Title 19.CONTINUTY AND DIFFERENTIABILITY.pdf ✅

( ) ( ) 1 8 4 3 3 1 + + = + + = − k x y k kx k y k has no solution, is [JEE (Main)-2013] (a.) Infinite (b.) 1 (c.) 2 (d.) 3 (7.) If 1 3 1 3 3 2 4 4      =       P is the adjoint of a 3 3 matrix A and A = 4 , then  is equal to [JEE (Main)-2013] (a.) 4 (b.) 11 (c.) 5 (d.) 0 (8.) If  , 0  , and ( ) = +   n n f n and ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 3 1 1 1 2 1 1 1 2 1 3 (1 ) (1 ) ( ) 1 2 1 3 1 4     + + + + + = − − − + + + f f f f f K f f f , then K is equal to [JEE (Main)-2014] (a.) 1 (b.) -1 (c.)  (d.) 1  (9.) The set of all values of  for which the system of linear equations 1 2 3 1 1 2 3 2 1 2 3 2 2 2 3 2 2    − + = − + = − + = x x x x x x x x x x x has a non-trivial solution [JEE (Main)-2015] (a.) Is an empty set (b.) Is a singleton (c.) Contains two elements (d.) Contains more than two elements (10.) The system of linear equations 0 0 0    + − = − − = + − = x y z x y z x y z has a non-trivial solution for [JEE (Main)-2016] (a.) Exactly one value of  (b.) Exactly two values of  (c.) Exactly three values of  (d.) Infinitely many values of  (11.) Let  be a complex number such that 2 1 + = z where z = −3 . If 2 2 2 7 1 1 1 1 1 3 1     − − = k , then k is equal to (a.) z (b.) -1 (c.) 1 (d.) −z
(12.) If S is the set of distinct values of b for which the following system of linear equations 1 1 0 + + = + + = + + = x y z x ay z ax by z has no solution, then S is [JEE (Main)-2017] (a.) An infinite set (b.) A finite set containing two or more elements (c.) A singleton (d.) An empty set (13.) If ( ) 2 4 2 2 2 4 2 ( ) 2 2 4 − − = + − − x x x x x x A Bx x A x x x , then the ordered pair ( A B, ) is equal to [JEE (Main)-2018] (a.) (− − 4, 5) (b.) (−4,3) (c.) (−4,5) (d.) (4,5) (14.) If the system of linear equations 3 0 3 2 0 2 4 3 0 + + = + − = + − = x ky z x ky z x y z has a non-zero solution ( x y z , , ) , then 2 xz y is equal to [JEE (Main)-2018] (a.) -10 (b.) 10 (c.) -30 (d.) 30 (15.) The system of linear equations ( ) 2 2 2 3 2 5 2 3 1 1 + + = + + = + + − = + x y z x y z x y a z a [JEE (Main)-2019] (a.) has infinitely many solutions for a = 4 (b.) is inconsistent when a = 3 (c.) has a unique solution for a = 3 (d.) is inconsistent when a = 4 (16.) If the system of linear equations 4 7 3 5 2 5 9 − + = − = − + − = x y z g y z h x y z k is consistent, then [JEE (Main)-2019] (a.) g h k + + = 0 (b.) g h k + + = 2 0 (c.) g h k + + = 2 0 (d.) 2 0 g h k + + =