## MP BOARD PAPER OF mp-board-class-10-e-mathematics-2017

MP BOARD CLASS 10 MATHEMATICS 2017 QUESTION PAPER

Q.1.     Choose the correct option and write it in your answer book :                                     1×1=5

1.         When  then the system of equations  and

:

(a)  Has two solutions

(b)  Has no solution

(c)  Has infinitely many solutions

(d)  Has unique solution.

2.         In equation 2x + 3y = 6, if y = 0 then write the value of x :

(a)  3

(b) — 3

(c)  0

(d)  .

3.         The discriminate of the quadratic equation is :

(a) —b2 +4ac

(b) b2 —4ac

(c) —b2 —4ac

(d) b2 +4ac.

4.         All circles are :

(a) Congruent

(b) Equal

(c) Similar

(d) All of these.

5.         Relation between arc of circle, angle subtended at the centre by arc and radius is :

(a)

(b)

(c) Arc = radius + angle

(d)

Q 2.     Write True/False in the following :                                                                             1 × 5 = 5

1.         Algebraic expression   is a polynomial.

2.         Education cess is an indirect tax.

3.         Sum of the opposite angles of a cyclic quadrilateral is 360° .

4.         All four diagonals of a cuboid are equal.

5.         The arithmetic mean of 7, 8, 9 is 9.

Q 3.     Fill in the blanks :                                                                                                         1 × 5 = 5

1.         Zero of linear polynomial ax + b is

2.         Amount paid in installments is always than the cash price or cash down payment.

3.         Three medians of a triangle are

4.         The two tangents drawn from an external point to a circle are

5.         The probability of impossible event is

Q. 4.    Write the answer in one word/sentence of each :                                         1 × 5 = 5

1.         What will be duplicate ratio of 9 : 25 ?

2.         Write the definition of professional tax.

3.         Define the segment of a circle.

4.         Define sight line.

5.         Write the formula of whole surface of hollow cylinder.

Q. 5.    Match the correct column :                                                                                          1 × 5 = 5

Column 'A'                                                   Column 'B'

1. tan(90° —q)                                             (a)

2.                                                            (b)

3. tan 90°                                                      (c) 1

4. sin  × cosec                                         (d) cot

5. sin                                                          (e) cos

(f)

(g) .

Q.6    Write the characteristics property of side-angle-side similarity.    2

Or

Q.7  in two triangles the measure of side and angles are as follows. Show that ABC,  PQR are similar or not?

AB = 4 cm, AC = 5 cm,  A = 60°, PQ cm, PR = 7.5 cm,  P = 60°.                                   2

Or

Write the statement of converse of fundamental proportionality theorem (Thale's Theorem).

Q. 8  Check whether 8 cm, 15 cm and 17 cm are the sides of right angled triangle?   2

Or

What is the meaning of similar and similarity?

Q. 9 The speeds of 10 motor cyclists are recorded in kilometer per hour as following :

47, 53, 49, 60, 39, 42, 53, 52, 53, 55. Find the mean from above data.                        2

Or

Write the names of two methods used to determine the mean of grouped data.

Q. 10   In the probability of raining tomorrow is 0.4 then what will be the probability of not raining tomorrow.                                                                                   2

Or

Find the probability of getting a number than 4 in a single throw of a die.

Q. 11   Find the length of a chord which is at distance of 3 cm from the centre of circle of radius 5 cm.                                                                                            3

Or

Prove that the angle in the semicircle is right angle.

Q. 12   Find the value of x and y in the given figure.

Or

Prove that the perpendicular from the centre of a circle to a chord bisects the chord.

Q. 13   Compute the mean of the marks obtained in the examination by the students of any class from the following grouped data :                                                                                                           3

 Marks obtained 0-10 10-20 20-30 30-40 40-50 50-60 Number of students 12 18 27 20 17 06

Or

Find the probability that a leap year, selected randomly, will contain 53 Thursdays.

Q. 14   Find the mode of following frequency table :                                                                         3

 Class interval 0-20 20-40 40-60 60-80 80-100 Frequency 10 17 26 22 15

Or

Write any three uses of cost of living index number.

Q. 15   Solve the following system of equation by substitution method :

3x + 2y = 14, - x + 4y = 7.                                                                                                          4

Or

By adding 5 to the denominator and subtracting 5 from its numerator  is obtained. If 4 is subtracted from its numerator then   is obtained. Find that number.

Q. 16   Solve for x and y the system equations :

x + ay = b, ax – by = c.                                                                                                              4

Or

In triangle PQR, Ð P = x°, Ð Q = 3x° , Ð R = y° . If 3y — 5x = 30, then find the value of each angle of triangle PQR .

Q 17    If  then prove that                                                                                 4

Or

If  then prove that .

Q 18    If a and b are the roots of quadratic equation ax2 + bx + c = 0, then find the value of   .                                                                                  4

Or

Solve the following equation by factorization method :

Q. 19   A building is surmounted by a flag, from a point on the ground 20 metre away from the foot of a building, the angle of elevation of the top of building and flag are 45° and 60°. Find the height of the building and the length of the flag.              4

Or

From the top of 50 metre high hill, the angle of depression of the top and the bottom of a tower are 30° and 45°. Find the height of the tower.

Q. 20   Find the length of arc and area of sectors, if the angles subtended at the centre and the radii are 120° and 21 cm respectively.                                                                                                             4

Or

The radius and height of a cylinder are in the ratio of 2 : 3. If the volume of the cylinder is 1617 cm3, then find its whole surface area.

Q. 21   Three solid spheres having the diameters 2 cm, 12 cm and 16 cm respectively, are melted to form a sphere. Find the radius of the sphere.         4

Or

An iron sphere of diameter 6 cm is melted and drawn into a cylindrical wire. If the diameter of wire is 0.2 cm, then find the length of wire.            4

Q. 22   Find all other zeroes of polynomial f (x)=x3 +13x2 + 32x+20, if one of its zeroes is –2.       4

Or

Factorise :

a2 (b + c)+ b2(c +a)+ c2 (a+ b)+ 2abc.

Q. 23   Solve by using formula 10y2 –11y – 6 = 0.                                                                               5

Or

The sum of the ages of a man and his son is 45 years. Four years ago, the product of their age was 160. Find their present ages.

Q. 24   Find the difference between compound interest and simple interest for Rs. 2,000 at the rate of 5% per annum interest for 3 years.                                     5

Or

A watch is sold for Rs. 960 cash or for Rs. 480 cash down payment and two monthly installments of Rs. 245 each. Find the rate of interest charged under to installment plan.

Q. 25   Construct the in circle of the equilateral triangle whose one side is 8 cm. Measure its radius.                                                                                      5

Or

Construct A A' BC' similar to a  ABC given whose sides are in the ratio 7 : 5.

Q. 26   Simplify the expression (1 + cot  – cosec )(1 + tan  + sec ) .                                          5

Or

Prove it, without using table :