CBSE Class 10th Maths Question Paper Solved 2017 18 19 20 with solutions

Here we are providing CBSE Previous Year Question Papers Class 6 to 12 solved with soutions CBSE Class 10th Maths Question Paper Solved 2017 18 19 20 with solutions class 10 Maths sample paper 2020 solved, sample paper class 10 Maths, cbse class 10 Maths question paper 2018, sample paper class 10 Maths 2019, Maths question paper for class 10, cbse previous year question papers class 10 Maths, cbse sample paper f Practice of previous year question papers and sample papers protects each and every student to score bad marks in exams.If any student of CBSE Board continuously practices last year question paper student will easily score high marks in tests. Fortunately earlier year question papers can assist the understudies with scoring great in the tests. Unraveling previous year question paper class 10 Maths is significant for understudies who will show up for Class 10 Board tests.

Class 10 Subject Maths Paper Set 4 with Solutions

SECTION A

Question numbers 1 to 20 carry 1 mark each.

Choose the correct option in question numbers 1 to 10

Question 1: (Marks 1)

Given that HCF (156, 78) = 78, LCM (156, 78) is

(A) 156

(B) 78

(D) 156 × 2

Answer :

(A) 156

Question 2: (Marks 1)

Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio

(A) 4 : 9

(B) 2 : 3

(D) 16 : 81

Answer :

(D) 16 : 81

Question 3: (Marks 1)

$The distance between the points$

Answer :

$The distance between the points$

Question 4: (Marks 1)

$The discriminant of the quadratic equation$

Roots of the quadratic equation 2x² – 4x + 3 = 0 are

(A) real and equal

(B) real and distinct

(D) real

Answer :

(A) –8

Question 5: (Marks 1)

$Number of zeroes of the polynomial p(x) shown in Figure-1, are$

Answer :

Question 6: (Marks 1)

$A dice is thrown once. The probability of getting an odd number is$

Answer :

$dice is thrown once. The probability of getting an odd number is$

Question 7: (Marks 1)

$The value of k for which the equations$

Answer :

(D) –2

Question 8: (Marks 1)

If sin A = cos A, 0 < A < 90°, then the angle A is equal to

(A) 30°

(B) 60°

(D) 45°

Answer :

(D) 45°

Question 9: (Marks 1)

The second term from the end of the A.P. 5, 8, 11, ..., 47 is

(A) 50

(B) 45

(D) 41

Answer :

Question 10: (Marks 1)

$Total surface area of a solid hemisphere is$

Answer :

(A) 3πr²

Fill in the blanks in question numbers 11 to 15.

Question 11: (Marks 1)

The roots of the equation, x² + bx + c = 0 are equal if _______.

Answer :

b² = 4c

Question 12: (Marks 1)

The mid-point of the line segment joining the points (– 3, – 3) and (– 3, 3) is _______.

Answer :

(–3, 0)

Question 13: (Marks 1)

The lengths of the tangents drawn from an external point to a circle are _______.

Answer :

Equal

Question 14: (Marks 1)

For a given distribution with 100 observations, the ’less than’ ogive and ’more than’ ogive intersect at (58, 50). The median of the distribution is _______.

Answer :

Question 15: (Marks 1)

In the quadratic polynomial t² – 16, sum of the zeroes is _______.

Answer :

Answer the following question numbers 16 to 20.

Question 16: (marks 1)

Write the 26th term of the A.P. 7,4,1, –2, ... .

Answer :

d = –3

a₂₆ = –68

Question 17: (Marks 1)

Find the coordinates of the point on x-axis which divides the line segment joining the points (2, 3) and (5, – 6) in the ratio 1 : 2.

Answer :

Let the point on x-axis be (x, 0)

∴ Required point is (3, 0)

Question 18: (Marks 1)

$If cosec θ$

Find the value of sin 42° – cos 48°.

Answer :

$If cosec θ$

sin 42° = cos (90° – 42°) = cos 48°

∴ sin 42° – cos 48° = 0

Question 19: (Marks 1)

The angle of elevation of the top of the tower AB from a point C on the ground, which is 60 m away from the foot of the tower, is 30°, as shown in Figure-2. Find the height of the tower.

$The angle of elevation of the top of the tower AB from a point$

Answer :

$The angle of elevation of the top of the tower AB from a point$

Question 20: (Marks 1)

In Figure-3, find the length of the tangent PQ drawn from the point P to a circle with centre at O, given that OP = 12 cm and OQ = 5 cm. P Q O 5 cm 12 cm

$In Figure-3, find the length of the tangent PQ drawn from the point P to a circle with centre at$

Answer :

$In Figure-3, find the length of the tangent PQ drawn from the point P to a circle with centre at$

SECTION B

Question numbers 21 to 26 carry 2 marks each.

Question 21: (Marks 2)

$A cylindrical bucket, 32 cm high and with radius of base 14 cm, is filled completely with sand.$

Answer :

$A cylindrical bucket, 32 cm high and with radius of base 14 cm, is filled completely with sand.$

Question 22: (Marks 2)

$n Figure-4, ΔABC and ΔXYZ are shown. If AB = 3.8 cm, AC$

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

Answer :

ΔABC ~ ΔXZY

⇒ ∠Y = ∠C = 180° – (∠A + ∠B)

⇒ ∠Y = 45º

$If the areas of two similar triangles are equal, show that they are congruent.$

Question 23: (Marks 2)

If sec 2A = cosec (A – 30°), 0° < 2A < 90°, then find the value of ∠A.

Answer :

sec 2A = cosec (A – 30°)

⇒ cosec (90° – 2A) = A – 30°

⇒ 90º – 2A = A – 30°

⇒ ∠A = 40º

Question 24: (Marks 2)

Show that every positive even integer is of the form 2q and that every positive odd integer is of the form 2q + 1, where q is some integer.

Answer :

Let ‘a’ be any positive integer and b = 2

Using Euclid’s Division lemma

a = 2q + r, r = 0,

∴ a = 2q or 2q + 1

Because 2q is an even integer and every positive ineger is either even or odd.

∴ a = 2q + 1 is an odd positive integer.

Question 25: (Marks 2)

How many two-digit numbers are divisible by 6?

In an A.P. it is given that common difference is 5 and sum of its first ten terms is 75. Find the first term of the A.P.

Answer :

Two digit numbers divisible by 6 are 12, 18, 24,...96

96 = 12 + (n – 1) × 6

⇒ n = 15

$In an A.P. it is given that common difference is 5 and sum of$

Question 26: (Marks 2)

$The following table shows the ages of the patients admitted in a hospital during a year$

Answer :

$The following table shows the ages of the patients admitted in a hospital during a year$

SECTION C

Question numbers 27 to 34 carry 3 marks each.

Question 27: (Marks 3)

Seema has a 10 m × 10 m kitchen garden attached to her kitchen. She divides it into a 10 × 10 grid and wants to grow some vegetables and herbs used in the kitchen. She puts some soil and manure in that and sows a green chilly plant at A, a coriander plant at B and a tomato plant at C.
Her friend Kusum visited the garden and praised the plants grown there. She pointed out that they seem to be in a straight line. See the below diagram carefully and answer the following questions:

$Seema has a 10 m × 10 m kitchen garden attached to her kitchen. She divides it into a$

(i) Write the coordinates of the points A, B and C taking the 10 × 10 grid as coordinate axes.

(ii) By distance formula or some other formula, check whether the points are collinear.

Answer :

$Seema has a 10 m × 10 m kitchen garden attached to her kitchen. She divides it into a$

Question 28: (Marks 3)

In Figure-5, a circle is inscribed in a ΔABC touching BC, CA and AB at P, Q and R respectively. If AB = 10 cm, AQ = 7 cm, CQ = 5 cm, find the length of BC.

$In Figure-5, a circle is inscribed in a ΔABC touching BC, CA and AB at P, Q and R respectively.$

In Figure-6, two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2 ∠OPQ.

$In Figure-6, two tangents TP and TQ are drawn to a circle with centre O from an external point$

Answer :

AR = AQ = 7 cm

BR = AB – AR = 10 – 7 = 3 cm

BC = BP + PC

= BR + CQ

= 3 + 5 = 8 cm

$In Figure-6, two tangents TP and TQ are drawn to a circle with centre O from an external point$

Question 29: (Marks 3)

$Prove that$

Answer :

$Prove that$

Question 30: (Marks 3)

$Prove that:$

Answer :

$Prove that:$

Question 31: (Marks 3)

5 pencils and 7 pens together cost ` 250 whereas 7 pencils and 5 pens together cost ` 302. Find the cost of one pencil and that of a pen.

Solve the following pair of equations using cross-multiplication method:

x – 3y – 7 = 0

3x – 5y – 15 = 0

Answer :

Let the cost of 1 pencil be ` x and cost of 1 pen be ` y.

5x + 7y = 250 ...(i)

7x + 5y = 302 ...(ii)

Solving (i) and (ii)

x = 36 and y = 10

Hence, cost of 1 pencil = ` 36

cost of 1 pen = ` 10

$Solve the following pair of equations using cross-multiplication method$

Question 32: (Marks 3)

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour.

(ii) the queen of diamonds.

(iii) an ace.

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears

(i) a two-digit number.

(ii) a perfect square number.

(iii) a prime, number less than 15.

Answer :

$One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting$

Question 33: (Marks 3)

In Figure-7, ABCD is a square of side 14 cm. From each corner of the square, a quadrant of a circle of radius 3.5 cm is cut and also a circle of radius 4 cm is cut as shown in the figure. Find the area of the remaining (shaded) portion of the square.

$In Figure-7, ABCD is a square of side 14 cm. From each corner of the square, a quadrant of$

Answer :

$In Figure-7, ABCD is a square of side 14 cm. From each corner of the square, a quadrant of$

Question 34: (Marks 3)

Draw a circle of radius 3 cm. Take a point P outside the circle at a distance of 7 cm from the centre O of the circle and draw two tangents to the circle.

Answer :

Drawing a circle and locating point P.

Constructing tangents from P.

Question 35: (Marks 4)

In a right-angled triangle, prove that the square of the hypotenuse is equal to the sum of the squares of the remaining two sides.

Answer :

For correct given, to prove, figure and construction.

Correct proof

Question 36: (Marks 4)

Divide polynomial – x^{3^{+ 3x² – 3x – 3x + 5 by the polynomial x² + x – 1 and verify the division algorithm.}}

$Find other zeroes of the polynomial$

Answer :

On dividing –x3 + 3x2 – 3x + 5 by x2 + x – 1

We get quotient = –x + 4

and Remainder = –8x + 9

Verification

(x² + x – 1) (–x + 4) + (9 – 8x)

= x³ - x² + x + 4x² + 4x - 4 + 9 - 8x

= -x³ + 3x² - 3x + 5

$Find other zeroes of the polynomial$

Question 37: (Marks 4)

$From a point on the ground, the angles of elevation of the bottom and the top of a transmission$

Answer :

$From a point on the ground, the angles of elevation of the bottom and the top of a transmission$

Question 38: (Marks 4)

A bucket is in the form of a frustum of a cone of height 30 cm with the radii of its lower and upper circular ends as 10 cm and 20 cm respectively. Find the capacity of the bucket. (Use π = 3.14)

Water in a canal 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hr. How much area will it irrigate in 30 minutes if 4 cm of standing water is needed?

Answer :

$A bucket is in the form of a frustum of a cone of height 30 cm with the radii of its lower and$

Question 39: (Marks 4)

$Draw a ‘more than’ ogive for the following distribution$

Answer :

Points to be plotted for more than type ogive

(40, 100), (44, 96), (48, 86), (52, 56), (56, 32), (60, 14), (64, 2)

For drawing correct ogive

Question 40: (Marks 4)

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Find the original speed of the train.

Sum of the areas of two squares is 468 m2 . If the difference of their parameters is 24 m, find the sides of the two squares.

Answer :

$From a point on the ground, the angles of elevation of the bottom and the top of a transmission$

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