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 5. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.
CBSE Sample Papers for Class 10 Maths Paper 5
Board | CBSE |
Class | X |
Subject | Maths |
Sample Paper Set | Paper 5 |
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 5 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:
- All questions are compulsory.
- The question paper consists of 30 questions divided into four sections A, B, C and D.
- 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.
- 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.
- Use of calculators is not permitted.
SECTION-A
Question 1.
Write the prime factors of 84.
Question 2.
Write the next term of the AP \(\sqrt { 2 } \), \(\sqrt { 8 } \), \(\sqrt { 18 } \).
Question 3.
If \(cos\quad A=\frac { 3 }{ 5 } \), find 9 cot2 A – 1.
Question 4.
In the given figure, ∠ ABC = 90° and P is the mid point of AC. Find the length of AP.
Question 5.
If ax2 + bx + c = 0 has equal roots, find the value of c.
Question 6.
Find the value of a, so that the point (3, a) lie on the line 2x – 3y = 5.
SECTION-B
Question 7.
If the vertices of a triangle are (1, k), (4, – 3), (- 9, 7) and its area is 15 square units, find the value of k.
Question 8.
A box contains cards bearing numbers from 6 to 70. If one card is drawn at random from the box, find the probability that it bears
- a one digit number.
- a number divisible by 5.
Question 9.
Explain why 3 x 5 x 7 + 7 is a composite number.
Question 10.
Is x = 2, y = 3 a solution of the linear equation 2x + 3y – 13 = 0 ?
Question 11.
If the sum of the first p terms of an AP is ap2 + bp, find its common difference.
Question 12.
What is the probability of having 53 Mondays in a leap year?
SECTION-C
Question 13.
Using prime factorization method, find the HCF and LCM of 72,126 and 168. Also show that HCF x LCM ≠ Product of the three numbers.
Question 14.
Represent the following system of linear equations graphically. From the graph, find the points where the lines intersect x-axis.
2x – y = 2, 4x – y = 8
Question 15.
Prove that: \(\frac { cos\theta -sin\theta +1 }{ cos\theta +sin\theta -1 } =2cosec\theta +cot\theta \)
OR
Prove that: \(\left( cosec\theta -sin\theta \right) \left( sec\theta -cos\theta \right) =\frac { 1 }{ tan\theta +cot\theta } \)
Question 16.
The line joining the points (2, -1) and (5, – 6) is bisected at P. If P lies on the line 2x + Ay + k = 0, find the value of k.
OR
Show that the points (5, 6), (1, 5), (2,1) and (6, 2) are the vertices of square.
Question 17.
In AABC, if AD is the median, show that AB2 + AC2 = 2 (AD2 + BD2).
OR
In ∆ABC, ∠A is acute. BD and CE are perpendicular on AC and AB respectively. Prove that AB x AE = AC x AD.
Question 18.
In the given figure AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 14 cm, find the area of the shaded region.
Question 19.
Find the zeros of the quadratic polynomial 2x2 – 9 – 3x and verify the relationship between the zeros and the coefficients.
OR
Write the polynomial whose zeros are \(2+\sqrt { 3 } \) and \(2-\sqrt { 3 } \).
Question 20.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Question 21.
A girl empties a cylindrical bucket, full of sand, of base radius 18 cm and height 32 cm, on the floor to form a conical heap of sand. If the height of this conical heap is 24 cm, then find its slant height correct up to one place of decimal.
Question 22.
Find the mean for the following data:
Classes | 10-20 | 20-30 | 30-0 | 40-50 | 50-60 | 60-70 | 70-80 |
Frequency | 4 | 8 | 10 | 12 | 10 | 4 | 2 |
SECTION-D
Question 23.
₹65,00 is divided equally among a certain number of persons. Had there been 15 more persons, each would have got ₹30 less. Find the original number of persons.
OR
A train travels 360 km at a uniform speed. If the speed of the train had been 5 km/h more, it would have taken one hour less for the same journey. Find the original speed of the train.
Question 24.
The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud.
Question 25.
Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Using the above, prove the following:
If the areas of two similar triangles are equal, prove that they are congruent.
Question 26.
A bucket is in the form of a frustum of a cone whose radii of bottom and top are 7 cm and 28 cm respectively. If the capacity of the bucket is 21560 cm3, find the whole surface area of the bucket.
Question 27.
Find the sum of all two digit natural numbers which when divided by 7 yield 1 as remainder.
OR
Find the sum of all two digit numbers greater than 50 which when divided by 7 leave a remainder 4.
Question 28.
Draw a circle of radius 4 cm, from a point P, 7 cm from the centre of the circle, draw a pair of tangents to the circle. Measure the length of each tangent segment.
Question 29.
Prove the following:
Without using trigonometric tables, evaluate the following:
Question 30.
The amount donated by some households in their religious organisations are as follows:
Calculate the arithmetic mean for the above data.
What values do these households possess?
Answers
SECTION-A
Answer 1.
84 = 2 x 2 x 3 x 7
Answer 2.
Answer 3.
Answer 4.
Answer 5.
For equal roots D = 0
i.e., b2-4ac=0 ⇒ b2=4ac ⇒ \(a=\frac { 1 }{ 3 } \)
Answer 6.
Since (3, a) lies on the line 2x – 3y = 5
Then 2(3) – 3(a) = 5
-3a = 5- 6 -3a = -1 ⇒ \(c=\frac { 1 }{ 3 } \)
SECTION-B
Answer 7.
Answer 8.
- Total outcomes, S = (6, 7, 8, 70), i.e., n(S) = 65
Favourable outcomes, A = {6, 7, 8,9), i.e., n(A) = 4
∴ Required probability \(=\frac { n(A) }{ n(S) } =\frac { 4 }{ 65 } \) - Favourable outcomes, B = {10,15,20,25,30,35,40,45,50,55,60,65,70}, i.e., n(B) = 13
∴ Required probability \(=\frac { n(A) }{ n(S) } =\frac { 13 }{ 65 } =\frac { 1 }{ 5 } \)
Answer 9.
3 x 5 x 7 + 7= 7 (3 x 5 +1) = 7 x 16, which has more than two factors.
Answer 10.
Since 2×2 + 3×3-13 = 4 + 9-13 = 13-13 = 0
Hence, x = 2 and y = 3 is solution of the linear equation.
Answer 11.
ap = Sp-Sp-1 = (ap2 + bp) -[a(p -l)2 + b(p-l)]
= ap2 + bp- (ap2 + a- lap + bp-b)
= ap2 + bp- ap2 -a + lap -bp + b = lap + b-a
∴ a1 = la + b-a=a + b and a2-4a + b – a = 3a + b
=> d = a2– a1 = (3a + b) – (a + b) = 2a
Answer 12.
There are 366 days in a leap year.
We have,
366 days = 52 weeks and 2 days
Thus, a leap year has always 52 Mondays.
The remaining two days can be
- Monday and Tuesday
- Tuesday and Wednesday
- Wednesday and Thursday
- Thursday and Friday
- Friday and Saturday
- Saturday and Sunday
- Sunday and Monday
Thus, elementary events associated with this random experiment are seven.
Let A be the event that a leap year has 53 Mondays.
Thus, the event A will happen if the last two days of the leap year are either Monday and Tuesday or Sunday and Monday.
∴ Favourable number of elementary events = 2
Hence, required probability = \(\frac { 2 }{ 7 } \).
SECTION-C
Answer 13.
Answer 14.
From first equation
2x-y=2
⇒ y=2x-2
Answer 15.
Answer 16.
Answer 17.
Answer 18.
Answer 19.
Answer 20.
Let O be the common centre of two concentric circles and let AB be a chord of larger circle touching the smaller circle at P. Join OP.
Since OP is the radius of the smaller circle and AB is tangent to this circle at P,
∴ OP ⊥ AB
We know that the perpendicular drawn from the centre of a circle to any chord of the circle bisects the chord.
Answer 21.
Volume of cylindrical bucket = Volume of conical heap of sand.
Answer 22.
SECTION-D
Answer 23.
Let total number of persons = x
Answer 24.
In ∆CMP, we have
Answer 25.
Given: Two triangles ABC and PQR such that ∆ABC ~ ∆PQR
Answer 26.
Answer 27.
The required series is 15,22, 29, ……………., 99
These are in AP where a = 15, d = 7
Answer 28.
Steps of Construction:
Step I: Take a point O in the plane of the
paper and draw a circle of radius 4 cm.
Step II: Mark a point P at a distance of 7 cm from the centre O and join OP.
Step III: Draw perpendicular bisector of OP, intersecting OP at M.
Step IV: Taking M as centre and OM = MP as radius draw a circle to intersect the given circle at Q and R.
Step V: Join PQ and PR to get the required tangents.
Step VI: By actual measurement, we find PQ = PR = 5.5 cm.
Justification:
Answer 29.
Answer 30.
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