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10th standard CBSE Mathematics Board Exam Model Question Paper III 2019-2020 QB365 - Question Bank Software Feb-13 , 2020

10th standard CBSE Mathematics Board Exam Model Question Paper III 2019-2020

QB365 - Question Bank Software

Public Exam Model Question Paper 2019 - 2020 Part-V

10th Standard CBSE

Maths

General Instruction

1. All questions are compulsory.

2. This question paper consists of 30 questions divided into four sections – A, B, C and D.

3. 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.

4. There is no overall choice. However, an internal choice has been provided in two questions of 1 mark, two questions of 2 marks, four questions of 3 marks each and three questions of 4 mark each. You have to attempt only one of the alternatives in all such questions.

5. Use of calculator is not permitted.

Time : 03:00:00 Hrs

Total Marks : 80

Section A

In the figure, AE is the bisector of exterior angle CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then CE is equal to

(a)

8 cm

(b)

7.2 cm

(c)

18 cm

(d)

10 cm

In the above fig Q and α respectively are

(a)

Angle of Depression and Angle of Depression

(b)

Angle of Elevation and Angle of depression

(c)

Angle of Elevation and Angle of Elevation

(d)

Angle of depression and Angle of Elevation

A bucket is in the form of a frustum of a cone ad holds 28.490 liters of water. The radii of the top and bottom are 28cm and 21cm respectively. Find the height of the bucket.

(a)

20 cm

(b)

15 cm

(c)

10 cm

(d)

None of the above

Which of the following rational numbers has a denominator that can be expressed as a product of powers of 2 and 5?

(a)

0.143245

(b)

0.141414

(c)

1.34573457

(d)

0.23452345

Find the next term of the series \(\sqrt { 2 } ,\sqrt { 8 } ,\sqrt { 18 } ,\sqrt { 32 } ....\)
1

(a)
Here, \(a=\sqrt { 2 } ,a+d=\sqrt { 8 } =2\sqrt { 2 } \)
\(d=2\sqrt { 2 } -\sqrt { 2 } =\sqrt { 2 } \\ \therefore Next\quad term=\sqrt { 32 } +\sqrt { 2 } \\ =4\sqrt { 2 } +\sqrt { 2 } \\ =5\sqrt { 2 } \\ =\sqrt { 50 } \)
In fig., PA and PB are tangents to the circle with centre O such that \(\angle APB={ 50 }^{ ° }\) Write the measure of \(\angle OAB\) .
1

(a)
Here, \(\angle APB={ 50 }^{ ° }\)
\(\angle PAB=\angle PBA=\frac { { 180 }^{ ° }-{ 50 }^{ ° } }{ 2 } ={ 65 }^{ ° }\)
\(\angle OAB={ 90 }^{ ° }-\angle PAB\)
\(={ 90 }^{ ° }-{ 65 }^{ ° }={ 25 }^{ ° }\)

To divide the line segment AB in the ratio 2 : 3, a ray AX is drawn such that LBAX is acute, AX is then marked at equal intervals. Find minimum number of these marks
1

(a)
Minimum number of marks = 2 + 3 = 5
The centroid of triangle divides the median in the ratio ...........
1

(a)
2:1

Section B

Find the discriminant of quadratic equation \(x^{ 2 }+4x-1\)

Find the sum of first five multiples of 3.

In the given figure, O is the centre of the circle. If PA and PB are tangents from an external point P to the circle, then find the measure of \(\angle AQB\) .

A school has five houses A, B, C, D and E.A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from houseE.A single student is selected at random to be the class monitor.Find the probability that the selected student is not from A, B, and C.

Draw a circle of radius 4cm. Take two points P and Q on one of its extended diameter each at a distance of 6 cm from its centre. Draw tangents to the circle from these two points P and Q.
2

(a)
Draw a triangle ABC with \(AB=6cm,\ <A=60^o\) and \(<B=60^o\). Then construct another triangle whose sides are \(4\over 5\) times the corresponding sides of \(\triangle ABC.\)
2

(a)

If A is a point on Y-axis, whose ordinate is 3 and B is a point (- 5, 2), then find the distance AB.
2

(a)
Here, point A lies on Y-axis, so its abscissa is zero and its ordinate is 3. So, the point A on Y: axis is A(0, 3).
Here, A=(x₁,y₁)=(0, 3) and B=(x₂,y₂)=(-5, 2)
\(\therefore \)AB =\(\sqrt { { \left( { x }_{ 2 }-{ x }_{ 1 } \right) }^{ 2 }-{ \left( { y }_{ 2 }-{ y }_{ 1 } \right) }^{ 2 } } \)
=\(\sqrt { { \left( -5-0 \right) }^{ 2 }+{ (2-3) }^{ 2 } } =\sqrt { { (-5) }^{ 2 }+{ (-1) }^{ 2 } } \)
=\(\sqrt { 25+1 } =\sqrt { 26 } \) units
Hence, the distance between A and B is \(\sqrt { 26 } \) units.
Write first four terms of the AP, when the first term a and the common difference d are given as follows: a = -2, d = 0
2

(a)

Section C

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30^o with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Prabhsimran and Tavleen planted some trees in her garden as shown in the figure and both arguing that they planted them in straight line. Find who is correct ? P stands for Prabhsimran and T for Tavleen. Which social value is depicted in the question?

The figure shows the quadrant of a circle of radiius 4.2 cm. Find the perimeter of the quadrant.

A sector of a circle of radius 12cm has the angle 120⁰.It is rolled up so that two bounding radii are joined together to form a cone.Find the volume of the cone.

Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 6 respexctively. Hence find the zeroes.

If \(\sqrt { 3 } \sin { \theta } -\cos { \theta } =0\) and \({ 0 }^{ ° }<\theta <{ 90 }^{ ° }\), find the value of \(\theta\)

Find the ratio in which the line joining points (a + b, b + a) and (a - b, b - a) is divided by the point (a, b).
3

(a)
From a rectangular sheet of paper ABCD with AB=40cm and AD=28cm, a semicircular portion with BC as diameter is cut off.Find the area of the remaining paper.[Use \(\pi={22\over7}\)]

3

(a)

A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60^o and angle of depression of the base of the hill as 30^o. Find the distance of the hill from the ship and height of the hill.
3

(a)
A card is drawn from a well shuffled deck of 52 cards.Find the probability of getting:
(i)A king of red colour
(ii)A face card
(iii)The queen of diamonds.
3

(a)

A circle is inscribed in a ΔBC having sides AB=8 cm, BC = 10 cm and CA = 12 cm as shown in figure. Find AD, BE and CF

3

(a)
Construct triangle D'EF' \(\sim \) triangle DEF in which EF = 10 cm, DE = 5 cm and angle D = 60^o using a scale-factor \(\frac { 1 }{ 2 } \)
3

(a)

Find the median of the following data.

Class interval 0-10 10-20 20-30 30-40 40-50 Total

Frequency 8 16 36 34 6 100

3

(a)
Find the sum of all three-digit natural numbers, which are multiples of 11.
3

(a)

Class interval	0-10	10-20	20-30	30-40	40-50	Total
Frequency	8	16	36	34	6	100

Section D

State which pairs of triangles in the given figure are similar? Also, state the similarity criterion used.

If a boy's age and his father's age amount together to 24years. Fourth part of the product of their ages exceeds the boy's age by 9years. Find how old they are.

The angle of elevation of the top of a building from the foot of a tower is 30^o.The angle of elevation of the top of the tower from the foot of the building is 60^o. If the tower is 60 m high, find the height of the building.

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number 1,2,3,....15,16 as shown in the given figure.what is the probability that it will point to
(i)13
(ii)8
(iii)An odd number
(iv)A number which is multiple of 4"
(v)An even number
(vi)Multiple of 5

Four cows are tethered at the four corner of a square plot of side 50 m, so that they just cannot reach one another. What area will be left ungrazed?

Evaluate : sin² 30° cos² 45° + 4 tan² 30° + \(\frac{1}{2}\) sin² 90° - 2 cos² 90° + \(\frac{1}{24}\)
4

(a)
Find the mean of following data by direct method.

Class 7.5-12.5 12.5-17.5 17.5-22.5 22.5-27.5 27.5-32.5

Frequency 5 10 7 8 2

4

(a)

Class	7.5-12.5	12.5-17.5	17.5-22.5	22.5-27.5	27.5-32.5
Frequency	5	10	7	8	2

If one zero of polynomial 3x²-8x+2k+1 is seven times the other. Then find the zeroes and the value of k.
4

(a)
Solve the following pair of linear equations by the substitution and cross-multiplication methods.
8x+5y=9, 3x+2y=4
4

(a)

A solid ball is exactly fitted inside the cubical box of side a. What is the volume of remaining space inside the cubical box?
4

(a)
Write the missing numbers is the following factorisation.
(i) (ii)
4

(a)

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