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

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

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જવાબ : No solution

If y² = 4 then the value of y are ____________

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જવાબ : {-2, 2}

If y² = 16 then the value of y is ____________

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જવાબ : {-4, 4}

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

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જવાબ : No solution

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

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જવાબ : (-8, ∞)

Solve: (x + 1)² + (x² + 3x + 2)² = 0

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જવાબ : x = -1

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

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જવાબ : No solution

Sum of two rational numbers is ______ number.

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જવાબ : rational

Solve: 1 ≤ |y – 1| ≤ 3

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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 ____________

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જવાબ : 2 ± √12

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

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જવાબ : 0

If p, q is the roots of the equation x^{2+ xs+}1=0, then p²+q²= ____________

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જવાબ : 1

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

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જવાબ : −3/7

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

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જવાબ : −1, −3

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

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જવાબ : 2

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

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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) = ____________

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જવાબ : b²−a²

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

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જવાબ : 2

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

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જવાબ : 2

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

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જવાબ : [1/3, 3]

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

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જવાબ : 1

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

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જવાબ : 12 & 24

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

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જવાબ : 5, −7

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

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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

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જવાબ : 49/4

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

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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

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જવાબ : (−4, −3]

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

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જવાબ : 1

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

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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 ____________

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જવાબ : bx²−ax+1=0

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

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જવાબ : 1

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

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જવાબ : 1 – c

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

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જવાબ : 7

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

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જવાબ : y²−2y+2=0

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

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જવાબ : 2 < x < 3 and x < 1

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

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જવાબ : (-1/2, 3/2)

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

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જવાબ : (-1, 3)

If | x − 1| > 5, then x∈ ____________

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જવાબ : (−∞, −4)∪(6, ∞)

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

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જવાબ : (2, 4) ∪ (4, 6)

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

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જવાબ : (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

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

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જવાબ : -56/3 < y < 14/3

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

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જવાબ : No solution

Solve: |y – 3| < 5

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જવાબ : (-2, 8)

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

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

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

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જવાબ : (-5, 5)

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

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જવાબ : (-∞, 1] ∪ (2, 3)

If x² = 4 then the value of x is ____________

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જવાબ : -2, 2

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

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જવાબ : 27 < y < 2

Solve: 3x + 2 ≥ −x + 18

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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

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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 ∈ R

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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

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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

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જવાબ : We have, 12x<50

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

⇒x<25/6

x∈N Then, the solution of the given inequation is {1, 2, 3, 4}.

Solve: −4x > 30, when x ∈ R

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જવાબ : −4x>30 ⇒x<−30/4

⇒x<−15/2

x∈R Then, the solution of the given inequation is (−∞, −152).

Solve: −4x > 30, when x ∈ Z

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જવાબ : −4x>30

⇒x<−30/4

⇒x<−15/2

x∈Z Then, the solution of the given inequation is {..........−9, −8}.

Solve: −4x > 30, when x ∈ N

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જવાબ : −4x>30

⇒x<−30/4

⇒x<−15/2

x∈N Then, the solution of the given inequation is ϕ.

Solve: 4x − 2 < 8, when x ∈ R

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જવાબ : We have, 4x−2<8

⇒4x<8+2

⇒4x<10

⇒x<10/4

⇒x<5/2

x∈R Then, the solution of the given inequation is (−∞, 52).

Solve: 4x − 2 < 8, when x ∈ Z

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જવાબ : We have, 4x−2<8

⇒4x<8+2

⇒4x<10

⇒x<10/4

⇒x<5/2

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

Solve: 4x − 2 < 8, when x ∈ N

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જવાબ : We have, 4x−2<8

⇒4x<8+2

⇒4x<10

⇒x<10/4

⇒x<5/2

x∈N Then, the solution of the given inequation is {1, 2}.

Solve : x + 5 > 4x − 1

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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

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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

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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

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જવાબ : We have, x+5>4x−7⇒5+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

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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

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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

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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

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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

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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 ∈ R

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

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જવાબ :

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

when x ∈ R

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

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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}

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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)

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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,}

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જવાબ :

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

x ∈ 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}

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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, ∞)

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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)

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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

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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}

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જવાબ :

1-B, 2-C, 3-A

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

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