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Sample Paper Class 10 Maths 2018 2019 2020 Standard CBSE Board U Like Arhint

Here we are providing CBSE Previous Year Question Papers Class 6 to 12 solved with soutions Sample Paper Class 10 Maths 2018 2019 2020 Standard CBSE Board U Like Arhint 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 5 with Solutions

SECTION A

Question 1: (Marks 1)

If a pair of linear equations is consistent, then the lines represented by them are

(A) parallel

(B) intersecting or coincident

(C) always coincident

(D) always intersecting


Answer :

(B) Intersecting or coincident.


Question 2: (Marks 1)

The distance between the points (3, – 2) and (– 3, 2) is


Answer :

The distance between the points (3, – 2) and (– 3, 2) is


Question 3: (Marks 1)

 8 cot2


Answer :

(C) –8


Question 4: (Marks 1)

The total surface area of a frustum-shaped glass tumbler


Answer :

The total surface area of a frustum-shaped glass tumbler is


Question 5: (Marks 1)

120 can be expressed as a product of its prime factors as

(A) 5 × 8 × 3

(B) 15 × 23

(C) 10 × 22 × 3

(D) 5 × 23 × 3


Answer :

(D) 5 × 23 × 3


Question 6: (Marks 1)

The discriminant of the quadratic equation 4x2 – 6x + 3 = 0 is

The discriminant of the quadratic equation


Answer :

(D) –12


Question 7: (Marks 1)

If (3, –6) is the mid-point of the line segment joining (0, 0) and (x, y), then the point (x, y) is


Answer :

(C) (6, –12)


Question 8: (Marks 1)

In the given circle in Figure-1, number of tangents parallel to tangent PQ is

In the given circle in Figure-1, number of tangents parallel to tangent PQ is

(A) 0

(B) many

(C) 2

(D) 1


Answer :

(D) 1


Question 9: (Marks 1)

For the following frequency distribution:

For the following frequency distribution:

The upper limit of median class is

(A) 15

(B) 10

(C) 20

(D) 25


Answer :

(A) 15


Question 10: (Marks 1)

The probability of an impossible event is


Answer :

(D) 0

Fill in the blanks in question numbers 11 to 15


Question 11: (Marks 1)

A line intersecting a circle in two points is called a _______.


Answer :

Secant


Question 12: (Marks 1)

If 2 is a zero of the polynomial ax2 – 2x, then the value of ’a’ is _______.


Answer :

1


Question 13: (Marks 1)

All squares are _______ (congruent/similar).


Answer :

Similar


Question 14: (Marks 1)

If the radii of two spheres are in the ratio 2 : 3, then the ratio of their respective volumes is _______.


Answer :

8/27 or 8 : 27


Question 15: (Marks 1)

If ar (Δ PQR) is zero, then the points P, Q and R are _______.


Answer :

Collinear


Question 16: (Marks 1)

In Figure-2, the angle of elevation of the top of a tower AC from a point B on the ground is 60°. If the height of the tower is 20 m, find the distance of the point from the foot of the tower.

In Figure-2, the angle of elevation of the top of a tower AC from a point B on the ground is 60°


Answer :

In Figure-2, the angle of elevation of the top of a tower AC from a point B on the ground is 60°.


Question 17: (Marks 1)

Evaluate:

tan 40° × tan 50°

OR

If cos A = sin 42°, then find the value of A.


Answer :

cos A = sin (90° – 48°)

= cos 48°

⇒ A=48°


Question 18: (Marks 1)

A coin is tossed twice. Find the probability of getting head both the times.


Answer :

A coin is tossed twice. Find the probability of getting head both the times.


Question 19: (Marks 1)

Find the height of a cone of radius 5 cm and slant height 13 cm.


Answer :

Find the height of a cone of radius 5 cm and slant height 13 cm.


Question 20: (Marks 1)

Find the value of x so that – 6, x, 8 are in A.P.

OR

Find the 11th term of the A.P. – 27, – 22, –17, –12, ... .


Answer :

x + 6 = 8 – x

x = 1

OR

a = –27, d = 5

a11 = –27 + 50 = 23

SECTION B

Question numbers 21 to 26 carry 2 marks each.


Question 21: (Marks 2)

Find the roots of the quadratic equation


Answer :

Find the roots of the quadratic equation


Question 22: (Marks 2)

Check whether 6n can end with the digit ’0’ (zero) for any natural number n.

OR

Find the LCM of 150 and 200.


Answer :

6n = (2 × 3)n = 2n × 3n

It is not in form of 2n × 5m

∴ 6n can’t end with digit ‘0’

OR

150 = 2 × 3 × 52

200 = 23 × 52

LCM = 23 × 52 × 3

= 600


Question 23: (Marks 2)

 If tan (A + B) = 3 and tan (A – B)


Answer :

 If tan (A + B) = 3 and tan (A – B)


Question 24: (Marks 2)

In Figure-3, ?ABC and ?XYZ are shown. If AB = 3 cm BC = 6 cm, AC


Answer :

In Figure-3, ?ABC and ?XYZ are shown. If AB = 3 cm BC = 6 cm, AC = 2 3 cm, ?A = 80°


Question 25: (Marks 2)

14 defective bulbs are accidentally mixed with 98 good ones. It is not possible to just look at the bulb and tell whether it is defective or not. One bulb is taken out at random from this lot. Determine the probability that the bulb taken out is a good one.


Answer :

14 defective bulbs are accidentally mixed with 98 good ones. It is not possible to just look at


Question 26: (Marks 2)

Find the mean for the following distribution


Answer :

Find the mean for the following distribution

SECTION C

Question numbers 27 to 34 carry 3 marks each.


Question 27: (Marks 3)

Aquadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.


Answer :

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that


Question 28: (Marks 3)

The difference between two numbers is 26 and the larger number exceeds thrice of the smaller number by 4. Find the numbers.

OR

 The difference between two numbers is 26 and the larger number exceeds thrice of the smaller


Answer :

Let larger No. = x

Let smaller No = y

x – y = 26 ...(i)

x – 3y = 4 ...(ii)

By solving (i) & (ii), we get

∴ x = 37

y = 11

OR

The difference between two numbers is 26 and the larger number exceeds thrice of the smaller


Question 29: (Marks 2)

Prove that


Answer :

Prove that


Question 30: (Marks 3)

Krishna has an apple orchard which has a 10 m × 10 m sized kitchen garden attached to it. She divides it into a 10 × 10 grid and puts soil and manure into it. She grows a lemon plant at A, a coriander plant at B, an onion plant at C and a tomato plant at D. Her husband Ram praised her kitchen garden and points out that on joining A, B, C and D they may form a parallelogram. Look at the below figure carefully and answer the following questions:

 Krishna has an apple orchard which has a 10 m × 10 m sized kitchen garden attached to it. She

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

(ii) Find whether ABCD is a parallelogram or not.


Answer :

Krishna has an apple orchard which has a 10 m × 10 m sized kitchen garden attached to it. She


Question 31: (Marks 3)

If the sum of the first 14 terms of an A.P. is 1050 and its first term is 10 then find the 21st term of the A.P.


Answer :

If the sum of the first 14 terms of an A.P


Question 32: (Marks 3)

Construct a triangle with its sides 4 cm, 5 cm and 6 cm

OR

Draw a circle of radius 2.5 cm. Take a point P at a distance of 8 cm from its centre. Construct a pair of tangents from the point P to the circle.


Answer :

For correct construction of Δ

For construction of similar Δ

OR

For draw the correct circle & exterior pt.

For construction of the pair of tangents


Question 33: (Marks 3)

Prove that:


Answer :

Prove that:


Question 34: (Marks 3)

In Figure-4, 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 = 7 cm, then find the area of the shaded region.

If OA = 7 cm, then find the area of the shaded region.

OR

In Figure-5, ABCD is a square with side 7 cm. A circle is drawn circumscribing the square. Find the area of the shaded region.

In Figure-5, ABCD is a square with side 7 cm. A circle is drawn circumscribing the square.


Answer :

In Figure-4, AB and CD are two diameters of a circle (with centre O) perpendicular to each

SECTION D

Question numbers 35 to 40 carry 4 marks each.


Question 35: (Marks 4)

Find other zeroes of the polynomial

OR

Divide the polynomial g(x) = x3 – 3x2 + x + 2 by the polynomial x2 – 2x + 1 and verify the division algorithm.


Answer :

 Find other zeroes of the polynomial


Question 36: (Marks 4)

From the top of a 75 m high lighthouse from the sea level, the angles of depression of two ships are 30° and 45°. If the ships are on the opposite sides of the lighthouse, then find the distance between the two ships.


Answer :

From the top of a 75 m high lighthouse from the sea level, the angles of depression of two ships


Question 37: (Marks 4)

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio.

OR

If Figure-6, in an equilateral triangle ABC, AD ⊥ BC, BE ⊥ AC and CF ⊥ AB.

Prove that 4(AD2 + BE2 + CF2 ) = 9 AB2.

If Figure-6, in an equilateral triangle ABC, AD ? BC, BE ? AC and CF ? AB


Answer :

For correct given, To prove, Construction, Figure

For correct proof

OR

If Figure-6, in an equilateral triangle ABC, AD ? BC, BE ? AC and CF ? AB


Question 38: (Marks 4)

A container open at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 14 cm with radii of its lower and upper circular ends as 8 cm and 20 cm, respectively. Find the capacity of the container.


Answer :

A container open at the top and made up of a metal sheet, is in the form of a frustum of a cone


Question 39: (Marks 4)

Two water taps together can fill a tank in

OR

A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the Rectangular park and of altitude 12 m. Find the length and breadth of the park.


Answer :

Let smaller diameter tap takes x hours to fill the tank

Then, time taken by larger diameter tap to fill the tank = (x – 10) hr

Two water taps together can fill a tank in


Question 40: (Marks 4)

 Draw a ‘less than’ ogive for the following frequency distribution


Answer :

getting the pts (10, 7), (20, 21)

(30, 34), (40, 46), (50, 66)

(60, 77), (70, 92), (80, 100)

Plotting and Joining the pts to get the correct ogive

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Sample Paper Class 10 Maths 2018 2019 2020 Standard CBSE Board U Like Arhint

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