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JEE Revision Plan - Maths 12.2

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Question 1

and Q=PAP^T then P^TQ²⁰¹⁵P is :

Question 2

Let A and B be any two 3 × 3 matrices. If A is symmetric and B is skew symmetric, then the matrix AB – BA is:

Question 3

For two 3×3 matrices A and B, let A+B=2B’ and 3A+2B=I₃, where B’ is the transpose of B and I₃ is 3×3 identity matrix. Then:

Question 4

If A =

is a matrix satisfying the equation AA^T = 9I, where I is 3 × 3 identify matrix, then the ordered pair (a, b) is equal to

Question 5

and A adj A = A A^T, then 5a + b is equal to

Question 6

If a, b, c are non-zero real numbers and if the system of equations

has a non-trivial solution, then

equals :

Question 7

The number of real values of λ for which
the system of linear equations
2x+4y-λz=0
4x+λy+2z=0
λx+2y+2z=0
has infinitely many solutions, is:

Question 8

If x=a, y=b, z=c is a solution of the system of linear equations

such that the point (a, b, c) lies on the plane x+2y+z=6, then 2a+b+c equals:

Question 9

If S is the set of distinct values of ‘b’ for which the following system of linear equations
x+y+z=1,
x+ay+z=1,
ax+by+z=0,
has no solution, then S is:

Question 10

The set of all value of λ for which the system of linear equations:
2x₁ - 2x₂ + x₃ = λx₁
2x₁ - 3x₂ + 2x₃ = λx₂
- x₁ + 2x₂ = λx₃
has a non-trivial solution,

Question 11

The number of values of k for which the linear equations
4x + ky + 2z = 0
kx + 4y + z = 0
2x + 2y + z = 0
posses a non-zero solution is: