JEE Advanced Mathematics: Algebra Practice Questions

12 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$The number of ways to arrange the letters of the word APPLE is$
Easy
Q2.
$The sum of the first 10 terms of the arithmetic progression 2, 5, 8, 11, ... is$
Easy
Q3.
$If a matrix A is equal to [[1, 2], [3, 4]], then the determinant of A is$
Easy
Q4.
$I f t h er oo t so f t h e q u a d r a t i ce q u a t i o n x^{2} - 8 x + k = 0 a r ee q u a l, t h e n t h e v a l u eo f k i s$
Easy
Q5.
$If log base 2 of x is equal to 5, then the value of x is$
Easy
Q6.
$I f t h es u m o f t h e f i r s t n t er m so f ana r i t hm e t i c p r o g r ess i o ni s S_{n} = 3 n^{2} + 5 n, t h e n t h eco mm o n d i f f er e n ce i s :$
Medium
Q7.
$T h e v a l u eo f t h ee x p r ess i o n l o g_{2} (l o g_{3} (81)) i s :$
Medium
Q8.
$T h e n u mb er o f r e a l so l u t i o n s t o t h ee q u a t i o n ∣ x^{2} - 2 x - 3∣ = x + 1 i s :$
Medium
Q9.
$L e t o m e g ab e a co m pl e x c u b er oo t o f u ni t y . I f t h e ma t r i x A i s d e f in e d a s [[1, o m e g a, o m e g a^{2}], [o m e g a, o m e g a^{2}, 1], [o m e g a^{2}, 1, o m e g a]], t h e n t h e v a l u eo f t h e$
Medium
Q10.
$L e t f (x) b e a p o l y n o mia l s u c h t ha t f (x^{2} + 1) = x^{4} + x^{2} + 1. F in df (x^{2} - 1) .$
Hard
Q11.
$I f o m e g ai s a co m pl e x c u b er oo t o f u ni t y, f in d t h e v a l u eo f t h e p r o d u c t (1 - o m e g a) (1 - o m e g a^{2}) (1 - o m e g a^{4}) (1 - o m e g a^{8}) .$
Hard
Q12.
$F in d t h e n u mb er o f r e a l so l u t i o n s t o t h ee q u a t i o n 2^{x} + 3^{x} + 4^{x} = 5^{x} + 6^{x} .$
Hard

Track your progress on Algebra

Start Practising Free →