Determinants Basics: JEE Questions & Solutions

Among the statements: I: If the given determinants are equal, then ^2 + ^2 + ^2 = 32, and II: If the polynomial determinant equals px + q,…

For some a, b, let f(x) = | matrix a + xx & 1 & b a & 1 + xx & b a & 1 & b + xx matrix |, where x 0, x 0 f(x) = + a + b. Then ( + +)^2 is…

If y(x) = vmatrix x & x & x + x + 1 27 & 28 & 27 1 & 1 & 1 vmatrix, x R, then d^2ydx^2 + y is equal to

The number of singular matrices of order 2, whose elements are from the set 2, 3, 6, 9 is:

The values of for which the determinant vmatrix 1 & 3 & 2 +3 & 2 & 1 1 & 1 & 3 vmatrix = 0 lie in the interval:

Let A = [ [1, 0, 0], [0,, ], [0,, ] ] and |2A|^3 = 221, where, Z. Then a value of is:

If f(x) = 2 ^4 x3 + 2 ^4 x + 2 ^4 x3 + 2 ^4 x, then 15 f'(0) is equal to:

If f(x) = x^3 + 2x^2 + 1 + 3x, then 2f(0) + f'(0) is equal to:

Let A = [ [1, 0, 0], [0,, ], [0,, ] ] and |2A|^3 = 2^21, where, Z. Then a value of is:

For, R and a natural number n, let Ar = vmatrix r & 1 & n^2 + 2r & 2 & n^2 - 3r - 2 & 3 & n(3n - 1)2 vmatrix Then 2A10 - A5 is:

If a, b, c and | matrix & b & c a & & c a & b & matrix | = 0 then: a -a+ b -b+ -c is equal to:

The set of all values of t R, for which the matrix bmatrix e^t & e^-t( t - 2 t) & e^-t(-2 t - t) e^t & e^-t(2 t + t) & e^-t( t - 2 t) e^t &…

Let A = bmatrix m & n p & q bmatrix, d = |A| 0, and |A - d( Adj A)| = 0. Then:

Let A be an n n matrix such that |A| = 2. If the determinant of the matrix Adj(2 Adj(2A^-1)) is 2^84, then n is equal to:

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If: vmatrix x + 1 & x & x x & x + & x x & x & x + ^2 vmatrix = 98(103x + 81) then, 3 are the roots of the equation:

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