CBSE Sample Papers for Class 10 Maths Paper 8

These Sample papers are part of CBSE Sample Papers for Class 10 Maths. Here we have given CBSE Sample Papers for Class 10 Maths Paper 8. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

CBSE Sample Papers for Class 10 Maths Paper 8

Board	CBSE
Class	X
Subject	Maths
Sample Paper Set	Paper 8
Category	CBSE Sample Papers

Students who are going to appear for CBSE Class 10 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme as prescribed by the CBSE is given here. Paper 8 of Solved CBSE Sample Paper for Class 10 Maths is given below with free PDF download solutions.

Time Allowed: 3 hours
Maximum Marks: 80

General Instructions:

1.  All questions are compulsory.
2. The question paper consists of 30 questions divided into four sections A, B, C and D.
3. Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each.
4. There is no overall choice. However, an internal choice has been provided in four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions.
5. Use of calculators is not permitted.

SECTION-A

Question 1.
Find the [HCF x LCM] for the numbers 100 and 190.

Question 2.
If sec² θ (1 + sin θ) (1- sin θ) = k, then find the value of k.

Question 3.
Find the discriminant of the quadratic equation 3\(\sqrt { 3 } \) x² + 10x + \(\sqrt { 3 } \) = 0.

Question 4.
If \(\frac { 4 }{ 5 } \), a, 2 are three consecutive terms of an AP, then find the value of a.

Question 5.
∆ABC with vertices A (-2, 0), B(2, 0) and C (0, 2) is similar to ADEF with vertices D (- 4, 0), E (4, 0) and F (0, 4). State true or false and justify your answer.

Question 6.
In Figure (1), ∆ABD is a right triangle, right angled at A and AC 1 BD. Prove that AB² = BC.BD.

SECTION-B

Question 7.
Which term of the AP 3, 15, 27, 39,… will be 120 more than its 21st term?

Question 8.
If the points A(4,3) and B(x, 5) are on the circle with the centre 0(2,3), find the value of x.

Question 9.
Find the sum of 0.68 + 0.73.

Question 10.
If x – a, y – b is the solution of the pair of equations x-y = 2 and x + y = 4, then find the value of a and b.

Question 11.
Two dice are thrown simultaneously. What is the probability that

1. 5 will not come up on either of them?
2. 5 will come up on at least one?

Question 12.
A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a king.

SECTION-C

Question 13.
Prove that \(3+\sqrt { 2 } \) is an irrational number.

Question 14.
Solve for x and y:
\(\frac { ax }{ b } -\frac { by }{ a } =a+b;\) ax-by=2ab
                                                                     OR
The sum of two numbers is 8. Determine the numbers if the sum of their reciprocals is \(\frac { 8 }{ 15 } \).

Question 15.
In Figure (2), AD ⊥ BC and BD = \(\frac { 1 }{ 3 } \) CD. Prove that 2CA² = 2AB² + BC².

                                                                                        OR
In figure (3), M is mid-point of side CD of a parallelogram ABCD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL = 2BL.

Question 16.
Find the ratio in which the point (2, y) divides the line segment joining the points A(-2, 2) and B(3, 7). Also find the value of y.
                                                                                        OR
Find the area of quadrilateral ABCD whose vertices a re A (- 4, – 2), B(- 3, – 5), C(3, – 2) and D(2,3).

Question 17.
The area of an equilateral triangle is 49 \(\sqrt { 3 } \) cm². Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circles. [Take \(\sqrt { 3 } \) = 1.73]

Question 18.
Figure (4) shows a decorative block which is made of two solids — a cube and a hemisphere. The base of the block is a cube with edge 5 cm and the hemisphere, fixed on the top, has a diameter of 4.2 cm. Find the total surface area of the block. [Take π = \(\frac { 22 }{ 7 } \)]

Question 19.
Find all the zeros of the polynomial x³ + 3x² – 2x – 6, if two of its zeros are \(-\sqrt { 2 } \) and \(\sqrt { 2 } \).

Question 20.
Prove that the lengths of the tangents drawn from an external point to a circle are equal.
Using the above theorem prove that:
If quadrilateral ABCD is circumscribing a circle, then AB + CD = AD + BC.

Question 21.
If \(cot\theta =\frac { 15 }{ 8 } \), then evaluate \(\frac { \left( 2+2sin\theta \right) \left( 1-sin\theta \right) }{ \left( 1+cos\theta \right) \left( 2-2cos\theta \right) } \)
                                                      OR
Find the value of tan 60° geometrically.

Question 22.
If the mean of the following distribution is 6, find the value of p.

x	2	4	‘ 6	10	p + 5
f	3	2	3	1	2

SECTION-D

Question 23.
Solve the following equation for x:
9x² – 9(a+ b)x + (2a² + 5ab + 2b²) = 0
                                           OR
If (- 5) is a root of the quadratic equation 2x² + px-15 = 0 and the quadratic equation p (x² + x) + k = 0 has equal roots, then find the values of p and k.

Question 24.
An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the distance between the two planes at that instant.

Question 25.
A juice seller serves his customers using a glass as shown in Figure. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity Fig. (5).
(Use π = 3.14)

                                                                                         OR
A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of

1. water displaced out of the cylindrical vessel.
2. water left in the cylindrical vessel.[Take π = \(\frac { 22 }{ 7 } \) ]

Question 26.
During the medical check-up of 35 students of a class their weights were recorded as follows:

Weight (in kg)	38-40	40-42 |	42-44	44 – 46	46-48	48-50	50-52
Number of Students	3	2	4	5	14	4	3

Draw a less than type and a more than type ogive from the given data. Hence obtain the median weight from the graph. Why medical check-up is necessary for everyone?

Question 27.
The sum of first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first and the thirteenth term of the A.P.

Question 28.
Prove that the area of an equilateral triangle described on a side of a right-angled isosceles triangle is half the area of the equilateral triangle described on its hypotenuse.
                                                         OR
In Figure, O is a point in the interior of a triangle ∆ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that

1. OA² + OB² + OC² – OE² – OF² = AF² + BD² + CE²
2. AF² + BD² + CE² = AE² + CD² + BE²

Question 29.
Draw a right triangle in which sides (other than hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are \(\frac { 3 }{ 4 } \) times the corresponding sides of the first triangle.

Question 30.
Evaluate:

Answers

SECTION-A

Answer 1.
HCF (100,190) x LCM (100,190) = 100 x 190 = 19000

Answer 2.
We have,

Answer 3.
\(D\quad =\quad { b }^{ 2 }-4ac\quad =\quad { 10 }^{ 2 }-4\times 3\sqrt { 3 } \times \sqrt { 3 } \quad =\quad 100-36\)

Answer 4.

Answer 5.

Answer 6.
In ∆BAD and ∆BCA

SECTION-B

Answer 7.
3, 15, 27, 39, ………………..
Here a = 3, d = 15-3=12, m = 21
a_m = a+(m-1)d

Answer 8.
Given that OA = OB – r

Answer 9.

Answer 10.

Answer 11.
Total number of outcomes (6×6 = 36) are

Answer 12.
Let £ be the event in which card drawn is neither an ace nor a king.
Then, the number of outcomes favourable to the event E = 44 (4 kings and 4 aces are not there)
∴ \(P\left( E \right) \quad =\quad \frac { 44 }{ 52 } =\frac { 11 }{ 13 } \)

SECTION-C

Answer 13.
Let us assume, to the contrary, that \(3+\sqrt { 2 } \) is a rational number.
That is, we can find coprime a and b (b ≠ 0) such that

Answer 14.

Answer 15.

Answer 16.

Answer 17.

Answer 18.

Answer 19.

Answer 20.
Given: AP and AQ are two tangents from a point A to a circle C (O, r).
To Prove: AP = AQ.
Construction: Join OP, OQ and OA.
Proof: In order to prove that AP = AQ, we shall first prove that ∆OP A ≅ ∆OQA.
Since a tangent at any point of a circle is perpendicular to the radius through the point of contact.

Answer 21.

Answer 22.
Calculation of mean

SECTION-D

Answer 23.

Answer 24.

Answer 25.
We have,

Answer 26.

Answer 27.

Answer 28.

Answer 29.

Step I: Draw BC – 6 cm.
Step II: At B, construct ∠CBX = 90°
Step III: With centre B, and radius 8 cm draw an arc which intersect BX at A.
Step IV: Join AC. ABC is the required triangle.
Step V: Draw any ray BY making an acute angle on the side opposite to the vertex A.
Step VI: Along BX, mark off four points B₁,B₂,B₃, B₄ such that BB₁
Step VII: Join B₄C.
Step VIII: From B₃, draw B₃D || B₄C meeting BC at D.
Step IX: From D, draw ED || AC, meeting AB at E.
Then EBD is the required triangle whose sides are \(\frac { 3 }{ 4 } \) times the corresponding sides of ∆ABC.

Answer 30.

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