Section A contains 6 questions of 1 mark each. Scroll down for explanatory answer and video solution for all six one mark questions. Questions appeared from Quadratic Equations, Real Numbers, Coordinate Geometry, Arithmetic Progressions, Trigonometry, and Triangles.

Question 1

Find the value of a, for which point P(\\frac{a}{3}) , 2) is the mid-point of the line segment joining the points Q(-5,4) and R(-1,0).

**Hint to solve this Coordinate Geometry question**Substitute the coordinate of the points Q and R in the midpoint formula and solve it to find the value for a.

Question 2 | Internal Choice A

Find the value of k, for which one root of the quadratic equation kx

^{2}- 14x + 8 = 0 is 2.**Hint to solve this Quadratic equations question**One of the roots of the equation is 2. So, substituting x = 2 will satisfy the equation. By substituting the value of x as 2, we can find the value of k.

ORQuestion 2 | Internal Choice B

Find the value(s) of k for which the equation x

^{2}+ 5kx + 16 = 0 has real and equal roots.**Hint to solve this Quadratic equations question**Roots of the quadratic equation are real and equal.

If the roots are real and equal, the discriminant (D) of the equation is 0.

Express discriminant b^{2}- 4ac in terms of k and equate it to zero to compute the value of k.

Question 3 | Internal Choice A

Write the value of cot

^{2}θ − \\frac{1}{sin^2θ})**Hint to solve this Trignometric Identities Question**__Step 1__:Express cot θ in terms of cos θ and sin θ

__Step 2__: The denominator of both the terms of the expression will become sin^{2}θ

__Step 3__>: Simplify the numerator and cancel like terms in the numerator and denominator to find the value of the expression.**OR**Question 3 | Internal Choice B

If sin θ = cos θ, then find the value of 2 tanθ + cos

^{2}θ**Hint to solve this Trignometric Ratios Question**__Step 1__: Compute value of θ for which sin θ = cos θ

__Step 2__: Substitute value of θ computed in step 1 into the given expression to find the value of the expression.

Question 4

If n

^{th}term of an A.P. is (2n + 1), what is the sum of its first three terms?**Hint to solve this CBSE 2019 sample paper 1 mark Arithmetic Progressions problem****Approach**: Compute the 1st, 2nd, and 3rd term by susbtituting n = 1, n = 2, and n = 3 in the expression (2n + 1). Subsequently, find the sum of the 3 terms.

Question 5

In figure if AD = 6cm, DB = 9cm, AE = 8cm and EC = 12cm and ∠ADE = 48°. Find ∠ABC.

**Hint to solve this CBSE 2019 sample paper 1 mark Triangles question****Concept**: Check whether Basic Proportionality theorem applies in this case.

__Step 1__: Compute ratio between AD and DB and between AE and EC

__Step 2__: If the ratios are same, by converse of Basic Proportionality Theorem, DE will be parallel to BC.

__Step 3__: If DE is parallel to BC, corresponding angles will be equal and the answer can be computed.

Question 6

After how many decimal places will the decimal expansion of \\frac{23}{2^4 × 5^3}) terminate?

**Hint to solve this CBSE 2019 sample paper 1 mark Real Numbers question**__Step 1__: Rewrite the fraction such that the powers of 2s and 5s in the denominator is the same. This ensures that we get the denominator as a power of 10

__Step 2__: The power of 10 in the denominator is the number of decimal places in the decimal expansion of the fraction.

Question 1: Find the value of a, for which point P(\\frac{a}{3}) , 2) is the mid-point of the line segment joining the points Q(-5,4) and R(-1,0).

Scroll down further for explanatory answer text

Midpoint of 2 points (x_{1}, y_{1}) and (x_{2}, y_{2}) = \\frac{x_1 + x_2}{2}), \\frac{y_1 + y_2}{2})

The points given here are Q(-5, 4) and R(-1, 0) and the midpoint is P(\\frac{a}{3}), 2)

∴\\frac{-5 + (-1)}{2}) = \\frac{a}{3}) and \\frac{4 + 0}{2}) = 2

\\frac{-6}{2}) = \\frac{a}{3})

a = -9

Question 2: Find the value of k, for which one root of the quadratic equation kx^{2} - 14x + 8 = 0 is 2.

Scroll down further for explanatory answer text

If 2 is one of the roots of the quadratic equation kx^{2} - 14x + 8 = 0, then it will satisfy the equation

Substitute x = 2 in the above equation.

∴ k(2)^{2} – 14(2) + 8 = 0

4k – 28 + 8 = 0

4k = 20

k = 5

Question 2 Internal Choice 2: Find the value(s) of k for which the equation x^{2 }+ 5kx + 16 = 0 has real and equal roots.

Scroll down further for explanatory answer text

If a quadratic equation has real and equal roots, then the discriminant (D) of the equation is 0.

Discriminant of a quadratic equation ax^{2} + bx + c = 0 is b^{2} – 4ac

In the given equation, a = 1, b = 5k, and c = 16

b^{2} – 4ac = 0

(5k)^{2} – 4(1)(16) = 0

25k^{2} – 64 = 0

k^{2} = \\frac{64}{25})

**k = ± \\frac{8}{5}) **

Question 3 Internal Choice 1: Write the value of cot^{2}θ − \\frac{1}{sin^2θ})

Scroll down further for explanatory answer text

cot^{2} θ − \\frac{1 }{sin^2 θ})

= \\frac{cos^2 θ}{sin^2 θ}) − \\frac{1}{sin^2 θ}) [Because cot θ = \\frac{cos θ}{sin θ})]

= \\frac{cos^2 θ − 1}{sin^2 θ})

= \\frac{− sin^2 θ}{sin^2 θ}) [Because sin^{2} θ + cos^{2} θ = 1 => sin^{2} θ = 1 - cos^{2} θ]

= -1

Question 3 Internal Choice 2: If sin θ = cos θ, then find the value of 2tan θ + cos2 θ

Scroll down further for explanatory answer text

**For what values of θ will sin θ = cos θ?**

sin θ = cos θ only when θ = 45°

**Substitute θ = 45° in given expression**

2tan θ + cos^{2} θ = 2tan 45° + cos^{2} 45°

= 2tan (1) + cos^{2} (\\frac{1}{√2}))

= 2 + (\\frac{1}{2}))

= \\frac{5}{2})

Question 4: If nth term of an A.P. is (2n + 1), what is the sum of its first three terms?

Scroll down further for explanatory answer text

nth term of the given A.P. is (2n + 1)

Substitute n = 1 to find the first term of the A.P. a_{1} = 2(1) + 1 = 3

Substitute n = 2 to find the second term of the A.P. a_{2} = 2(2) + 1 = 5

Substitute n = 3 to find the third term of the A.P. a_{3} = 2(3) + 1 = 7

Sum of the first three terms = 3 + 5 + 7 = **15**

Question 5: In figure if AD = 6 cm, DB = 9 cm, AE = 8 cm and EC = 12 cm and ∠ADE = 48°. Find ∠ABC.

Scroll down further for explanatory answer text

**Basic Proportionality Theorem:** If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

AD = 6 cm, DB = 9 cm, AE = 8 cm and EC = 12 cm

\\frac{AD}{DB}) = \\frac{6}{9}) = \\frac{2}{3}); \\frac{AE}{EC}) = \\frac{8}{12}) = \\frac{2}{3})

\\frac{AD}{DB}) = \\frac{AE}{EC}) ∴ DE is parallel to BC

If DE is parallel to BC, corresponding angles will be equal.

**∴ ∠ADE = ∠ABC = 48°**

Question 6: After how many decimal places will the decimal expansion of \\frac{23}{2^4 × 5^3}) terminate?

Scroll down further for explanatory answer text

Any real number which has a decimal expansion that terminates can be expressed as a rational number whose denominator is a power of 10 i.e., power of 2 and 5.

Express the fraction in an equivalent form such that the powers of 2 and 5 of the denominator are equal. Ensures that the denominator is a power of 10.

\\frac{23}{2^4 × 5^3}) = \\frac{23}{2^4 × 5^3}) × \\frac{5}{5}) = \\frac{23 × 5}{2^4 × 5^4}) = \\frac{115}{10^4}) = 0.0115

The answer is **4 places.**

Class 10 Maths

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CBSE Class 10 Maths - 2021

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
- Circles Revision Class
- Areas Related to Circles Revision Videos

1. Section A | 2018 CBSE Class 10 Maths 1 Mark **Questions 1 to 2** ▶

2. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 3 to 4** ▶

3. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 5 to 6** ▶

4. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 7** | Real Numbers ▶

5. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 8** | Arithmetic Progressions ▶

6. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 9** | Coordinate Geometry ▶

7. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 10** | Probability ▶

8. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 11** | Probability ▶

9. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 12** | Linear Equations ▶

10. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 13** | Real Numbers & HCF ▶

11. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 14** | Polynomials ▶

12. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 15** | Linear Equations ▶

13. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 16** | Coordinate Geometry ▶

14. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 17** | Trigonometric Ratios ▶

15. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 18** | Circles ▶

16. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 19** | Triangles ▶

17. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 20** | Areas Related to Circles ▶

18. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 21** | Statistics - Median ▶

19. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 22** | Statistics ▶

20. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 23** | Quadratic Equations ▶

21. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 24** | Arithmetic Progressions ▶

22. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 25** | Triangles ▶

23. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 27** | Trigonometry ▶

24. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 28** | Statistics ▶

25. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 29** | Surface Areas ▶

26. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 30** | Trigonometry ▶

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