Determinants DPP 01 (Of Lec 03) PDF

JEE Lakshya JEE 2025...

JEE Lakshya JEE 2025 Maths DPP: 1 Determinants Q1 ∣ 1 log b a ∣ Q5 ∣ a −1 0 ∣ The value of the determinant ∣ ∣ ∣ ∣ ∣ log a b 1 ∣ If f (x) = ax a −1 , then ∣ ∣ is equal to: ∣ ax 2 ax a ∣ (A) 1 f (2x) − f (x) equals (B) log a b (A) a(2a + 3x) (C) log b a (B) ax(2x + 3a) (D) 0 (C) ax(2a + 3x) (D) x(2a + 3x) Q2 ∣1 1 1 1 ∣ ∣ ∣ ∣1 2 3 4 ∣ Q6 ∣ a1 b1 c1 ∣ The value of the determinant ∣ ∣ ∣ 1 3 6 10 ∣ If a2 b2 c2 = 5 , then the value of ∣ ∣ ∣ ∣ ∣1 4 10 20 ∣ ∣ a3 b3 c3 ∣ is equal to ∣ b2 c3 − b3 c2 a3 c2 − a2 c3 a2 b3 − a3 b2 ∣ ∣ ∣ (A) 0 (B) -1 b3 c1 − b1 c3 a1 c3 − a3 c1 a3 b1 − a1 b3 is ∣ ∣ (C) 1 (D) 2 ∣ b1 c2 − b2 c1 a2 c1 − a1 c2 a1 b2 − a2 b1 ∣ (A) 5 (B) 25 Q3 The determinant (C) 125 (D) 0 ∣ cos(α + β) − sin(α + β) cos 2β ∣ ∣ ∣ D = sin α cos α sin β Q7 If the value of a third order determinant is 11 , ∣ ∣ ∣ − cos α sin α cos β ∣ then value of the square of the determinant independent of formed by the cofactors will be (A) α (A) 11 (B) 121 (B) β (C) 1331 (D) 14641 (C) α and β Q8 The cofactor of the element 4 in the (D) Neither α or β determinant Q4 If A + B + C = π , then value of ∣1 3 5 1∣ ∣ ∣ ∣ sin(A + B + C ) sin B cos C ∣ ∣2 3 4 2∣ ∣ ∣ is ∣ − sin B 0 tan A ∣ is ∣ 8 0 1 1 ∣ ∣ ∣ ∣ ∣ ∣ cos(A + B) − tan A 0 ∣ ∣0 2 1 1∣ (A) 0 (A) 4 (B) 10 (B) 1 (C) -10 (D) -4 (C) 2 sin B ⋅ tan A cos C Q9 (D) 2 sin A sin B ⋅ sin C Android App | iOS App | PW Website  JEE ∣ a b aα + b ∣ ∣ ∣ If b c bα + c = 0 then ∣ ∣ ∣ aα + b bα + c 0 ∣ (A) a, b, c are in A.P. (B) a, b, c are in G.P. (C) α is a root of ax2 + 2bx + c = 0 (D) (x − α) is a factor of ax2 + 2bx + c = 0 Q10 ∣ a b c∣ ∣ 6a 2b 2c ∣ ∣ ∣ ∣ ∣ If m n p , then = k 3m n p = ∣ ∣ ∣ ∣ ∣ x y z∣ ∣ 3x y z ∣ (A) k/6 (B) 2k (C) 3k (D) 6k Android App | iOS App | PW Website  JEE Answer Key Q1 (D) Q6 (B) Q2 (C) Q7 (D) Q3 (A) Q8 (B) Q4 (A) Q9 (B, C, D) Q5 (C) Q10 (D) Android App | iOS App | PW Website