JEE Main Mathematics: Algebra Practice Questions

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

Q1.
$What is the value of the determinant of the matrix [[2, 3], [1, 4]]?$
Easy
Q2.
$Find the number of ways to arrange the letters of the word CAT.$
Easy
Q3.
$F in d t h e v a l u eo f x i f 2^{(} x + 3) = 32.$
Easy
Q4.
$I f t h er oo t so f t h e q u a d r a t i ce q u a t i o n x^{2} - 6 x + k = 0 a r ee q u a l, f in d t h e v a l u eo f k .$
Easy
Q5.
$I f t h es u m o f t h e f i r s t n t er m so f ana r i t hm e t i c p r o g r ess i o ni s g i v e nb y S n = 3 n^{2} + n, f in d t h eco mm o n d i f f er e n ceo f t h e p r o g r ess i o n .$
Easy
Q6.
$The number of ways to arrange the letters of the word 'MATHEMATICS' such that the vowels always come together is:$
Medium
Q7.
$I f a l p haan d b e t aa r e t h er oo t so f t h ee q u a t i o n x^{2} - 6 x + 2 = 0, t h e n t h e v a l u eo f a l p h a^{4} + b e t a^{4} i s :$
Medium
Q8.
$T h e v a l u eo f t h e d e t er minan t o f a 3 x 3 ma t r i x w h er ee a c h e l e m e n t a_{i} j i s d e f in e d a s i + j i s :$
Medium
Q9.
$I f t h es u m o f t h e f i r s t n t er m so f ana r i t hm e t i c p r o g r ess i o ni s g i v e nb y S n = 3 n^{2} + 5 n, t h e n t h eco mm o n d i f f er e n ceo f t h e p r o g r ess i o ni s :$
Medium
Q10.
$T h e n u mb er o f r e a l so l u t i o n so f t h ee q u a t i o n ∣ x^{2} - 3 x + 2∣ = x - 1 i s :$
Medium
Q11.
$I f o m e g ai s a co m pl e x c u b er oo t o f u ni t y, f in d t h e v a l u eo f (1 + o m e g a) (1 + o m e g a^{2}) (1 + o m e g a^{4}) (1 + o m e g a^{8}) .$
Hard
Q12.
$F in d t h e n u mb er o f r e a l so l u t i o n s t o t h ee q u a t i o n 2^{x} + 3^{x} = 5^{x} .$
Hard
Q13.
$I f t h er oo t so f t h ee q u a t i o n x^{3} - 3 x^{2} + 4 x - 1 = 0 a r e a l p ha, b e t a, an d g amma, t h e n f in d t h e v a l u eo f (a l p h a^{2} + b e t a^{2} + g amm a^{2}) .$
Hard

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