Section A contains 6 questions of 1 mark each. Scroll down for explanatory answer and video solution to all six 1-mark questions. Questions appeared from Quadratic Equations, Real Numbers, Coordinate Geometry, Arithmetic Progressions, Trigonometry, and Triangles.
If x = 3 is one root of the quadratic equation x^{2} – 2kx – 6 = 0, then find the value of k.
Because 3 is a root of the equation, substitute the value of x as 3 in the equation and solve to find the value of k.
What is the HCF of smallest prime number and the smallest composite number?
What is the smallest prime number? What is the smallest composite number?
Compute the HCF of these two numbers.
Find the distance of a point P(x, y) from the origin.
Concept: The formula to compute the distance between two points whose coordinates are (x_{1}, y_{1}) and (x_{2}, y_{2}).
Approach: One of the points is the origin (0, 0). Let it be (x_{1}, y_{1})
The second point is P(x, y). Let it be (x_{2}, y_{2}).
Substitute these values in the formula to find the distance between two points to find the answer.
In an AP, if the common difference (d) = - 4, and the seventh term (a_{7}) is 4, then find the first term.
Approach: The nth term of an AP a_{n} = a_{1} + (n - 1)d, where a_{1} is the first term of the AP and 'd' is the common difference.
Given Data: a_{7} = 4 and d = (-4). So, n = 7.
Substitute: The above values in the equation to find the nth term a_{n} and find a_{1}.
What is the value of (cos^{2} 67° - sin^{2} 23°)?
Concept: Trigonometric values of complementary angles.
Step 1: Rewrite cos 67 as cos (90 - 23).
Step 2: Apply properties of trigonometric values of complementary angles and compute the answer.
Given ∆ ABC is similar to ∆ PQR. If \\frac{AB}{PQ} = \frac{1}{3}), then find \\frac{ar ∆ ABC}{ar ∆ PQR})
Concept / Theorem: Ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.
Given Data: Ratio of corresponding sides of the two similar triangles is given.
Apply Theorem: Apply the theorem about the relation between the ratio of corresponding sides of two similar triangles and their areas to compute the answer.
Question 1: If x = 3 is one root of the quadratic equation x^{2} – 2kx – 6 = 0, then find the value of k.
Scroll down further for explanatory answer text
x = 3 is one root of x^{2} - 2kx - 6 = 0
Because 3 is one of the roots of the equation, substituting x= 3 will satisfy the equation.
3^{2} - 2 × k × 3 - 6 = 0
9 - 6k - 6 = 0
6k = 3 or k = \\frac{3}{6}) = \\frac{1}{2})
Question 2: What is the HCF of smallest prime number and the smallest composite number?
Scroll down further for explanatory answer text
Smallest prime number is 2.
Smallest composite number is 4.
HCF(2, 4) = 2.
Question 3: Find the distance of a point P(x, y) from the origin.
Scroll down further for explanatory answer text
Distance between two points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2})
∴ distance between (x, y) and (0, 0) = \\sqrt{(x - 0)^2 + (y - 0)^2})
= \\sqrt{x^2 + y^2})
Question 4: In an AP, if the common difference (d) = - 4, and the seventh term (a_{7}) is 4, then find the first term.
Scroll down further for explanatory answer text
Common difference, d = -4
7th term a_{7} = 4
Let a_{1} be the first term of this AP.
∴ a_{7} = a_{1} + (7 - 1)d
4 = a_{1} + 6(-4)
4 = a_{1} - 24
a_{1} = 28
Question 5: What is the value of (cos^{2} 67° - sin^{2} 23°)?
Scroll down further for explanatory answer text
The given trigonometric expression is cos^{2}67° – sin^{2}23°
The expression is of the form (a^{2} - b^{2})
(a^{2} - b^{2}) = (a + b)(a - b)
∴ cos^{2}67° – sin^{2}23° = (cos 67° + sin 23°) (cos 67° - sin 23°) ... eqn(1)
Trigonometric Ratio of Complementary Angles: sin (90 - θ) = cos θ
Let us express sin 23° = sin(90° - 67°)
sin (90° - 67°) = cos 67°
Substitute sin 23° as cos 67° in eqn(1): (cos 67° + sin 23°) (cos 67° - sin 23°) = (cos 67° + cos 67°) (cos 67° - cos 67°)
(2 cos 67°) (0) = 0.
Question 6: Given ∆ ABC is similar to ∆ PQR. If \\frac{AB}{PQ} = \frac{1}{3}), then find \\frac{ar ∆ ABC}{ar ∆ PQR})
Scroll down further for explanatory answer text
Theorem: Ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.
\\frac{\text{Area of Δ ABC}}{\text{Area of Δ PQR}}) = \\frac{\text{Square of corresponding side of ABC}}{\text{Square of corresponding side of PQR}}) = \\frac{{AB}^2}{{PQ}^2})
\\frac{{AB}^2}{{PQ}^2}) = \\frac{1^2}{3^2}) = \\frac{1}{9})
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1. Section A | 2018 CBSE Class 10 Maths 1 Mark Questions 1 to 6
2. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 7 | Real Numbers - Irrational Numbers
3. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 8 | Linear Equations in 2 variables
4. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 9 | Sum of Arithmetic Progressions
5. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 10 | Coordinate Geometry Section Formula
6. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 11 | Probability of Rolling 2 dice
7. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 12 | Probability of selecting numbers
8. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 13 | Real Numbers - LCM & HCF
9. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 14 | Polynomial Factorization
10. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 15A | Coordinate Geometry - Parallelogram
11. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 15B | Coordinate Geometry - Area of Triangles
12. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 16 | Quadratic Equations - Speed Time Distance
13. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 17 | Similar & Congruent Triangles
14. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 19 | Trigonometric Ratios
15. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 20 | Areas related to circles - sector area
16. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 21 | Surface Areas & Volumes - Cylinder, hemisphere and cone
17. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 22 | Statistics - Median
18. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 23 | Quadratic Equations _ Speed Distance Time
19. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 24 | Arithmetic Progressions
20. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 25A | Equilateral & Right Triangles and Congruence
21. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 25B | Pythagoram Theorem Proof
22. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 27 | Trigonometric Ratios & Identities
23. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 28 | Surface Area of Frustum
24. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 29 | Applications of Trigonometry - Heights & Distances
25. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 30 | Statistics - 2 Alternatives
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