wbbse.org Mathematics Model Question Papers for Madhyamik Pariksha Examination : West Bengal Board of Secondary Education

Organisation : West Bengal Board of Secondary Education
Exam : Model Question Papers for Madhyamik Pariksha
Document Type : Model Question Papers
Year : 2017
Category or Subject : Mathematics

Website : https://wbbse.wb.gov.in/Web/Home?l=Z%2F%2F2JeEw6P%2FkXiUjdLauQg%3D%3D
Download Model Question Paper :
Maths English : https://www.pdfquestion.in/uploads/9206-Mathematics.pdf
Maths Bengali : https://www.pdfquestion.in/uploads/9206-Maths-Bengali.pdf

Mathematics Model Question Papers for Madhyamik Pariksha Examination :

Time : 3 hours 15 minutes
Full marks : 90 (For Regular candidates)
Full marks : 100 (For External candidates)

Related : West Bengal Board of Secondary Education English Model Question Papers for Madhyamik Pariksha Exam : www.pdfquestion.in/9201.html

1. Choose the correct option in each case from the following questions : 1 * 6 = 6
(i) If the total interest in 5 years be th of the principal then the rate of simple interest per annum is
(a) 4%
(b) 5%
(c) 10%
(d) 25%

(ii) If 3 + 2 = x, then 3 – 2 is
(a) 3
(b) 2
(c) 2/x
(d) 1/x

(iii) AB is a diameter of a circle with centre O; C is a point on the circle. If OAC = 450 then the measure of OCB is
(a) 900
(b) 450
(c) 300
(d) 600

(iv) If sin 2 = then the value of is
(a) 300
(b) 600
(c) 450
(d) 150

(v) The sum of the edges of a solid cube is 36cm. The volume of the cube is
(a) 27cu.cm
(b) 36cu.cm
(c) 9 cu.cm
(d) 54 cu.cm.

(vi) In a frequency distribution the classes are 1-10, 11-20, 21-30, 31-40, 41-50. The length of each class is
(a) 9
(b) 9.5
(c) 5.5
(d) 10.

2. Fill in the blanks (any five) : 1 * 5 = 5
(i) The amount on Rs 2P for 2 years at 2r% per annum compound interest is Rs _____ Â (1+ )
(ii) If 2A = 3B = 4C, then A : B :C = 6 : 4 : ________
(iii) Maximum number of tangents can be drawn to a circle from an external point of that circle is _________
(iv) If Sec2 = 4 then the value of tan2 is ________
(v) Number of plane surfaces of a solid right circular cylinder is ________
(vi) Median of the data 2, 3, 4, 5 is _______

3. Write True or False (any five) : 1 * 5 = 5
(i) The present price of an article is Rs 100. The price of the article depriciates each year at the rate of 10%. The price of the article after 2 years is Rs 81.
(ii) If x y then xn yn.
(iii) Through three collinear points only one circle can be drawn.
(iv) The value of sin2 5 + cos2 5is 5.
(v) If the volume of a solid right circular cone is V cubic unit and the area of the base is A sq unit, then the height of the cone is unit.
(vi) The value of mode of the data 4, 6, 4, 5, 4, 7, 4, 8, 5, 9, 5, 7 is 4.

4. Answer the following questions (any ten) : 2 * 10 = 20
(i) The ratio of the capitals of three persons is 4 : 7 : 9 and the profit of the first person is Rs 100 less than the third person. Find the profit of the second person.
(ii) Find in what time a sum of money becomes double at the rate of 6 % simple interest per annum?
(iii) Find the sum of 3 – 2 and its conjugate.
(iv) I f two roots of the equation 5×2 – 3x + 6 = 0 be alpha and beta then find the value of alpha,beta.
(v) The length of diameter of a circle is 20 cm. If the distance of a chord from the centre of the circle is 8 cm, find the length of the chord.

(vi) PQ and PR are two chords of a circle with centre 0. Two tangents drawn at the points Q and R intersect each other of the point S. If QSR = 700 , find the value of QPR.
(vii) In ABC, a straight line parallel to BC intersect AB and AC at the points P and Q respectively. If AQ = 2AP, then find the value of the ratio PB : QC.

(viii) Find the circular measure of 67
(ix) If Sec 3 = Cosec 2 and 3 is a positive acute angle, then find the value of <QSR.

(x) The numerical value of the total surface area and volume of a solid hemisphere are equal. Find the length of the radius of the base of the hemispher.
(xii) The length of the diagonal of a cube is 4 3 cm. Find the total surface area of the cube.

5. Answer any one question : 5
(i) Find the compound interest on Rs 40000 for 3 years at the rate of 5% compound interest per annum.
(ii) Rajib started a business with a capital of Rs 3750. After 6 months Sayan joined that business with a capital of Rs 15000. If at the end of the year there was a profit of Rs 6900, find the share of profit of each.

6. Answer any one question :
(ii) A train travels 200 k m. at a uniform speed. If the speed would have been 5 km./hr more, it would have taken 2 hours less for the same journey. Find the speed of the train.

9. Answer any one question : 5
(i) Prove that angles in the same segment are equal.
(ii) Prove that, if a perpendiacular is drawn on the hypotenuse from the right angular point of a right angled triangle, the two triangles so formed on the two sides of the perpendicular are each similar to the original triangle and also similar to each other.

11. Answer any one question : 5
(i) Draw a triangle ABC whose BC = 7cm, AB = 5cm and AC = 6cm. Draw the circumcircle of that triangle. (Only traces of Construction are required).
(ii) Find the mean proportion of 4 cm and 3 cm by gemetrical method. (Only traces of construction are required).

13. Answer any one question : 5
(i) From a point on the roof of a house 11 metre high, it is observed that the angles of depression of the top and foot of a lamp post are 300 and 600 respectively. Find the height of the lamp post.
(ii) When sun’s altitude increases from 450 to 600, the length of the shadow of a post decreases by 3 metre. Find the height of the post.

14. 14. Answer any two questions : 4 * 2 = 8
(i) The ratio of the length, breadth and height of a solid cuboid is 4 : 3 : 2 and the area of a whole surface is 468 sq.cm. Find the volume of the cuboid.
(ii) The length of radius of the base of a solid right circular rod is 3.2 dm. By melting the rod 21 solid spheres are made. If the length of the radius of each sphere is 8 cm., find the length of the rod.
(iii) The slant height of a solid right circular cone is 7 cm. and the total surface area is 147.84 sq.cm. Find the length of radius of the base of the cone.

Alternative Question for Sightless Candidates :
11. Answer any one Question : 5
(i) Describe the procedure of Constructing the circumcircle of a triangle whose length of three sides are given.
(ii) Describe the procedure of finding geometrically the mean proportion of two line segments of given length.

17. Answer any FOUR questions : 1+ 1 + 1 +1
(a) Express radian in degree.
(b) The ratio of annual profit of two persons in a joint business is 2 : 3. If the capital of the first person is Rs 2000, find the capital of the second person.
(c) The length of the radius of the base of a solid right circular cylinder is r unit and the height is h unit. Write the curved surface area of the cylinder.
(d) Find the mixed ratio of x : yz, y : zx and z : xy.
(e) Write the mode of the data 3, 1, 2, 5, 3.