CBSE BOARD EXAM PAPER ANSWER - 2018

                       Class 10 - Mathematics

                           Set – 1, Code - 30/1

 

 

                              Mathematics (Standard)

                             Previous Year Paper 2018

 

 

Max. Marks: 80                                                                                Duration: 3 hrs.

 

 

General Instructions:

 

a) All questions are compulsory

b) The question paper consists of 30 questions divided into four sections A, B, C & D.

c) Section A comprises of 6 questions of 1 mark each.

d) Section B comprises of 6 questions of 2 marks each.

e) Section C comprises of 10 questions of 3 marks each.

f) Section D comprises 8 questions of 4 marks each.

g) There is no overall choice. However internal choices have been provided in two questions of 1 mark each, two questions of 2 marks each, three 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.

h) Use of calculators is not permitted.

 

SECTION – A

 

Question 1:

If x = 3 is one root of the quadratic equation x² – 2kx – 6 = 0, then find the value of k.

 

Question 2:

What is the HCF of smallest prime number and the smallest composite number?

 

Question 3:

Find the distance of a point P(x, y) from the origin.

 

Question 4:

In an AP, if the common difference (d) = -4 and the seventh term (a₇) is 4, then find the first term.

 

Question 5:

What is the value of (cos² 67⁰ – sin² 23⁰)?

 

Question 6:

Given ΔABC ~ ΔPQR, if , then find .

 

SECTION - B

 

Question 7:

Given that √2 is irrational, prove that 5 + 3√2 is an irrational number.

 

Question 8:

In the figure, ABCD is a rectangle. Find the value of x and y.

 

Question 9:

Find the sum of first 8 multiples of 3.

 

Question 10:

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence find the m.

 

Question 11:

Two different dice are tossed together. Find the probability:

(i) of getting a doublet

(ii) of getting a sum 10, of the numbers on the two dice

 

Question 12:

An integer is chosen at random between 1 and 100. Find the probability that it is:

(i) divisible by 8                                     (ii) not divisible by 8

 

SECTION – C

 

Question 13:

Find HCF and LCM of 404 and 96 and verify that HCF * LCM = Product of the two given numbers

 

Question 14:

Find all zeroes of the polynomial (2x⁴ – 9x³ + 5x² + 3x – 1) if two of its zeroes are (2 + √3) and

(2 - √3).

 

Question 15:

If A(-2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.

OR

If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of quadrilateral ABCD.

 

Question 16:

A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/hr from the usual speed. Find its usual speed.

 

Question 17:

Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.

                                                          OR

If the areas of two triangles are equal, prove that they are congruent.

 

Question 18:

Prove that the lengths of tangents drawn from an external point to a circle are equal.

 

Question 19:

If 4 tan θ = 3, evaluate

                                                            OR

If tan 2A = cot(A - 18⁰), where 2A is an acute angle, find the value of A.

 

Question 20:

Find the area of the shaded region as shown in the figure,

where arcs drawn with centres A, B, C and D intersect in

pairs at mid-points P, Q, R and S of the sides AB, BC, CD

and DA respectively of a square ABCD of side 12 cm.

[Use π = 3.14]

 

Question 21:

A wooden article was made by scooping out a hemisphere

from each end of a solid cylinder as shown in the figure.

If the height of the cylinder is 10 cm and its base is of radius

3.5 cm, find the total surface area of the article.

OR

A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

 

Question 22:

The table below shows the salaries of 280 persons:

Calculate the median salary of the data.

 

SECTION - D

Question 23:

A motor boat whose speed is 18 km/h in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

OR

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed?

 

Question 24:

The sum of four consecutive numbers is an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

 

Question 25:

In an equilateral triangle ABC, D is a point on side BC such that BD =  . Prove that

9(AD)² = 7(AB)²

OR

Prove that, in a right angle triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

 

Question 26:

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are  of the corresponding sides of the Δ ABC.

 

Question 27:

Prove that   

 

Question 28:

The diameters of the lower and upper ends of a bucket in the form of frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find

(i) The area of the metal sheet used to make the bucket.

(ii) Why we should avoid the bucket made by ordinary plastic?

[Use π = 3.14]

 

Question 29:

An observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30⁰ and 45⁰. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use √3 = 1.732]

 

Question 30:

The mean of the following distribution is 18. Find the frequency f of the class 19-21.

OR

The following distribution gives the daily income of 50 workers of a factory:

Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.

 

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