# CBSE Solutions for Class 11 English

#### GSEB std 10 science solution for Gujarati check Subject Chapters Wise::

If y² = -16 then the value of y are ____________

જવાબ : No solution

If y² = 4 then the value of y are ____________

જવાબ : {-2, 2}

If y² = 16 then the value of y is ____________

જવાબ : {-4, 4}

If y² = -9 then the value of y is ____________

જવાબ : No solution

If (x + 3)/(x – 2) > 1/2 then x lies in the interval ____________

જવાબ : (-8, ∞)

Solve: (x + 1)² + (x² + 3x + 2)² = 0

જવાબ : x = -1

If x² = -4 then the value of x has ____________

જવાબ : No solution

Sum of two rational numbers is ______ number.

જવાબ : rational

Solve: 1 ≤ |y – 1| ≤ 3

જવાબ : [-2, 0] ∪ [2, 4]

The complete set of values of l, for which the quadratic equation x2−lx+l+2=0 has equal roots, consists of ____________

જવાબ : 2 ± √12

For the equation |x|2+|x|−6=0, the sum of the real roots is ____________

જવાબ : 0

If pq is the roots of the equation x 2+ xs+1=0, then p2+q2= ____________

જવાબ : 1

If a, b are roots of the equation 4x2+3x+7=0, then 1/a + 1/b is equal to ____________

જવાબ : −3/7

The values of y satisfying log3 (y2+4y+12) =2 are ____________

જવાબ : −1, −3

The number of real roots of the equation (y2+2y) 2−(y+1)2−55=0 is ____________

જવાબ : 2

If α, β are the roots of the equation ax2+bx+c=0, then 1/ (AA+b) + 1/ (aβ+b) = ____________

જવાબ : b/ac

If α, β are the roots of the equation x2+ax+1=0; γ, δ the roots of the equation x2+bx+1=0, then (α−γ) (α+δ) (β−γ) (β+δ) = ____________

જવાબ : b2−a2

The number of real solutions of ∣2x−x2−3∣=1 is ____________

જવાબ : 2

The number of solutions of y2+|y−1|=1 is ____________

જવાબ : 2

If x is real and m= (x2−x+1)/(x2+x+1), then m ∈ ____________

જવાબ : [1/3, 3]

If the roots of x2−bx+c=0 are two consecutive integers, then b2 − 4c is ____________

જવાબ : 1

The value of k such that x2−11x+k=0 and x2−14x+2k=0 may have a common root is

જવાબ : 12 & 24

The values of l for which the quadratic equation lx2+1=lx+3x−11x2 has real and equal roots are

જવાબ : 5, −7

If the equations x2+2x+3k=0 and 2x2+3x+5k=0 have a non-zero common roots, then k =

જવાબ : −1

If one root of the equation x2+ax+12=0 is 4, while the equation x2+ax+b=0 has equal roots, the value of b is

જવાબ : 49/4

The value of a and b (a ≠ 0, b ≠ 0) for which ab are the roots of the equation x2+ax+b=0 are

જવાબ : a = 1, b = −2

The set of all values of k for which both the roots of the equation x2− (k+1) x+k+4=0 are real and negative, is

જવાબ : (−4, −3]

The number of roots of the equation (y+2) (y−5)/ (y−3) (y+6) = (y−2)/(y+4) is ____________

જવાબ : 1

If α and β are the roots of 4x2+3x+7=0, then the value of 1/α+1/β is ____________

જવાબ : −3/7

If α, β are the roots of the equation x2+ax+b=0 then −1/a+1/b are the roots of the equation ____________

જવાબ : bx2−ax+1=0

If the difference of the roots of x2−ax+b=0 is unity, then a2−4b= ____________

જવાબ : 1

If α, β are the roots of the equation x2−a(x+1) −c=0, then (α+1) (β+1) = ____________

જવાબ : 1 – c

The least value of which makes the roots of the equation x2+5x+m=0 imaginary is ____________

જવાબ : 7

The equation of the smallest degree with real coefficients having 1 + I as one of the roots is ____________

જવાબ : y2−2y+2=0

The interval in which f(x) = (x – 1) × (x – 2) × (x – 3) is negative is ____________

જવાબ : 2 < x < 3 and x < 1

If -2 < 2x – 1 < 2 then the value of x lies in the interval ____________

જવાબ : (-1/2, 3/2)

The solution of the inequality |x – 1| < 2 is ____________

જવાબ : (-1, 3)

If | x − 1| > 5, then x∈ ____________

જવાબ : (−∞, −4)∪(6, ∞)

The solution of |2/(x – 4)| > 1 where x ≠ 4 is ____________

જવાબ : (2, 4) ∪ (4, 6)

If (|y| – 1)/ (|y| – 2) ‎≥ 0, y ∈ R, y ‎± 2 then the interval of y is ____________

જવાબ : (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

The solution of the -12 < (4 -3y)/ (-5) < 2 is ____________

જવાબ : -56/3 < y < 14/3

If y² = -4 then the value of y are ____________

જવાબ : No solution

Solve: |y – 3| < 5

જવાબ : (-2, 8)

The graph of the in equations x ≥ 0, y ≥ 0, 3x + 4y ≤ 12 is ____________

જવાબ : interior of a triangle including the points on the sides

If |y| < 5 then the value of y lies in the interval ____________

જવાબ : (-5, 5)

Solve: f (p) = {(p – 1) × (2 – p)}/ (p – 3) ≥ 0

જવાબ : (-∞, 1] ∪ (2, 3)

If x² = 4 then the value of x is ____________

જવાબ : -2, 2

The solution of the 15 < 3(y – 2)/5 < 0 is

જવાબ : 27 < y < 2

Solve: 3x + 2 ≥ −x + 18

જવાબ : 3x+2≥−x+18

⇒3x+x≥18−2

⇒4x≥16

⇒x≥4

Hence, the solution set of the given in equation is [4, ∞)

Solve : 3x + 8 ≥ −x + 18

જવાબ : 3x+8≥−x+18

⇒3x+x≥18−8

⇒4x≥10

⇒x≥5/2

Hence, the solution set of the given in equation is [5/2, ∞).

Solve: 12x < 50, when x

જવાબ : We have, 12x<50

x<50/12

[Dividing both the sides by 12]

x<25/6

X-ray Then, the solution of the given in equation is (−∞, 25/6).

Solve: 12x < 50, when x  Z

જવાબ : We have, 12x<50

x<50/12                  [Dividing both the sides by 12]

x<25/6

X Z Then, the solution of the given in equation is {..........−3, −2, −1, 0, 1, 2, 3, 4}.

Solve: 12x < 50, when
x  N

જવાબ : We have, 12x<50

x<50/12                  [Dividing both the sides by 12]

x<25/6

xN Then, the solution of the given inequation is  {1, 2, 3, 4}.

Solve: −4x > 30, when x  R

જવાબ : −4x>30 x<−30/4

x<−15/2

xR Then, the solution of the given inequation is (−∞, −152).

Solve: −4x > 30, when x  Z

જવાબ : −4x>30

x<−30/4

x<−15/2

xZ Then, the solution of the given inequation is {..........−9, −8}.

Solve: −4x > 30, when x  N

જવાબ : −4x>30

x<−30/4

x<−15/2

xN Then, the solution of the given inequation is ϕ.

Solve: 4x − 2 < 8, when x  R

જવાબ : We have, 4x−2<8

4x<8+2

4x<10

x<10/4

x<5/2

xR Then, the solution of the given inequation is (−∞, 52).

Solve: 4x − 2 < 8, when x  Z

જવાબ : We have, 4x−2<8

4x<8+2

4x<10

x<10/4

x<5/2

xZ Then, the solution of the given inequation is {.......−3, −2, −1, 0, 1, 2}.

Solve: 4x − 2 < 8, when x  N

જવાબ : We have, 4x−2<8

4x<8+2

4x<10

x<10/4

x<5/2

xN Then, the solution of the given inequation is {1, 2}.

Solve :  x + 5 > 4x − 1

જવાબ : We have, x+5>4x−1

5+1 > 4x−x

6>3x

3x<6

x<2

x(−∞, 2)

Hence, the solution set of the given inequation is (−∞, 2).

Solve :  x + 5 > 4x − 13

જવાબ : We have, x+5>4x−13

5+13 > 4x−x

18>3x

3x<18

x<6

x(−∞, 6)

Hence, the solution set of the given inequation is (−∞, 6).

Solve :  x + 3 > 4x − 12

જવાબ : We have, x+3>4x−12

3+12 > 4x−x                 (Transposing x to the RHS and −10 to the LHS)

15>3x

3x<15

x<5

x(−∞, 5)

Hence, the solution set of the given inequation is (−∞, 5).

Solve :  x + 5 > 4x − 7

જવાબ : We have, x+5>4x−75+7 > 4x−x                 (Transposing x to the RHS and −10 to the LHS)

12>3x

3x<12

x<4

x(−∞, 4)

Hence, the solution set of the given inequation is (−∞, 4).

Solve :  x − 7 > x+1

જવાબ : 3x−7>x+1

3x−x>7+1

2x>8

x>4

Hence, the  solution set of the given inequation is (4, ∞)

Solve :  3x − 7 > x+3

જવાબ : 3x−7>x+3

3x−x>7+3

2x>10

x>5

Hence, the  solution set of the given inequation is (5, ∞)

Solve :  3x − 7 > x-1

જવાબ : 3x−7>x-1

3x−x>7-1

2x>6

x>3

Hence, the  solution set of the given inequation is (3, ∞)

Solve :  3x − 7 > x=5

જવાબ : 3x−7>x+5

3x−x>5+7

2x>12

x>6

Hence, the  solution set of the given inequation is (6, ∞)

Solve :  3x − 7 > x

જવાબ : 3x−7>x

3x−x>7

2x>7

x>7/2

Hence, the  solution set of the given inequation is (7/2, ∞)

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when x

 1 12x < 50 A (25 , ∞) 2 12x > 50 B (−∞,25) 3 2x < 50 C (25/6 , ∞) 4 2x > 50 D (−∞,25/6)

જવાબ :

1-D, 2-C, 3-B, 4-A

when x

 1 −4x > 30 A ( −15/2 , ∞) 2 4x > 30 B (15/2 , ∞) 3 −4x < 30 C (−∞, −15/2) 4 4x < 30 D (−∞, 15/2)

જવાબ :

1-C, 2-D, 3-A, 4-B

when x  Z

 1 12x < 50 A {26, 27,} 2 12x > 50 B {..........−3, −2, −1, 0, 1, 2, 3, 4} 3 2x < 50 C {5, 6, 7,} 4 2x > 50 D {..........−3, −2, −1, 0, 1, 2, 3…. 24}

જવાબ :

1-B, 2-C, 3-D, 4-A

−5x > 31

 1 x ∈ R A {….., -8,-7} 2 x ∈ Z B Φ 3 x ∈ N C (−∞ , -7)

જવાબ :

1-C, 2-A, 3-B

when x  Z

 1 −4x > 30 A {……, 6, 7} 2 4x > 30 B {-7,-6,} 3 −4x < 30 C {..........−9, −8} 4 4x < 30 D {8, 9,}

જવાબ :

1-C, 2-D, 3-B, 4-A

N

 1 12x < 50 A {26, 27,} 2 12x > 50 B {1, 2, 3, ……., 24} 3 2x < 50 C {5, 6,} 4 2x > 50 D {1, 2, 3, 4}

જવાબ :

1-D, 2-C, 3-B, 4-A

7x > -34

 1 x ∈ R A {-4, -3, -2…….} 2 x ∈ Z B {1, 2, 3…..} 3 x ∈ N C (-4, ∞)

જવાબ :

1-C, 2-A, 3-B

-4x>0

 1 x ∈ R A Φ 2 x ∈ Z B {…., -2,-1} 3 x ∈ N C (-∞, -1)

જવાબ :

1-C, 2-B, 3-A

x  N

 1 −4x > 30 A {8, 9,} 2 4x > 30 B {1, 2, …….7 } 3 4x < 30 C {1, 2} 4 14x < 30 D Φ

જવાબ :

1-D, 2-A, 3-B, 4-C

-8x > 6

 1 x ∈ R A Φ 2 x ∈ Z B (-∞, -1) 3 x ∈ N C {…., -2,-1}

જવાબ :

1-B, 2-C, 3-A

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