of 3 × 3 non-singular matrices, with four entries as I and all other entries as 0 is

1) less than 4 2) 5 3) 6 4) at least 7 Solution: (4) at least 7... View Article

[latex]\begin{bmatrix} 1 &1 &1 \\ a&b &c \\ a^{2}-bc&b^{2}-ca &c^{2}-ab \end{bmatrix}[/latex] =

1) 0 2) 1 3) abc 4) (a– b) (b – c) (c – a) Solution: (1) 0... View Article

If Z = [latex]begin{vmatrix} 1 &1+2i &-5i \ 1-2i&-3 &5+3i \ 5i&5-3i &7 end{vmatrix}[/latex] then (I = – √-1)

1) z is purely real 2) z is purely imaginary 3) 4) is purely imaginary Solution: (1) z is purely real... View Article

If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then |3AB| is equal to

1) – 9 2) –81 3) – 27 4) 81 Solution: (2) –81... View Article

Statement I. Determine if a skew-symmetric matrix of order 3 is zero. Statement II. For any matrix A , det (A^T) = det (A) and det (-A) = – det (A). Where det (B) denotes the determinant of matrix B. Then,

1) Statement I is correct, Statement II is incorrect 2) both statements are correct 3) both statements are incorrect 4) Statement I is... View Article