Student Copy. CAPS-2
Student Copy. CAPS-2
Student Copy. CAPS-2
TARGET : JEE-ADVANCED-2024
1 1
(A) (0, ) (B) ,1 (C) [1, 2] (D) ,1
2 4
5. If [x]2 –7[x] + 10 < 0 and 4[y]2 –16[y] + 7 < 0, then [x + y] cannot be ([] denotes greatest integer
function) :
(A) 7 (B) 8 (C) 9 (D) Both (B) and (C)
6. The function f(x) satisfy the equation f(1 – x) + 2f(x) = 3x x R, then f(0) =
(A) –2 (B) –1 (C) 0 (D) 1
7. If a, b, c are in GP, a – b, c – a, b – c are in HP, then the value of a + 4b + c is
(A) 12 (B) 0 (C) 11 (D) 2
2 6 12 20
8. Find the value of ... upto terms :
13 13 23 13 2 3 33 13 23 33 43
1 1
(A) 2 (B) (C) 4 (D)
2 4
MCQ (One or more than one correct) :
9. Let , , , are roots of x4 – 12x3 + x2 – 54x + 14 = 0. If + = + , then
(A) = 45 (B) = –45
7 2
(C) If 2 + 2 < 2 + 2 then (D) If 2 + 2 < 2 + 2
2 7
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10. If the equation cot4 x – 2 cosec2 x + a2 = 0 has at least one solution then possible integral values of a
can be :
(A) –1 (B) 0 (C) 1 (D) 2
11. Consider the function f(x) = n ((cosx)cosx + 1); x ,
2 2
(A) f(x) is an even function (B) Range of f(x) is (n(1 + e1/e ), n2)
1
1 e
(C) Range of f(x) is n 1 , n2 (D) f(x) is neither an even nor an odd function
e
12. If numbers of ordered pairs (p, q) from the set S = {1, 2, 3, 4, 5} such that the function
x3 p 2
f(x) = x qx 10 defined from R to R is injective, is n then n is divisible by
3 2
13. Let x, y, z 0, are first three consecutive terms of an arithmetic progression such that cos x + cos y
2
1
+ cos z = 1 and sin x + sin y + sin z = , then which of the following is/are correct ?
2
3 2
(A) cot y = 2 (B) cos (x – y) =
2 2
2 2
(C) tan2 y = (D) sin(x – y) + sin(y – z) = 0
3
2x 2 3x a
14. f(x) = log4 2
has range [, ] such that + = 0, then find ‘a’.
2x 3x 3
15. Find the number of integers satisfying the inequality log1/2 2 x 4log2 x < 2 (4 – log16x4).
17. Let f(x) = x2 – bx + c, b is an odd positive integer. Given that f(x) = 0 has two prime numbers as roots
and b + c = 35. If the least value of f(x) x R is , then is equal to
3
(where [] denotes greatest integer function)
18. Consider the equation (x2 + x + 1)2 – (m – 3)(x2 + x + 1) + m = 0, where m is a real parameter. The
number of positive integral values of m for which equation has two real roots, is :
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19. If the equation (m2 – 12)x4 – 8x2 – 4 = 0 has no real roots, then the largest value of m is p q where p,
q are coprime natural numbers, then p + q =
********
8. (C) 9. (AC) 10. (ABC) 11. (AC) 12. (AB) 13. (AB) 14. 3
3
15. 3 16. 12 17. 6 18. 1 19. 5 21.
4
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