Wednesday, May 31, 2017

Girls outshine boys in Maharashtra Board class XII exams

Girls outperformed boys in the Maharashtra State Board of Secondary and Higher Secondary Education class XII examinations, the results of which were declared on Tuesday. The overall pass percentage in Maharashtra stood at 89.50. The passing percentage for girls was 93.20, compared to 86.65 of boys, a senior official said.

The results for all the nine divisions - Pune, Mumbai, Nagpur, Nashik, Amravati, Aurangabad, Kolhapur, Latur and Konkan - were simultaneously declared.

14,29,478 students appeared for the exam this year and of them 12,79,406 passed, he said. Konkan division scored highest passing percentage with 95.20 whereas Mumbai was lowest with 88.21, the official added.

Tuesday, May 30, 2017

MICRO ATM MAGNET COLLECTION

Monday, May 29, 2017

Maharashtra HSC 12th result 2017 to be declared on May 30 at 1 pm; check...

Maharashtra HSC 12th result 2017 to be declared on May 30 at 1 pm; check on mahresult.nic.in

The Maharashtra HSC Result (Class 12) 2017 is to be declared on May 30 at 1 pm. An official notification on the date is put up on the official website mahresult.nic.in. please check it to confirm. All the best for HSC students who appeared for the exam. OMTEX Classes heartily wishes for all the students success.

Sunday, May 28, 2017

13 Similarity

Saturday, May 27, 2017

11 Similarity

12 Similarity

Monday, May 22, 2017

5 Similarity

3 Similarity

2 Similarity

4 Similarity

15 Probability

14 Probability

16 Probability

12 Probability

13 Probability

Sunday, May 21, 2017

11 Probability SSC 10th Standard Algebra 4th Chapter

10 Probability SSC 10th Standard Algebra 4th Chapter

8 Probability

7 Probability

9 Probability

5 Probability

6 Probability

Saturday, May 20, 2017

4 Probability

Tuesday, May 16, 2017

87 Quadratic Equation. 100 Important Quadratic Equations Practice Questions for SSC Class 10

For all your study Materials Visit : omtexclasses.com

Part 1: Top 10 Solved Quadratic Equations

Q1. Solve by factorization: $x^2 + 5x + 6 = 0$

Step 1: Find two numbers whose sum is 5 and product is 6. The numbers are 2 and 3. Step 2: $x^2 + 2x + 3x + 6 = 0$ Step 3: $x(x + 2) + 3(x + 2) = 0$ Step 4: $(x + 2)(x + 3) = 0$ Step 5: $x + 2 = 0$ or $x + 3 = 0$ Final Answer: $x = -2, x = -3$

Q2. Solve by factorization: $x^2 - 3x - 10 = 0$

Sum = -3, Product = -10. Numbers are -5 and 2. $x^2 - 5x + 2x - 10 = 0$ $x(x - 5) + 2(x - 5) = 0$ $(x - 5)(x + 2) = 0$ Final Answer: $x = 5, x = -2$

Q3. Solve using Formula Method: $x^2 + 6x + 5 = 0$

Comparing with $ax^2 + bx + c = 0$, $a=1, b=6, c=5$ Discriminant $(\Delta) = b^2 - 4ac = 6^2 - 4(1)(5) = 36 - 20 = 16$ Using formula: $x = \frac{-b \pm \sqrt{\Delta}}{2a}$ $x = \frac{-6 \pm \sqrt{16}}{2} = \frac{-6 \pm 4}{2}$ $x = \frac{-2}{2} = -1$ or $x = \frac{-10}{2} = -5$ Final Answer: $x = -1, -5$

Q4. Solve: $2y^2 + 27y + 13 = 0$

Sum = 27, Product = $2 \times 13 = 26$. Numbers: 26, 1. $2y^2 + 26y + 1y + 13 = 0$ $2y(y + 13) + 1(y + 13) = 0$ $(y + 13)(2y + 1) = 0$ Final Answer: $y = -13, y = -1/2$

Q5. Find the value of Discriminant for $x^2 + 7x - 1 = 0$

$a = 1, b = 7, c = -1$ $\Delta = b^2 - 4ac$ $\Delta = (7)^2 - 4(1)(-1) = 49 + 4 = 53$ Final Answer: $\Delta = 53$

Q6. Determine the nature of roots for $x^2 - 4x + 4 = 0$

$\Delta = (-4)^2 - 4(1)(4) = 16 - 16 = 0$ Since $\Delta = 0$, the roots are real and equal. Final Answer: Real and Equal roots.

Q7. Form a quadratic equation whose roots are 3 and 10.

Let $\alpha = 3, \beta = 10$ $\alpha + \beta = 13$, $\alpha\beta = 30$ Equation: $x^2 - (\alpha + \beta)x + \alpha\beta = 0$ Final Answer: $x^2 - 13x + 30 = 0$

Q8. Find $k$ if $x = 3$ is a root of $kx^2 - 10x + 3 = 0$

Substitute $x = 3$ in the equation: $k(3)^2 - 10(3) + 3 = 0$ $9k - 30 + 3 = 0 \implies 9k - 27 = 0$ $9k = 27 \implies k = 3$ Final Answer: $k = 3$

Q9. Solve: $x^2 - 15x + 54 = 0$

Numbers: -9, -6 (Sum -15, Product 54) $(x - 9)(x - 6) = 0$ Final Answer: $x = 9, 6$

Q10. Solve by completing the square: $x^2 + x - 20 = 0$

$x^2 + x = 20$ Add $(\frac{1}{2})^2 = \frac{1}{4}$ to both sides. $x^2 + x + \frac{1}{4} = 20 + \frac{1}{4} \implies (x + \frac{1}{2})^2 = \frac{81}{4}$ $x + \frac{1}{2} = \pm \frac{9}{2}$ $x = \frac{8}{2} = 4$ or $x = \frac{-10}{2} = -5$ Final Answer: $x = 4, -5$

Part 2: Practice Questions (Q11 - Q100)

Solve the following Quadratic Equations (Factorization/Formula):

$x^2 - 4x - 5 = 0$
$x^2 + 8x + 15 = 0$
$x^2 - 7x + 12 = 0$
$2x^2 - 5x + 2 = 0$
$3x^2 - x - 10 = 0$
$x^2 - 11x + 24 = 0$
$x^2 + 2x - 48 = 0$
$5m^2 = 22m + 15$
$2x^2 - 2x + \frac{1}{2} = 0$
$6x - \frac{2}{x} = 1$
$x^2 - 25 = 0$
$3y^2 = 15y$
$x^2 + 4x + 1 = 0$
$m^2 - 5m - 3 = 0$
$x^2 + 5x + 5 = 0$
$y^2 + \frac{1}{3}y = 2$
$5x^2 + 13x + 8 = 0$
$x^2 + 10x + 24 = 0$
$x^2 - x - 72 = 0$
$x^2 - 16x + 63 = 0$
$2x^2 + 9x + 10 = 0$
$x^2 - 2x - 3 = 0$
$x^2 + 6x + 9 = 0$
$x^2 - 10x + 25 = 0$
$x^2 + 14x + 49 = 0$
$4x^2 - 4x + 1 = 0$
$x^2 - 1 = 0$
$2x^2 - 7x + 6 = 0$
$3x^2 + 8x + 5 = 0$
$x^2 - 12x + 32 = 0$

Find the Discriminant and State Nature of Roots:

$x^2 + x + 1 = 0$
$2x^2 - 5x - 3 = 0$
$x^2 - 6x + 9 = 0$
$3x^2 + 2x - 1 = 0$
$x^2 + 4x + 5 = 0$
$2x^2 - 7x + 3 = 0$
$x^2 - 2x + 1 = 0$
$x^2 + 5x + 6 = 0$
$4x^2 - 12x + 9 = 0$
$x^2 - 8x + 15 = 0$
$2x^2 + 5x + 5 = 0$
$x^2 - x - 1 = 0$
$x^2 + 10x + 25 = 0$
$3x^2 + 7x + 2 = 0$
$x^2 + 2x + 3 = 0$
$5x^2 - 4x + 1 = 0$
$x^2 - 4x + 3 = 0$
$2x^2 - 6x + 3 = 0$
$x^2 + 12x + 36 = 0$
$x^2 - 5x + 7 = 0$

Form Quadratic Equations from Roots:

Roots: 2, 5
Roots: -3, -4
Roots: 0, 4
Roots: 1/2, 1/2
Roots: $\sqrt{2}, -\sqrt{2}$
Roots: 7, -7
Roots: 6, 1
Roots: -5, 2
Roots: 8, 3
Roots: -1, -1
Roots: 10, -2
Roots: 0, 0
Roots: 5, 5
Roots: -6, 6
Roots: 4, -3
Roots: 1, 9
Roots: -2, -8
Roots: 3, -3
Roots: 1/3, 3
Roots: -10, -10

Advanced and Word-Based Conditions:

Find $k$ if roots of $x^2 + kx + 12 = 0$ are real and equal.
Find $k$ if one root of $x^2 - kx + 18 = 0$ is 6.
Sum of roots is 10 and product is 21. Find equation.
One root is $2 + \sqrt{3}$, find the other root.
Solve $x^4 - 5x^2 + 4 = 0$ (Reducible to quadratic).
Solve $(x-3)(x+4) = 0$.
Solve $x^2 = 49$.
Solve $5x^2 = 20$.
Find $k$ if $\Delta = 0$ for $kx(x-2) + 6 = 0$.
Solve $x + 1/x = 2.5$.
Product of two consecutive natural numbers is 20.
Find $x$ if $x^2 - 9x + 20 = 0$.
Solve $y^2 + 10y + 21 = 0$.
Solve $x^2 - 11x + 30 = 0$.
Solve $x^2 - 2x - 8 = 0$.
Roots are 1 and -1. Form equation.
Roots are 4 and 0. Form equation.
Find $\Delta$ for $x^2 + 5x + 5 = 0$.
Solve $x^2 - 3x = 0$.
Solve $2x^2 = 8$.

Answer Key (Q11 - Q100)

11. 5, -1

12. -3, -5

13. 4, 3

14. 2, 0.5

15. 2, -5/3

16. 8, 3

17. 6, -8

18. 5, -3/5

19. 0.5, 0.5

20. 2/3, -1/2

21. 5, -5

22. 0, 5

23. $-2 \pm \sqrt{3}$

24. $\frac{5 \pm \sqrt{37}}{2}$

25. $\frac{-5 \pm \sqrt{5}}{2}$

26. 4/3, -3/2

27. -1, -1.6

28. -4, -6

29. 9, -8

30. 9, 7

31. -2, -2.5

32. 3, -1

33. -3, -3

34. 5, 5

35. -7, -7

36. 0.5, 0.5

37. 1, -1

38. 2, 1.5

39. -1, -5/3

40. 8, 4

41. -3 (Not Real)

42. 49 (Real, Uniq)

43. 0 (Real, Equal)

44. 16 (Real, Uniq)

45. -4 (Not Real)

46. 25 (Real, Uniq)

47. 0 (Real, Equal)

48. 1 (Real, Uniq)

49. 0 (Real, Equal)

50. 4 (Real, Uniq)

51. -15 (Not Real)

52. 5 (Real, Uniq)

53. 0 (Real, Equal)

54. 25 (Real, Uniq)

55. -8 (Not Real)

56. -4 (Not Real)

57. 4 (Real, Uniq)

58. 12 (Real, Uniq)

59. 0 (Real, Equal)

60. -3 (Not Real)

61. $x^2-7x+10=0$

62. $x^2+7x+12=0$

63. $x^2-4x=0$

64. $4x^2-4x+1=0$

65. $x^2-2=0$

66. $x^2-49=0$

67. $x^2-7x+6=0$

68. $x^2+3x-10=0$

69. $x^2-11x+24=0$

70. $x^2+2x+1=0$

71. $x^2-8x-20=0$

72. $x^2=0$

73. $x^2-10x+25=0$

74. $x^2-36=0$

75. $x^2-x-12=0$

76. $x^2-10x+9=0$

77. $x^2+10x+16=0$

78. $x^2-9=0$

79. $3x^2-10x+3=0$

80. $x^2+20x+100=0$

81. $k = \pm \sqrt{48}$

82. $k = 9$

83. $x^2-10x+21=0$

84. $2-\sqrt{3}$

85. $\pm 1, \pm 2$

86. 3, -4

87. 7, -7

88. 2, -2

89. $k = 6$

90. 2, 0.5

91. 4, 5

92. 4, 5

93. -3, -7

94. 6, 5

95. 4, -2

96. $x^2-1=0$

97. $x^2-4x=0$

98. 5

99. 0, 3

100. 2, -2

86 Quadratic Equation

10 Important Quadratic Equations Questions and Solutions for Class 10

10 Quadratic Equations Questions with Solutions

10 Quadratic Equations Questions with Solution

Solutions

Question 1:

Solve the quadratic equation $x^2 - 5x + 6 = 0$ by factorization method.

Solution:

Given equation: $x^2 - 5x + 6 = 0$

To factorize, we look for two numbers whose sum is $-5$ and product is $6$. These numbers are $-2$ and $-3$.

$x^2 - 2x - 3x + 6 = 0$

$x(x - 2) - 3(x - 2) = 0$

$(x - 2)(x - 3) = 0$

Therefore, $x - 2 = 0$ or $x - 3 = 0$

$x = 2$ or $x = 3$

Question 2:

Solve the following equation using the Quadratic Formula: $2x^2 + 7x + 5 = 0$.

Solution:

Comparing $2x^2 + 7x + 5 = 0$ with $ax^2 + bx + c = 0$, we get:

$a = 2, b = 7, c = 5$

Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-7 \pm \sqrt{7^2 - 4(2)(5)}}{2(2)}$

$x = \frac{-7 \pm \sqrt{49 - 40}}{4}$

$x = \frac{-7 \pm \sqrt{9}}{4} = \frac{-7 \pm 3}{4}$

Case 1: $x = \frac{-7 + 3}{4} = \frac{-4}{4} = -1$

Case 2: $x = \frac{-7 - 3}{4} = \frac{-10}{4} = -2.5$

Roots: $x = -1, -2.5$

Question 3:

Determine the nature of the roots of the quadratic equation: $3x^2 - 4x + 1 = 0$.

Solution:

Here, $a = 3, b = -4, c = 1$

Discriminant ($D$) $= b^2 - 4ac$

$D = (-4)^2 - 4(3)(1)$

$D = 16 - 12 = 4$

Since $D > 0$ and $D$ is a perfect square, the roots are real, rational, and unequal.

Question 4:

Solve $x^2 + 6x + 9 = 0$.

Solution:

Given: $x^2 + 6x + 9 = 0$

This is in the form of $(a + b)^2 = a^2 + 2ab + b^2$.

$(x)^2 + 2(x)(3) + (3)^2 = 0$

$(x + 3)^2 = 0$

$x + 3 = 0$

$x = -3, -3$ (Equal roots)

Question 5:

Find the value of $k$ if one root of the quadratic equation $kx^2 - 14x + 8 = 0$ is $2$.

Solution:

Since $x = 2$ is a root, it must satisfy the equation.

$k(2)^2 - 14(2) + 8 = 0$

$4k - 28 + 8 = 0$

$4k - 20 = 0$

$4k = 20$

$k = 5$

Question 6:

The sum of two numbers is 15 and the sum of their reciprocals is $3/10$. Find the numbers.

Solution:

Let the numbers be $x$ and $15 - x$.

According to the condition: $\frac{1}{x} + \frac{1}{15 - x} = \frac{3}{10}$

$\frac{15 - x + x}{x(15 - x)} = \frac{3}{10}$

$\frac{15}{15x - x^2} = \frac{3}{10}$

$150 = 3(15x - x^2)$

$50 = 15x - x^2$ (dividing by 3)

$x^2 - 15x + 50 = 0$

$(x - 10)(x - 5) = 0$

The numbers are 10 and 5.

Question 7:

Solve: $x^2 - 2x - 15 = 0$

Solution:

$x^2 - 5x + 3x - 15 = 0$

$x(x - 5) + 3(x - 5) = 0$

$(x - 5)(x + 3) = 0$

$x = 5$ or $x = -3$

Question 8:

Form a quadratic equation whose roots are $4$ and $-3$.

Solution:

Sum of roots ($\alpha + \beta$) $= 4 + (-3) = 1$

Product of roots ($\alpha\beta$) $= 4 \times (-3) = -12$

Equation: $x^2 - (\text{Sum})x + (\text{Product}) = 0$

$x^2 - (1)x + (-12) = 0$

$x^2 - x - 12 = 0$

Question 9:

Solve $4x^2 - 20x + 25 = 0$ using factorization.

Solution:

$4x^2 - 10x - 10x + 25 = 0$

$2x(2x - 5) - 5(2x - 5) = 0$

$(2x - 5)(2x - 5) = 0$

$2x - 5 = 0 \Rightarrow 2x = 5$

$x = 5/2$

Question 10:

Solve: $x + \frac{1}{x} = 2.5$

Solution:

Multiply the whole equation by $x$:

$x^2 + 1 = 2.5x$

$x^2 - 2.5x + 1 = 0$

Multiply by 2 to remove decimals: $2x^2 - 5x + 2 = 0$

$2x^2 - 4x - x + 2 = 0$

$2x(x - 2) - 1(x - 2) = 0$

$(x - 2)(2x - 1) = 0$

$x = 2$ or $x = 1/2$

84 Quadratic Equation

83 Quadratic Equation

10 Quadratic Equation Questions Important for Board Exam

Part 1: 10 Important Solved Questions

SSC Class 10 Algebra Quadratic Equations Important Solved Questions and Practice Set

Question 1: Factorization Method

Solve the quadratic equation by factorization: $x^2 - 15x + 54 = 0$

Solution:
Given: $x^2 - 15x + 54 = 0$
We need to find two numbers whose sum is $-15$ and product is $54$.
The numbers are $-9$ and $-6$.
$x^2 - 9x - 6x + 54 = 0$
$x(x - 9) - 6(x - 9) = 0$
$(x - 9)(x - 6) = 0$
$x - 9 = 0$ or $x - 6 = 0$
$x = 9$ or $x = 6$
Roots: 9, 6

Question 2: Formula Method

Solve using formula: $x^2 + 6x + 5 = 0$

Solution:
Comparing with $ax^2 + bx + c = 0$, we get:
$a = 1, b = 6, c = 5$
Discriminant $\Delta = b^2 - 4ac = (6)^2 - 4(1)(5) = 36 - 20 = 16$
Using formula $x = \frac{-b \pm \sqrt{\Delta}}{2a}$:
$x = \frac{-6 \pm \sqrt{16}}{2(1)} = \frac{-6 \pm 4}{2}$
$x = \frac{-6 + 4}{2} = \frac{-2}{2} = -1$ or $x = \frac{-6 - 4}{2} = \frac{-10}{2} = -5$
Roots: -1, -5

Question 3: Nature of Roots

Determine the nature of roots for $2x^2 - 5x + 7 = 0$

Solution:
$a = 2, b = -5, c = 7$
$\Delta = b^2 - 4ac = (-5)^2 - 4(2)(7) = 25 - 56 = -31$
Since $\Delta < 0$, the roots are not real.

Question 4: Finding 'k'

Find $k$ if the roots of $kx(x - 2) + 6 = 0$ are real and equal.

Solution:
Equation: $kx^2 - 2kx + 6 = 0$
For real and equal roots, $\Delta = 0$.
$a = k, b = -2k, c = 6$
$(-2k)^2 - 4(k)(6) = 0$
$4k^2 - 24k = 0$
$4k(k - 6) = 0$
Since $k \neq 0$ (as it is a quadratic equation), $k - 6 = 0 \implies \mathbf{k = 6}$.

Question 5: Forming Equation

Form a quadratic equation whose roots are 3 and -10.

Solution:
Let $\alpha = 3$ and $\beta = -10$.
Sum of roots $\alpha + \beta = 3 + (-10) = -7$
Product of roots $\alpha\beta = 3 \times (-10) = -30$
Equation: $x^2 - (\alpha + \beta)x + \alpha\beta = 0$
$x^2 - (-7)x + (-30) = 0$
Equation: $x^2 + 7x - 30 = 0$

Question 6: Sum and Product Relation

If $\alpha$ and $\beta$ are roots of $x^2 + 5x - 1 = 0$, find $\alpha^3 + \beta^3$.

Solution:
$\alpha + \beta = -b/a = -5$, $\alpha\beta = c/a = -1$
$\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta(\alpha + \beta)$
$= (-5)^3 - 3(-1)(-5)$
$= -125 - 15 = -140$
Value: -140

Question 7: Word Problem (Numbers)

Product of Pragati's age 2 years ago and 3 years hence is 84. Find her present age.

Solution:
Let present age be $x$.
$(x - 2)(x + 3) = 84$
$x^2 + 3x - 2x - 6 = 84$
$x^2 + x - 90 = 0$
$(x + 10)(x - 9) = 0$
$x = -10$ (Discarded) or $x = 9$.
Present age: 9 years

Question 8: Completing the Square

Solve $x^2 + x - 20 = 0$ by completing the square method.

Solution:
$x^2 + x = 20$
Add $(1/2 \times \text{coeff of } x)^2 = (1/2)^2 = 1/4$ to both sides:
$x^2 + x + 1/4 = 20 + 1/4$
$(x + 1/2)^2 = 81/4$
Taking square root: $x + 1/2 = \pm 9/2$
$x = 9/2 - 1/2 = 4$ or $x = -9/2 - 1/2 = -5$
Roots: 4, -5

Question 9: Alpha/Beta Expression

If roots of $x^2 - px + q = 0$ differ by 1, prove $p^2 = 4q + 1$.

Solution:
Let roots be $\alpha, \beta$. Given $|\alpha - \beta| = 1$.
$\alpha + \beta = p, \alpha\beta = q$.
We know $(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta$
$1^2 = p^2 - 4q$
$1 = p^2 - 4q \implies \mathbf{p^2 = 4q + 1}$. (Hence Proved)

Question 10: Speed/Distance

A train travels 360 km at uniform speed. If speed was 5 km/hr more, it would take 1 hr less. Find the speed.

Solution:
Let original speed be $x$ km/hr. Time $T_1 = 360/x$.
New speed $x + 5$. Time $T_2 = 360/(x + 5)$.
$T_1 - T_2 = 1$
$360/x - 360/(x + 5) = 1$
$360(x + 5 - x) = x(x + 5)$
$1800 = x^2 + 5x \implies x^2 + 5x - 1800 = 0$
$(x + 45)(x - 40) = 0$
Speed cannot be negative, so $x = 40$.
Speed: 40 km/hr

Part 2: 50 Practice Questions

1. $x^2 - 4x + 3 = 0$

2. $x^2 + 7x + 10 = 0$

3. $x^2 - 5x + 6 = 0$

4. $x^2 - 9 = 0$

5. $2x^2 - 7x + 3 = 0$

6. $x^2 - 10x + 25 = 0$

7. $3x^2 - 5x + 2 = 0$

8. $x^2 + 2x - 8 = 0$

9. $x^2 - 1 = 0$

10. $x^2 - 6x + 8 = 0$

11. $x^2 + 5x + 4 = 0$

12. $2x^2 + x - 6 = 0$

13. $x^2 - 3x - 10 = 0$

14. $x^2 - 11x + 30 = 0$

15. $x^2 + 8x + 15 = 0$

16. $x^2 - 13x + 40 = 0$

17. $x^2 - 4 = 0$

18. $5x^2 - 18x - 8 = 0$

19. $x^2 + 4x + 4 = 0$

20. $x^2 - 12x + 32 = 0$

21. $2x^2 - 5x - 3 = 0$

22. $x^2 - 2x - 15 = 0$

23. $x^2 + 9x + 20 = 0$

24. $x^2 - 7x + 12 = 0$

25. $3x^2 - 10x + 3 = 0$

26. $x^2 - 14x + 49 = 0$

27. $x^2 - 16 = 0$

28. $2x^2 + 7x + 5 = 0$

29. $x^2 - x - 12 = 0$

30. $x^2 - 15x + 56 = 0$

31. $x^2 + 10x + 21 = 0$

32. $x^2 - 8x + 12 = 0$

33. $4x^2 - 4x + 1 = 0$

34. $x^2 - 25 = 0$

35. $x^2 + x - 6 = 0$

36. $x^2 - 5x - 14 = 0$

37. $x^2 - 11x + 28 = 0$

38. $x^2 + 6x + 9 = 0$

39. $2x^2 - 3x + 1 = 0$

40. $x^2 - 100 = 0$

41. $x^2 - 17x + 72 = 0$

42. $x^2 + 12x + 35 = 0$

43. $x^2 - 2x + 1 = 0$

44. $3x^2 + 4x + 1 = 0$

45. $x^2 - 9x + 20 = 0$

46. $x^2 - 36 = 0$

47. $x^2 + 2x - 15 = 0$

48. $x^2 - 13x + 42 = 0$

49. $x^2 - 64 = 0$

50. $2x^2 - x - 1 = 0$

🔑 Answer Key

1: (3, 1)
2: (-2, -5)
3: (2, 3)
4: (3, -3)
5: (3, 0.5)
6: (5, 5)
7: (1, 2/3)
8: (2, -4)
9: (1, -1)
10: (4, 2)
11: (-1, -4)
12: (1.5, -2)
13: (5, -2)
14: (5, 6)
15: (-3, -5)
16: (5, 8)
17: (2, -2)
18: (4, -0.4)
19: (-2, -2)
20: (4, 8)
21: (3, -0.5)
22: (5, -3)
23: (-4, -5)
24: (3, 4)
25: (3, 1/3)
26: (7, 7)
27: (4, -4)
28: (-1, -2.5)
29: (4, -3)
30: (7, 8)
31: (-3, -7)
32: (2, 6)
33: (0.5, 0.5)
34: (5, -5)
35: (2, -3)
36: (7, -2)
37: (4, 7)
38: (-3, -3)
39: (1, 0.5)
40: (10, -10)
41: (8, 9)
42: (-5, -7)
43: (1, 1)
44: (-1/3, -1)
45: (4, 5)
46: (6, -6)
47: (3, -5)
48: (6, 7)
49: (8, -8)
50: (1, -0.5)

81 Quadratic Equation

71 Quadratic Equation

72 Quadratic Equation

80 Quadratic Equation

73 Quadratic Equation

79 Quadratic Equation

78 Quadratic Equation

77 Quadratic Equation

76 Quadratic Equation

75 Quadratic Equation

74 Quadratic Equation

Monday, May 15, 2017

70 Quadratic Equation

69 Quadratic Equation

68 Quadratic Equation

67 Quadratic Equation

66 Quadratic Equation

65 Quadratic Equation

64 Quadratic Equation

63 Quadratic Equation

62 Quadratic Equation

1 Similarity

61 Quadratic Equation

60 Quadratic Equation

59 Quadratic Equation

58 Quadratic Equation

57 Quadratic Equation

56 Quadratic Equation

55 Quadratic Equation

54 Quadratic Equation

53 Quadratic Equation

51 Quadratic Equation

When will the train arrive? [Seeking information about time]

Where have you put my bag? [Seeking information about place]

How does she sing? [Seeking information about manner]

Some common words used to seek information are:

What, when, where, why, how, who, whom, whose, which, how much/ many

Exercise:

Frame questions for the following sentences so as to get the underlined part as answer:

1. I’ve been asked to bring back a vaccine for a horse.

Ans. What have I been asked to bring back?

2. I went in search of a nearby shop where I had seen ties.

Ans. What did I go in search of?

3. The driver refused to wait.

Ans. Who refused to wait?

4. Parking was prohibited.

Ans. What was prohibited?

5. Nature soothes and nurtures.

Ans. What does nature do?

6. We went to a rocky beach and saw the spread of the majestic ocean.

Ans. Where did we go and see the spread of the majestic occean?

7. Their teamwork and preservance were impressive.

Ans. What was impressive?

8. Spider webs are delicate, yet very strong.

Ans. How are spider webs?

9. A rainbow colours the entier sky.

Ans. What colours the entire sky?

10. Dialogues throughout the book are lively.

Ans. How are the dialogues throughout the book?

11. The books have a few drawbacks.

Ans. What do the books have?

12. The books have a few drawbacks.

Ans. What do the books have?

13. Saina is exceptional.

Ans. Who is exceptional?

14. What is important is not to get carried away.

Ans. What is important?

Wh type questions.

The interrogative pronouns who, what, whom, whose, which and the interrogative adverbs where, when, why and how are used to frame information questions.

The structure ‘how + an adjective/adverb’ may also be used to frame information questions.

Frame WH questions to get the underline part as answers.

1. We lived downstairs of the hospital.

Ans. Where did we live?

2. He announced that he was going to be a doctor.

Ans. What did he announce?

3. He catches the bus.

Ans. What does he catch?

4. Nature heard the conversation.

Ans. What did Nature hear?

5. The queen of violets saw by her side the converted violet.

Ans. Whom did the queen of violets see by her side?

6. The morning routine started with tea.

Ans. How did the morning routine start?

7. I didn’t mind vegetable shopping.

Ans. What did I not mind?

8. The final indicator of a country’s independence is the way its children live.

Ans. What is the final indicator of a country’s independence?

9. He launched an independent partnership.

Ans. What did he launch?

10. The rain water rises the water table in the sand.

Ans. What does the rain water rise in the sand?

11. The monsoon starts in June.

Ans. When does the monsoon start?

12. We reached America.

Ans. Where did we reach?

13. Dimple breaks the glass.

Ans. Who does break the glass?

14. 20 billion messages are sent every month worldwide.

Ans. How many messages are sent every month worldwide?

Additional Examples

Frame questions which will give the following answers.

1. These are John’s books.

2. I want a pen.

3. We will stay with our cousins.

4. I am going with my aunt.

5. I went there to meet James.

6. My boy is the one in red shirt.

7. I come from Bangkok.

8. I met him last week.

9. This bridge is fifty feet long.

10. My father is sixty years old.

11. I have two brothers and two sisters.

12. Mr. Mathews is our headmaster.

13. We came to this place five years ago.

Answers

1. Whose books are these?

2. What do you want?

3. Whom will you stay with?

4. I am going with my aunt.

5. Why did you go there?

6. Which is your boy?

7. Where do you come from?

8. When did you meet him?

9. How long is this bridge?

10. How old is your father?

11. How many brothers and sisters do you have?

12. Who is your headmaster?

13. When did you come to this place?

Wednesday, May 31, 2017

Tuesday, May 30, 2017

Monday, May 29, 2017

Sunday, May 28, 2017

Saturday, May 27, 2017

Friday, May 26, 2017

Monday, May 22, 2017

Sunday, May 21, 2017

Saturday, May 20, 2017

Friday, May 19, 2017

Tuesday, May 16, 2017

Part 1: Top 10 Solved Quadratic Equations

Part 2: Practice Questions (Q11 - Q100)

Answer Key (Q11 - Q100)

10 Quadratic Equations Questions with Solution

Solutions

Part 1: 10 Important Solved Questions

SSC Class 10 Algebra Quadratic Equations Important Solved Questions and Practice Set

Part 2: 50 Practice Questions

🔑 Answer Key

Monday, May 15, 2017

Sunday, May 14, 2017

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