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Grade 10 CBSE Mathematics Important Model Question Paper Dec-29 , 2018

Class X Model Question

10th Standard CBSE

Maths

General Instructions:

1. All the questions are compulsory.

2. The questions paper consists of 30 questions divided into 4 sections A, B, C and D.

3. Section A comprises of 6 questions of 1 mark each. Section B comprises of 6 questions of 2

marks each. Section C comprises of 10 questions of 3 marks each. Section D comprises of 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 each, two questions of 2 marks each, 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.

5. Use of calculators is not permitted.

Time : 03:00:00 Hrs

Total Marks : 80

Find the roots of quadratic equation \(25x^{2}+20x+7 = 0\) .

From the figure, find the angle of depression of point C from the point P.

Find the area of a triangle with vertices A (3,0), B(7,0) and C(8,4).

Write the volume of a sphere of radius r.

If 7 times the 7th term of A.P. is equal to 11 times the 11th term, then find the 18th term.
1

(a)
0
A quadrilateral ABCD is drawn to circumscribe a circle.If AB = 12 cm, BC = 15 cm and CD = 14 cm, find AD
1

(a)

Now, AB + CD = BC + AD
⇒12 + 14 = 15 + AD
⇒ AD = 11 cm

The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?
1

(a)
probability that it will not rain tomorrow
= 1 - Probability that it will rain tomorrow = 1 - 0.85 = 0.15
The circumference of a circular field and perimeter of a square field are equal.If the area of the square field is 484m², then find the length of the diameter of the circular field.
1

(a)
Area of square field = 484 m²
∴ Side x Side = 22 x 22
⇒ Side = 22 m
∴ Perimeter of square field = 4 X 22 = 88 m
Since circumference of circular field = Perimeter of square field
\(\Rightarrow \pi d=88\Rightarrow \frac { 22 }{ 7 } d=88\)
\(\Rightarrow d=88\times \frac { 7 }{ 22 } =28m\)
Hence, the length of the diameter of the circular field is 28 m.

Solve the following quadratic equation for x :
x²-2ax-(4b²-a²)=0
2

(a)
Which of the following are AP's ? If they form an AP, then find the common difference d and write three more terms.. 2, \(\frac{5}{2}\) , 3, \(\frac{7}{2}\).......
2

(a)

In the given figure, AB is a chord of length 16 cm, of a circle of radius 10 cm. Tangents at A and B intersect at a point P. Find the length of tangent AP.

Prove that (-2,3),(8,3) and (6,7) are the vertices of a right-angled triangle.

If m and n are the zeroes of the polynomial 3x² + 11x - 4, find the value of \(\frac{m}{n}+\frac{n}{m}\)

Evaluate : \(\frac { \cos { { 45 }^{ ° } } }{ \sec { { 30 }^{ ° } } } +\frac { 1 }{ \sec { { 60 }^{ ° } } } \)

The king, queen and jack of clubs are removed from a pack of 52 playing cards and then the remaining pack is well shuffled. One card is selected from the remaining cards. Find the probability of getting:
(i) a heart,
(ii) a king,
2

(a)
In the adjoining figure, ABCD is a square of side 6cm.Find the area of the shaded region.

2

(a)

A rectangular field is 20 m long and 14 m wide. There is path of equal width all around it. having an area of 111 sq.m. Find the width of the path.

Find the sum of the first 1000 positive integers.

Tangents AP and AQ are drawn to circle with centre O from an external point A.Prove that ㄥPAQ = 2ㄥOPQ.

Construct a triangle ABC in which BC = 6 cm, AB = 5 cm and angle ABC = 60^o. Then construct another triangle whose sides are \(\frac { 3 }{ 4 } \) times the corresponding sides of triangle ABC.

In the given figure, AC = 24 cm, BC = 10 cm and O is the centre of the circle. Find the area of the shaded region. [Take, \(\pi =3.14\)].

Fin he HCF of 180, 252 and 324 by Euclid's Division algorithm.

Find the value of k for which the following pair of equations has no solution:
x + 2y = 3, (k-1)x + (k +1)y = (k + 2).

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

Find the value of sin 60° geometrically.

Find the mean of the following distribution using step deviation method

Class	20-30	30-40	40-50	50-60	60-70
Frequency	25	40	42	33	10

The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sunrays meet the ground at an angle of 60^o . Find the angle between the sunrays and the ground at the time of longer shadow.
3

(a)
A square of side 5 cm is drawn in the interior of another square of side 10 cm and shaded as shown in the following figure. A point is selected at random from the
interior of square ABeD. What is the probability that the point will be chosen from the shaded part?

3

(a)

Show that quadrilateral PQRS formed by vertices P(22, 5), Q(7, 10), R(12, 11) and S(3, 24) is not a parallelogram.
3

(a)
How many metres of cloth 1.1 m wide will be required to make a conical tent, whose vertical height is 12 m and base radius is 16 m ? Find also the cost of the cloth used at the rate of Rs. 14 per metre.
3

(a)

The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x
4

(a)
PA and PB are two tangents from an exterior point P to a circle of radius 5 cm. If length of the chord AB is 8 cm, then find the length of the tangent.
4

(a)

Find the common difference and the next two terms of the AP : 6,12,18,...

A man standing on the bank of a river observes that the angle of elevation of a tree opposite bank is 60⁰.When he moves 50m away from the bank, he find the angle of elevation to be 30⁰.Calculate:
(i)the width of the river and
(ii)the height of the tree

A horse is tethered to one corner of a field which is the shape of an equilateral triangle of side 16 m of the length of the rope is 10.5 m, find the area of the field which the horse cannot graze.

If the zeroes of the polynomial x³-3x²+x+1 are a-b and a+b, then find a and b.

If A, B and C are interior angles of a \(\triangle ABC,\) show that \(\sin { \left( \frac { B+C }{ 2 } \right) } =\cos { \frac { A }{ 2 } } .\)

Find the area of the triangle ABC with A(1,-4) and the mid-points of sides through A being (2,-1) and (0,-1).
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)

If HCF (253, 440) = 11 and LCM (253, 440) = 253 x R. Find the value of R.
4

(a)
Solve the following pair of linear equations graphically:
x - y = 1
2x + Y = 8.
Also find the co-ordinates of the points where the lines represented by the above equation intersect Y-axis.
4

(a)

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