DPP No.
# 7 (JEE–MAIN)
Total Marks : 38 Max. Time : 28 min.
Single choice Objective ('–1' negative marking) Q.1,2 (3 marks, 2 min.) [06, 04]
Multiple choice objective ('–1' negative marking) Q.3 (4 marks, 3 min.) [04, 03]
Subjective Questions ('–1' negative marking) Q.4 to Q.10 (4 marks, 3 min.) [28, 21]
Question No. 1 2 3 4 5 6 7 8 9 10 Total
Marks
Obtained
x 2 − 2x + 3 7x + 2 x+4
1. If 2x + 7 x −x+2
2
3x = ax6 + bx5 + cx4 + dx3 + ex2 + fx + g the value of g is
3 2x − 1 x 2 − 4x + 7
(A) 2 (B) 1 (C) − 204 (D) –108
1
2. If log3 M + 3log3 N = 1 + log0.0085, then
3
9 9 3 3
(A) M9 = (B) N9 = (C) M3 = (D) N9 =
N M N M
1 1 1 1
3. log3 1 + + log3 1 + + log3 1 + + .. + log3 1 + when simplified has the value equal
3 4 5 242
to :
(A) 2 (B) 4 (C) 6 (D) log216
(x − 5)2 (x + 2)3 (x − 4)
4. Solve: 0
(x − 3) 4
5. Which of the following sets are equal?
A = {x : x N, x < 4}, B = {1, 1, 2, 3, 3}, C = {1, 3}, D = {x : x is an odd natural number < 5}
E = {1, 2, 3}, F = {1, 1, 3}
6. Find the power set of the set {a, b, c}.
7. Let A = {1, 2, 3, 5}, B = {1, 2, 3} and C = {1, 2, 5}. Find all the sets X satisfying.
(i) X A, X B (ii) X A, X C
(iii) X B, X B, X C (iv) X A, X B, X C
8. Let A = {, {}, 2, {2, }, 3}, which of the following are true?
(i) A (ii) A (iii) {} A
(iv) {} A (v) 2A (vi) {2, } A
(vii) {{2}, {3}} A (viii) {2, 3} A (ix) {, 2, 3} A.
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9. Remove the irrationality in the denominator
2 −1 1
(i) (ii)
2 +1 1 + 2 + 3
10. Solve the following inequations
x−2
(i) <0
x2 − 9
(ii) (x + 1) (x – 3)2 (x – 5) (x – 4)2 (x – 2) < 0
(x − 1) (x + 2)2
(iii) <0
−1 − x
1 + x2
(iv) <0
x2 − 5x + 6
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DPP No. # 7
1. (D) 2. (B) 3. (BD) 4. [–2, 3) (3, 4] {5}
5. A=B=E
C=F=D
6. 23 = 8 elements { , {a}, {b} , {c} , {a, b} , {b, c} , {c, a}, {a, b, c}}
7. (i) {5}, {5, 1}, {5, 2}, {5, 3}, {5, 1,2}, {5,1,3}, {5,2,3}, {1, 2, 3}
(ii) {3}, {3, 1}, {3, 2}, {3,5}, {3,1,2}, {3,1,5}, {3,2,5}, {1, 2, 5}
(iii) {3}, {3, 1}, {3, 2} (iv) {1}, {2}, {1,2},
8. (i) T (ii) T (iii) T (iv) T (v) F (vi) T
(vii) F (viii) F (ix) T
2+ 2 − 6
9. (i) 2 −1 (ii) 10. (i) x (–, –3) (2, 3)
4
(ii) x (–, –1) (2, 3) (3, 4) (4, 5) (iii) x (–, –2) (–2, –1) (1, )
(iv) x (2, 3)
Solutions
x − 2x + 3
2
7x + 2 x+4
1. 2x + 7 x2 − x + 2 3x
3 2x − 1 x − 4x + 7
2
= ax6 + bx5 + cx4 + dx3 + ex2 + fx + g put x = 0 (x = 0)
3 2 4
7 2 0 =g 3(14) – 2 (49) + 4 (–7 –6) = g
3 –1 7
42 – 98 – 52 – 108 = g
2. log3 M + 9 log3 N = 3(1 + log0.008 5)
log3 MN9 = 3(log0.008 5 × 0.008)
2
log3 (MN9) = 3 log0.008 0.04 = 3 × so MN9 = 9
3
4 5 243 243
3. log3 . ............ = log3 = 4.
3 4 242 3
+ – – + +
4. –2 3 4 5
x [–2,3) (3, 4] {5}
5. Obvious
6. Obvious
7. Obvious
8. Obvious
9. (i)
2 −1
=
( 2 −1 ) ( 2 −1 ) = 2 –1
2 +1 ( 2 + 1) ( 2 − 1)
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1 1+ 2 − 3 1+ 2 − 3 2 +2− 6
(ii) = = =
1+ 2 + 3
(1 + 2 )
2 4
− 3 2 2
x−2
10. (i) 0
(x − 3)(x + 3)
– + – +
–3 2 3
x (–, –3) (2, 3)
(ii) (x + 1)(x + 3)2 (x – 5)(x – 4)2 (x – 2) < 0
+ +
– –1 2 – 3 – 4 – 5
x (–, –1) (2, 3) (3, 4) (4, 5)
(x − 1)(x + 2)2
(iii) 0
(x + 1)
+ + +
–2 –1 – 1
x (–, –2) (–2, –1) (1, )
1 + x2
(iv) 0
(x − 2)(x − 3)
+ – +
2 3
x (2, 3)
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