Supplement 11th Maths P 2013 E WA

SUPPLEMENT DPP [ REVIEW OF CLASS X ]

JEEnius DPP MATHEMATICS 

Class:XI

[ Review of Class X ]

Supplement-1

Evaluate each of the following: Q.1

4

(a) 3 (g)

(b) (– 2x)

31 x 2 y 4 2

 3y  (c)     4  

3

 2 3 3

x y

(h) (16)

1/4

(a)

(d)

( x  y) 2 3 ( x  y) 1 6

(e)

[(x  y) 2 ]1 4 1 2 2 3 1 6 3 2

(g)

c

(h)

82 3 a 1 3 b 2 3c5 2

(f) (2y –1) –1

(j) (– a3 b3) –2/3

13

(b)

21 · 20 · 23

a  b

(e) (–4x) –2

8 (l ) (103)0 (o) 3y2/3 y4/3

23 · 22 · 24

4

(d) 4 –3

82 3 (8) 2 3

(i)

(k) – 3(–1) –1/5(4) –1/2 (n) xy x4y Q.2

3

(m) (x – y)0 [(x – y)4] –1/2 (p) (4 · 103) (3 · 10 –5) (6 · 10 4)

10 x  y ·10 y x ·10 y1

(c)

10 y1 ·102 y1 (102 ) 3 (103 )1 6

31 2 · 31 3 [(x –1) –2] –3

(f)

10 · (104 ) 1 2

 28 · 34      54     

31 2 · 32 3

1 4

4

(i)

3

a 2  b5 c 2d 2

0

Q.3

Q.4

(a)

27  2 3  52 3 · 51 3

1

(d)

(27)2/3 – 3(3x)0 + (25)1/2

(c)

82/3 + 3 –2 – 

(e)

(8)2/3 · (16) –3/4 · 2 0 – 8 –2/3

(f)

3

(g)

x3/2 + 4x –1 – 5x0 when x = 4

(h)

y2/3 + 3y –1 – 2y0 when y = 1/8

9

(10)0

(b)

 1  4   2 1 -16 1 2·4 · 3 0  2 

  3 

4

(i)

64 –2/3 · 16 5/4 · 2 0 ·

(k)

  72 y 2n    · 90  ( 2 yn  2 ) 1   3    

(a)

(c)

(f)

(i)

0

(25) + (0.25)

1/2

 – 8

1/3

 –1/2

·4

(64)

+ (0.027)

(d)

3  4(3) 1 0

a · a 2 3

(j)

32  5( 2)0

 –2/3

( x  2)2 when x = – 6

 –2

 – 3(150) + 12(2)

6

1/3

x

2 3

 –2/3

(g) (0.125)

+

a5

1

(b)

30 x  4x 1

a

2 3

8

if x = 8

+

3 22

1

3

5 6

a 2 · a 1 2

+ 3a0 + (3a)0 + (27) –1/3 – 1 3/2

(e)

(h)

2  2 1 5 n

+ (– 8) – 4 3/2

32 25 n

(60000)3 (0.00002) 4 (100) 2 (72000000 )(0.0002)5 PAGE# 1

Q.5

(a)

(b)

 1  1  (5  x )1 2   (5  x )1 2  ( x 2  3x  4)  2 3 ( 2x  3)  2  3  if x = 1 2 23 ( x  3x  4)

( x 2  3x  4)1 3 

1  (9 x 2  5y)1 4 (2 x )  x 2  (9 x 2  5y) 3 4 (18x ) 4  if x = 2, y = 4 2 12 (9 x  5y)

(c)

1  2  ( x  1) 2 3  ( x  1) 1 2   ( x  1)1 2  ( x  1) 1 3  2  3 

(d)

x  1  x 2  2x  1

(e)

3x  2 y  4x 2  4xy  y 2

( x  1)

Class:XI

43

[ Review of Class X ]

Supplement-2

FACTORIZATION 2

2

Type-1 : (i) (iv)

E  – C = (E – C) (E + C) x4 – y4 4x2 – 9y2 – 6x – 9y

Type-2 : (i) (iii)

a3 ± b3  (a ± b) (a2  ab + b2) 8x3 – 27y3 8x3  - 125y3 + 2x – 5y

(ii) (v)

9a2 – (2x – y) 2 4x 2 – 12x + 9 – 4y2

(ii) (iv)

(iii)

(3x – y)2 – (2x – 3y) 2

a6 – b 6 8x 3 + 1

x2 + px + q / ax 2 + bx + r  Type-3 : (i) x2 + 3x – 40 (ii) x2 – 3x – 40 (iii) x 2 + 5x – 14 (iv) x2 + 6x – 187 (v) x 2 – 9x – 90 (vi) a 2 – 11a + 28 (vii) x2 – 3x – 4 (viii) x 2 – 2x – 3 ×—————×—————×—————×—————×—————× (i) 3x2 – 10x + 8 (ii) 12x2 + x – 35 (iii) 3x2 – 5x + 2 (iv) 3x2 – 7x + 4 (v) 7x 2 – 8x + 1 (vi) 2x 2 – 17x + 26 (vii) 3a2 – 7a – 6 (viii) 14a2 + a – 3 Type-4 : Factorisationalybyconvertingthe givenexpression into a perfect square. (i) a2 – 4a + 3 + 2b – b 2 (ii) a4 + a 2 b2 + b4 (iii) x4 + 324 (iv) x4 – y2 + 2x2 + 1 (v) a4 + a 2 + 1 (vi) 9x4 – 10x2 + 1 (vii) 4a4 – 5a2 + 1 (viii) 4x4 + 81. Type-5: Using Remainder Theorem (i) x3 – 13x – 12 (iv) 2x3 + 9x2 + 10x + 3 (vii) x3 – 4x2 + 5x – 2

(ii) (v)

x 3 – 7x – 6 x3 – 9x2 + 23x – 15

(iii) (vi)

x 3 – 6x2 + 11x – 6 2x 3 – 9x2 + 13x – 6

Type-6 : a3 + b3 + c3 – 3abc (i) 8a3 + b3 + c 3 – 6abc (ii) 8a6 + 5a3 + 1 (iii) Show that (x – y)3 + (y – z)3 + (z – x)3 = 3 (x – y) (y – z) (z – x). PAGE# 2

Type-7 : (i) (ii) (iii) (iv) (v)

f(x) = (x + 1) (x + 2) (x + 3) (x + 4) – 8 (x + 1) (x + 2) (x + 3) (x + 4) – 15 (x – 3) (x + 2) (x – 6) (x – 1) + 56 4x(2x + 3) (2x – 1) (x + 1) – 54 (x – 3) (x + 2) (x + 3) (x + 8) + 56

Class:XI

[ Review of Class X ]

Supplement-3

Rationalization

2.

1

Simplify: (a)

1.

 

3 2 1 x2  1 x2

Rationalize:

3.

 

Simplify:

4.

 

Simplify:

5.

 

Simplify: (i)

(iv)

2

1 x  1 x

2

74 3

.

3 6

.

5 3  2 12  32  50 3 2 3 6 3 22 3

– 

4 3 6 2

(ii)

3 22 3 3

(v)

2 3

Class:XI

Q.1

1

(b)

+

6 2 3

.

3 5 3

(iii)

5 3 3 5 2

 

(vi)

[ Review of Class X ]

2 1 2 1 3 5 3 5 Supplement-4

Match the values of x given in Column-II satisfying the exponential equation given in Column-I (Do not verify). Remember that for a > 0,the term ax is always greater than zero  x  R. Column-I Column-II (A) (B) (C) (D) (E)

5x – 24 =

25

5x (2x + 1) (5x) = 200 42/x – 5(41/x) + 4 = 0 22x + 1  – 33 (2 x – 1 ) + 4 = 0 2 x  1· 4 x  1 8

x 1

= 16

(F)

32x + 1 + 10 (3x) + 3 = 0

(G)

4x

(H) (I)

64 (9x) – 84 (12 x) + 27 (16x) = 0 52x – 7x – 52x (35) + 7x (35) = 0

2

2

x 2  2   9   2 8  0    

(P)

–3

(Q) (R) (S)

–2 –1 0

(T)

1

(U)

2

(V)

3

(X)

None

PAGE# 3

Q.2

Which ofthefollowingequation(s) has (have) onlyunity asthesolution 1

(A) 4 x

2

log 10



2

x+1

(C) 7 (3

Q.3

)–5

x+2

=3

x+4

 – 5

x+3

(D) 2

x 2 6

x2  6

·3



(6 x  1 ) 4 65

Which ofthe following equation(s) has (have)onlynatural solution(s). (A) 6 · 9 1/x – 13 · 61/x + 6 · 41/x = 0 (B) 3 · 2x/2 – 7 · 2x/4 = 20 x2  5

(C) 4x  Q.4

(base of the log is 10) (B) 2 (3x + 1) – 6 (3 x – 1) – 3x = 9

 6 · 2x 

x 2 5

(D) 5 x · 8x  1  500 x

8  0

Solve the following equations: (i)

4x – 10 · 2 x – 1 = 24.

(ii)

4 · 22x – 6x = 18 · 3 2x.

(iii)

32x – 3  – 9 x – 1 + 272x/3 = 675.

(iv)

7x  2 

 5 

x 1

   3 

(v)

  9  

x 2  2 x  11

·

  25 

9

 5    .  3 

(vi)

1 7

· 7 x  1  14 · 7 x  1  2 · 7 x  48

x 2  7.2 x  3.9    9 3  log (7  x )  0 . 3    

52x = 32x + 2 · 5x + 2 · 3x.

(vii)

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

Q.1

(a) 81 (b) – 8x

(h) 2

(i)

3

(c)

1

(a) 29 (b)

(h) Q.3

Q.4

(a)

1

(k)

2 2

a  b (p) 7200 1

(c) 1

10

1 64 3 2

(d) 1

(e)

1

(f)

16x 2

y

(g)

2 1

(l ) 1

(m)

(e) 10 –4

(f) x –6 (g)

( x  y)2

4x5 3y 7

(n) x5y

a  b 8c 4

14 56

4

(i)

15 16

(b)

3

(i) 18

(j)

(a) 0.8

(b)

(h)

(d)

64

(j)

2

(o) 3y2

Q.2

27 y3

1 2

(i)

a  b

d

7

(c)

2 2

(k)

a 22  3

c

(c)

46 15

4

(d) 11 (e)

1

(f)

4

1 4

(g) 4

(h)

89 4

2 y2 (d) 34

(e)

 31 2

(f)

1 16

(g)

26 5

150

PAGE# 4

Q.5

(a)

1

(b)

3

7

(c)

8

7x 6( x  1)1 2 ( x  1)5 3

(d)

2x if x  – 1, – 2 if x   – 1

x – y if 2x  y, 5x – 3y if 2x   y

(e)

########################

(i) (iv) (i) (iii) (i) (iv) (vii) (i) (iv) (vii) (i) (iii) (v) (vii)

2

2

(x + y ) (x + y) (x – y) (2x + 3y) (2x – 3y – 3)

Type-1 (3a + 2x – y) (3a – 2x + y) (2x – 3 + 2y) (2x – 3 – 2y)

(ii) (v)

2

(5x – 4y) (x + 2y)

Type-2 (ii) (a + b) (a2 – ab + b2) (a – b) (a2 + ab + b2) (iv) (1 + 2x) (1 – 2x + 4x 2)

2

(2x – 3y) (4x +6xy+9x ) (2x – 5y) (4x2 + 10xy + 25y2 + 1)

Type-3 (x + 8) (x – 5) (ii) (x – 8) (x + 5) (iii) (x + 7) (x – 2) (x + 17) (x – 11) (v) (x – 15) (x + 6) (vi) (a – 7) (a – 4) (x – 4) (x + 1) (viii) (x – 3) (x + 1) ×—————×—————×—————×—————×—————× (x – 2) (3x – 4) (ii) (4x + 7) (3x – 5) (iii) (3x – 2) (x – 1) (x – 1) (3x – 4) (v) (x – 1) (7x – 1) (vi) (2x – 13) (x – 2) (a – 3) (3a + 2) (viii) (2a + 1) (7a – 3) Type-4 (ii) (a2 + ab + b2) (a2 – ab + b2) (iv) (x 2 + 1 + y) (x2 + 1 – y) (vi) (3x + 1) (3x – 1) (x + 1) (x – 1)]

(a – b – 1) (a + b – 3) (x2 + 6x + 18) (x 2 – 6x + 18) (a2 + a + 1) (a2 – a + 1) (2a + 1) (2a – 1) (a + 1) (a – 1)

Type-5 (x + 2) (x – 3) (x + 1) (iii) (x – 1) (x – 3) (x – 5) (vi)

(i) (iv) (vii)

(x + 1) (x – 4) (x + 3) (x + 1) (x + 3) (2x + 1) (x – 2) (x – 1)2

(i)

Type-6 (2a + b + c) (4a + b + c  – 2ab – bc – 2ac)

(i) (iii) (v)

(iii)

2

(ii) (v)

2

2

(ii)

(x – 1) (x – 2) (x – 3) (x – 1) (x – 2) (2x – 3)

(2a2 – a + 1) (4a4 + 2a3 – a2 + a + 1)

Type-7 (ii) (x2 + 5x + 1) (x 2 + 5x + 9) (iv) 2(2x 2 + 2x + 3) (4x 2 + 4x – 9)

(x2 + 5x + 8) (x 2 + 5x + 2) (x2 – 4x – 4) (x – 5) (x + 1) (x2 + 5x – 22) (x + 1) (x + 4)

########################

2. 5.

1 1 x

4

.

3.

5 2 6   3.650

(ii)

x2 (i) (v)

(vi)

4.

3

( 2 3  6 )  (3 2  6 )  (3 2  2 3 ) = 0

(iii) 5.828 9  2 15 6.854 ########################

(iv)

6.464

Q.1 Q.2

(A) U, (B) U, (C) T, (D) Q, V, (E) P, Q, R, S, T, U, V, (F) X, (G) R, T, (H) T, U, (I) S AB Q.3 BD

Q.4

(i)

x=3

(v)

x=

7 2

,2

(ii)

x=–2

(vi)

x=

1 5

,6

(iii)

x=3

(vii)

x=1

(iv)

x=0 PAGE# 5