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 4. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

## CBSE Sample Papers for Class 10 Maths Paper 4

Board |
CBSE |

Class |
X |

Subject |
Maths |

Sample Paper Set |
Paper 4 |

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 4 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.**

If is rational number (q ≠ 0), what is condition on q so that the decimal representation of is terminating?

**Question 2.**

Write the zeros of the polynomial x^{2} + 2x + 1.

**Question 3.**

The n^{th} term of an AP is 7 – 4n. Find its common difference.

**Question 4.**

In the given figure, AD = 4 cm, BD = 3 cm and CB = 12 cm. Find cot θ.

**Question 5.**

In the given figure, P and Q are points on the sides AB and AC respectively of ∆ABC such that AP = 3.5 cm, PB = 7 cm, AQ = 3 cm and QC = 6 cm. If PQ = 4.5 cm, find BC

**Question 6.**

Find the distance of the point (- 6, 8) from the origin.

**SECTION-B**

**Question 7.**

For what value of p, points (2,1), (p, -1) and (-1, 3) are collinear?

**Question 8.**

A die is thrown once. Find the probability of getting

- a prime number.
- a number divisible by 2.

**Question 9.**

What is the HCF of 3^{3} x 5 and 3^{2} x 5^{2}?

**Question 10.**

Find the co-ordinate where the line x-y = 8 will intersect y-axis.

**Question 11.**

Find the 25th term of the AP: -5, 0, …

**Question 12.**

A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

**SECTION-C**

**Question 13.**

Show that is an irrational number.

**Question 14.**

Represent the following system of linear equations graphically. From the graph, find the points where the lines intersect y-axis.

3x + y – 5 = 0; 2x – y -5 = 0

**Question 15.**

Prove that:

** OR**

Prove that: (1 + cot A – cosec A) (1 + tan A + sec A) = 2

**Question 16.**

Determine the ratio in which the line 3x + 4y – 9 = 0 divides the line segment joining the points (1,3) and (2, 7).

** OR**

If the distances of P(x, y) from the points A(3, 6) and B(- 3, 4) are equal, prove that 3 x + y = 5.

**Question 17.**

If the diagonals of a quadrilateral divide each other proportionally, prove that it is a trapezium.

** OR**

Two ∆’s ABC and DBC are on the same base BC and on the same side of BC in which ∠ A= ∠D = 90°. If CA and BD meet each other at E, show that AE. EC = BE. ED.

**Question 18.**

In the figure, find the perimeter of shaded region where ADC, AEB and BFC are semi-circles on diameters AC, AB and BC respectively.

** OR**

Find the area of the shaded region in the figure, where ABCD is a square of side 14 cm.

**Question 19.**

Find the zeros of the quadratic polynomial 6x^{2} – 3 – 7x and verify the relationship between the zeros and the coefficients of the polynomial.

**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 toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

**Question 22.**

The lengths of 40 leaves of a plant are measured correctly to the nearest millimetre, and the data obtained is represented in the following table:

Length (in mm) |
118-126 | 127-135 | 136-144 | 145-153 | 154-162 | 163-171 | 172-180 |

Number of Leaves |
3 | 5 | 9 | 12 | 5 | 4 | 2 |

Find the median length of the leaves

**SECTION-D**

**Question 23.**

In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in Mathematics and 4 marks less in Science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately.

** OR**

The sum of the areas of two squares is 640 m2. If the difference in their perimeters be 64 m, find the sides of the two squares.

**Question 24.**

A statue of Mahatma Gandhi 1.46 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal. (Use = 1.73) Write two important messages of Mahatma Gandhi.

**Question 25.**

Prove that the ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

Using the above result, prove the following:

In a ∆ ABC, XY is parallel to BC and it divides ∆ ABC into two parts of equal area.

Prove that

**Question 26.**

A gulab jamun, when ready for eating, contains sugar syrup of about 30% of its volume. Find approximately how much syrup would be found in 45 such gulab jamuns, each shaped like a cylinder with two hemispherical ends, if the complete length of each of them is 5 cm and its diameter is 2.8 cm.

** OR**

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. This ice-cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.

**Question 27.**

A survey regarding the heights (in cm) of 50 girls of Class X of a school was conducted and the following data was obtained:

Height (in cm) |
120-130 | 130-140 | 140-150 | 150-160 | 160-170 | Total |

Number of girls |
2 | 8 | 12 | 20 | 8 | 50 |

Find the mean, median and mode of the above data.

** OR**

100 surnames were randomly picked up from a local telephone directory and the distribution of number of letters of the English alphabet in the surnames was obtained as follows:

Number of letters |
1-4 | 4-7 | 7-10 | 10-13 | 13-16 | 16-19 |

Number of surnames |
6 | 30 | 40 | 16 | 4 | 4 |

Determine the median and mean number of surnames. Also find the modal size of surname.

**Question 28.**

The sum of the first n terms of an AP is given by S_{n} = 3n^{2} – 4n. Determine the AP and the 12th term.

**Question 29.**

If 3Cot A = 4, check whether

**Question 30.**

Construct a ∆ ABC in which AB = 6.5 cm, ∠ B = 60° and BC = 5.5 cm. Also construct a similar triangle AB’C’, whose each side is times the corresponding side of the ∆ABC.

**Answers**

**SECTION-A**

**Answer 1.**

If is a rational number which is terminating then q must be of the form 2^{n}5^{m} where n and m are non-negative integers.

**Answer 2.**

**Answer 3.**

Given a_{n} = 7-3n

**Answer 4.**

**Answer 5.**

Here,

**Answer 6.**

Here x_{1}=-6, y_{1} = 8 and x_{2} = 0, y_{2} = 0

**SECTION-B**

**Answer 7.**

A(2, 1), B(p, -1), C(-1, 3) will be collinear if area of triangle formed is zero.

**Answer 8.**

- Total outcomes, S = {1, 2, 3, 4, 5, 6}, i.e., n(S) = 6

Favourable outcomes, A = (2, 3, 5), i.e., n(A) = 3

Probability of getting a prime number = - Favourable outcomes, B = {2, 4, 6}, i.e., n(B) = 3

Probability of getting a number divisible by

**Answer 9.**

HCF of 3^{3} x 5 and 3^{2} x 5^{2} = 32 x 5 = 45

**Answer 10.**

The given line will intersect y-axis when x = 0.

∴ 0-y = 8 => y = -8

Required coordinate is (0, – 8).

**Answer 11.**

**Answer 12.**

Number of possible outcomes = 52

Number of red cards and queens = 28

Number of favourable outcomes = 52 – 28 = 24

P (getting neither a red card nor a queen) =

**SECTION-C**

**Answer 13.**

Let us assume that is a rational number.

So, may be written as

where p and q are integers, having no common factor except 1 and

q ≠ 0.

⇒ ⇒

Since, is a rational number as p and q are integers.

∴ is also a rational number, which contradicts our assumption.

Thus, our supposition is wrong.

Hence, is an irrational number.

**Answer 14.**

Given equation, 3x+y-5=0

**Answer 15.**

**Answer 16.**

Let the line 3x + 4y – 9 = 0 divides the line segment joining A{ 1,3) and B(2, 7) in ratio k: 1 at point P.

**Answer 17.**

Let ABCD be any quadrilateral.

Now, AC and BD are its diagonals, which are intersecting each other at some point E.

**Answer 18.**

Perimeter of shaded region is AEBFCDA

**Answer 19.**

6x^{2}-3-7x=6x^{2}-9x+2x-3

=3x(2x-3)+1(2x-3)=(3x+1)(2x-3)

Hence zeros of the quadratic polynomial are and

**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.**

We have,

**Answer 22.**

Here, the classes are not in inclusive form. So, we first convert them in inclusive form by subtracting from the lower limit and adding y to the upper limit of each class, where h is the difference between the lower limit of a class and the upper limit of preceding class.

Now, we have

**SECTION-D**

**Answer 23.**

Let the marks obtained in mathematics be x and marks obtained in science by y.

**Answer 24.**

Let AD be a statue of height 1.46 m and BD be a pedestal.

Let BD = h

∴ Height of the pedestal = 2 m.

**Values:**

Two messages of Mahatma Gandhi are

- Be honest in work
- Believe in truth

**Answer 25.**

Given: Two triangles ABC and PQR such ∆ABC ~ ∆PQR

**Answer 26.**

**Answer 27.**

**Answer 28.**

We have, S_{n}=3n^{2}-4n …(i)

**Answer 29.**

Let us consider a right triangle ABC in which ∠ B = 90°

**Answer 30.**

**Steps of construction:**

**Step I:** Draw AB = 6.5 cm.

**Step II:** At B, construct ∠ABY = 60°.

**Step III:** Mark point C on BY such that BC = 5.5 cm.

**Step IV:** Join AC.

**Step V:** Draw any ray AX making an acute angle with AB on the side opposite to the vertex C.

**Step VI:** Mark 3 points as A_{1}, A_{2} and A_{3} on AX, so that AA_{1} = A_{1}A_{2} = A_{2}A_{3}.

**Step VII:** Join A_{2} (second point) to B and draw line through A_{3} parallel to A_{2}B, intersecting the extended line segment AB at B’.

**Step VIII:** Draw a line through B’ parallel to BC intersecting the extended line segment AC at C’.

Thus, ∆AB’C’ is the required triangle.

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