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 11. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.
CBSE Sample Papers for Class 10 Maths Paper 9
Board | CBSE |
Class | X |
Subject | Maths |
Sample Paper Set | Paper 11 |
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 11 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.
Has the rational number \(\cfrac { 441 }{ { 2 }^{ 2 }5^{ 7 }{ 7 }^{ 2 } } \) a terminating or a non-terminating decimal representation?
Question 2.
If α, β are the zeros of a polynomial, such that a + β = 6 and αβ = 4, then write the polynomial.
Question 3.
If the sum of first p terms of an AP, is ap2 + bp, find its common difference.
Question 4.
A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting a red face card.
Question 5.
Find the value of c for which the pair of equations cx-y=2 and 6x-2y=3 will have infinitely many solutions.
Question 6.
The length of the tangent to a circle from a point P, which is 25 cm away from the centre, is 24 cm. What is the radius of the circle?
SECTION-B
Question 7.
If two zeros of the polynomial x3 – 4x2 – 3x + 12 are \( \sqrt { 3 } \) and \( -\sqrt { 3 } \), then find its third zero.
Question 8.
Without using trigonometric tables, find the value of the following expression:
\(\cfrac { sec({ 90 }^{ o }-\theta ).cosec\quad \theta -tan({ 90 }^{ o }-\theta )cot\theta +{ cos }^{ 2 }{ 25 }^{ o }+{ cos }^{ 2 }{ 65 }^{ o } }{ 3tan{ 27 }^{ o }.{ tan63 }^{ o } } \)
Question 9.
If sin (x – 20)° = cos (3x – 10)°, then find the value of
Question 10.
“The product of three consecutive positive integers is divisible by 6”. Is this statement true or false? Justify your answer.
Question 11.
A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits. Find the number.
Question 12.
Difference between the circumference and radius of a circle is 37 cm. Find the area of circle.
SECTION-C
Question 13.
Prove that 2-3\( \sqrt { 5 } \) is an irrational number.
OR
If n is an odd positive integer, show that (n2 – 1) is divisible by 8.
Question 14.
The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes \(\cfrac { 1 }{ 2 } \). Find the fraction.
Question 15.
In an AP, the sum of first ten terms is -150 and the sum of its next ten terms is -550. Find the AP.
OR
Find the sum of all two digit natural numbers which when divided by 3 yield 1 as remainder.
Question 16.
In Figure, ABC is a right triangle, right angled at C and D is the mid-point of Prove that
AB2 – 4AD2 – 3AC2.
Question 17.
Point P divides the line segment joining the points A(2,1) and B(5, -8) such that
\(\cfrac { AP }{ AB } \) = \(\cfrac { 1 }{ 3 } \). If P lies on the line 2x – y + k = 0, find the value of k.
OR
If the point P(x, y) is equidistant from the points A(a + b,b – a) and B(a -b, a + b). Prove that bx – ay.
Question 18.
If R(x, y) is a point on the line segment joining the points P(a, b) and Q(b, a), then prove that
x + y = a + b.
Question 19.
Cards bearing numbers 1,3,5,…, 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing
(1) a prime number less than 15.
(2) a number divisible by 3 and 5.
Question 20.
1000 tickets of a lottery were sold and there are 5 prizes on these tickets. If Saket has purchased one lottery ticket, what is the probability of winning a prize?
Question 21.
If a and p are the zeros of the quadratic polynomial f(x) = 2x2 -5x + 7, find a polynomial whose zeros are 2α + 3β and 3α + 2β.
OR
If one zero of the polynomial 3x2 – 8x + 2k + 1 is seven times the other, find the value of k.
Question 22.
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
SECTION—D
Question 23.
Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46, find the integers.
OR
The difference of squares of two numbers is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
Question 24.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Using the above, prove the following:
If the areas of two similar triangles are equal, then prove that the triangles are congruent.
Question 25.
From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of the foot of the tower is 30°. Find the height of the tower.
Question 26.
A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 \(\cfrac { 22 }{ 7 } \) cm . The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in making the container at the rate of र1.40 per square centimeter. [ use π=\(\cfrac { 22 }{ 7 } \)]
OR
A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of base of the cone is 21 cm and its 2 volume is \(\cfrac { 2 }{ 3 } \) of the volume of the hemisphere, calculate the height of the cone and the surface area of the boy. [ use π=\(\cfrac { 22 }{ 7 } \)]
Question 27.
Find the mean, mode and median of the following frequency distribution
Question 28.
Prove that : \(\left( \cfrac { 1+{ tan }^{ 2 }A }{ 1+{ cot }^{ 2 }A } \right) =\left( \cfrac { 1-tanA }{ 1-cot\quad A\quad } \right) ^{ 2 }={ tan }^{ 2 }A\)
OR
If tan A = n tan B and sin A= m sin B, prove that cos2 A = \(\cfrac { { m }^{ 2 }-1 }{ { n }^{ 2 }-1 } \)
Question 29
Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ΔABC with scale factor \(\cfrac { 3 }{ 2 } \) . Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.
Question 30.
A child prepares a poster on ‘Save Energy’ on a square sheet whose each side measures 60 cm. At each comer of the sheet, she draws a quadrant of radius 17.5 cm in which she shows the ways to save energy. At the centre, she draws a circle of diameter 21 cm and writes a slogan in it. Find the area of the remaining sheet.
- Write down the four ways by which energy can be saved.
- Write a slogan on ‘Save Energy’.
- Why do we need to save energy?
SECTION-A
Answer 1.
Given rational number is \(\cfrac { 441 }{ { 2 }^{ 2 }5^{ 7 }{ 7 }^{ 2 } } \)
It can be written in the form of \(\cfrac { P }{ Q } \) such that p, q are coprime as \(\cfrac { 9 }{ { 2 }^{ 2 }{ 5 }^{ 7 } } \)
Here q is in the form of 2m 5n where m, n are non-negative integer.
∴ Given rational number is terminating.
Answer 2.
If α, β are zeros of a polynomial then the polynomial is
x2 – (α + β) x +αβ
.’. Required polynomial is x2 – 6x + 4
Answer 3.
Given, Sp = ap2 + bp
⇒ a1 = S1 = a.12 + b.1 = a + b
Also a2 = S2 – S1 = 4a + 2b – (a + b) = 3a + b
Common difference =a2-a1
= (3 a + b) -(a + b) = 2a
Answer 4.
We have
Number of red face cards = 6
Total number of cards = 52
.’. Required probability = \(\cfrac { 6 }{ 52 } \) \(\cfrac { 3 }{ 26 } \)
Answer 5.
The given system of equations will have infinitely many solutions if \(\cfrac { c }{ 6 } \) = \(\cfrac { -1 }{ -2 } \) = \(\cfrac { 2 }{ 3 } \) which is not possible
∴ For no value of c, the given system of equations have infinitely many solutions.
Answer 6.
SECTION-B
Answer 7.
Given polynomial is P(x) = x3 – 4x2 – 3x + 12
\( \sqrt { 3 } \) and \( -\sqrt { 3 } \) are zeros of P(x)
⇒ (x – \( \sqrt { 3 } \)), (x + \( \sqrt { 3 } \) ) are factors of P(x)
⇒ (x2 -3) is a factor of P(x)
We have, (x3 – 3x – 4x2 + 12) 4 (x2 – 3) = x – 4 obviously other zeros of given polynomial is in (x – 4)
⇒ x = 4 is the third zero of P(x)
Answer 8.
Answer 9.
Answer 10.
True, because n{n+ 1) (n + 2) will always be divisible by 6, as at least one of the factors will be divisible by 2 and at least one of the factors will be divisible by 3.
Answer 11.
Let the ten’s digit be x and unit’s digit = y
Number = 10x + y
10x + y = 4(x + y) ⇒ 6x = 3 y
⇒ 2x = y
Again 10x + y = 3xy
10x + 2x = 3x (2x) ⇒ 12x = 6x2
⇒ x=2 (rejecting x=0)
⇒ 2 x = y
⇒ y = 4
∴ The required number is 24
Answer 12.
SECTION-C
Answer 13.
Let 2-3 \( \sqrt { 5 } \) is a rational number, which contradict the fact that \( \sqrt { 5 } \) is an irrational number. Thus, our supposition is wrong
⇒ 2-3 \( \sqrt { 5 } \) is an irrational number.
We know that an odd positive integer n is of the form (4q+1) or (4q+3) for some integer q.
Case-I When n = (4q + 1)
In this case n2 -1 = (4q + l)2 -1 = 16q2 + 8q = 8q (2q + 1)
which is clearly divisible by 8.
Case-II When n=(4q + 3)
In this case, we have
n2 -1 – (4q + 3)2 -1 = 16q2 + 24q + 8 – 8 (2q2 + 3q +1)
which is clearly divisible by 8.
Hence (n2 -1) is divisible by 8.
Answer 14.
Let the fraction be \(\cfrac { x }{ y } \)
From Equation
x+y=2y-3 ⇒ x-y =-3……..(i)
and \(\cfrac { x-1 }{ y-1 } \) = \(\cfrac { 1 }{ 2 } \)
⇒ 2x – 2=y-1
⇒ 2x – y = 1……….(ii)
Now (ii) – (i) we have
2x – y- x + y= 1 +3
⇒ x=4
⇒ y=7
Hence ,required fraction is \(\cfrac { 4 }{ 7 } \)
Answer 15.
Answer 16.
Answer 17.
Answer 18.
Answer 19.
Total number of cards = 18
(1) Prime numbers less than 15 are 3,5, 7,11,13 – Five in number
∴ P (a prime number less than 15) = \(\cfrac { 5 }{ 18 } \)
(2) Numbers divisible by 3 and 5 is only 15 (one in number)
∴ P (a number divisible by 3 and 5) = \(\cfrac { 1 }{ 18 } \)
Answer 20
Out of 1000 lottery tickets, one ticket can be chosen in 1000 ways.
∴ Total number of elementary events = 1000 It is given that there are 5 prizes on these 1000 tickets.
Therefore, number of ways of selecting a prize ticket = 5
∴ Favourable number of elementary events = 5
Hence, P (Winning a prize) = \(\cfrac { 5 }{ 1000 } \) = \(\cfrac { 1 }{ 200 } \)
Answer 21.
Answer 22.
Let AB be the diameter of the given circle with centre 0, and two tangents PQ and LM are drawn at the end of diameter ABrespectivtly
Now, since the tangent at a point to a circle is perpendicular to the radius through the point of contact.
SECTION-D
Answer 23.
Answer 24.
Answer 25.
Let CD be the building and AB be the tower
Let AB = h m; BD = CE = x m
Given CD= BE – 7m ⇒ AE = (h-7) m
In ΔCBD
Answer 26.
Let h cm be the height of container
Given
Answer 27.
Answer 28.
Answer 29
Steps of Construction
Step I: Draw a line segment BC = 6 cm.
Step II: With centre B and radius 4 cm draw an arc.
Step III: With centre C and radius 9 cm draw another arc which intersects the previous at A.
Step IV: Join BA and CA. ABC is the required triangle.
Step V: Through B, draw an acute angle ∠CBX on the side opposite to vertex A.
Step VI: Locate three arcs B1 B2 and B3 on BX such that BB1 = B1B2 = B2B3.
Step VII: Join B2C.
Step VIII: Draw B3C’|| B2C intersecting the extended line segment BC at C’
Step IX: Draw CA’ || CA intersecting the extended line segment BA to A’ Thus, AA’BC is the required triangle (ΔA’BC’ ~ ΔABC).
Justification:
Answer 30.
Value:
(1)
- Saving electricity by using CFLs, switching off appliances when not in use.
- Saving water by using it efficiently.
- Saving petroleum resources by using public transport.
- Using solar energy.
(2) ‘Save Energy, Save Environment’ or any other given by students.
(3) We should save energy to save our environment so that we can give a better tomorrow to the forthcoming generations.
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