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Board Paper of Class 10 2015 Maths - Solutions

(1) Check the question paper for fairness of printing. If there is any lack of fairness, inform the Hall Supervisor immediately.(2) Use Blue or Black ink to write and underline and pencil to draw diagrams.Note : This question paper contains four sections.
  • Question 1
    If f : A → B is a bijective function and if n(A) = 5, then n(B) is equal to:

    (a) 10

    (b) 4

    (c) 5

    (d) 25 VIEW SOLUTION
  • Question 2
    The next term of 120 in the sequence 12, 16, 112, 120, ...... is:

    (a) 124

    (b) 122

    (c) 130

    (d) 118 VIEW SOLUTION
  • Question 3
    The common ratio of the G.P. am-n, am, am+n is :

    (a) am

    (b) a–m

    (c) an

    (d) a–n VIEW SOLUTION
  • Question 4
    The remainder when x2 – 2x + 7 is divided by x + 4 is:

    (a) 28

    (b) 29

    (c) 30

    (d) 31 VIEW SOLUTION
  • Question 5
    b = a + c and the equation ax2 + bx + c = 0 has equal roots then :

    (a) a = c

    (b) a = – c

    (c) a = 2c

    (d) a = – 2c VIEW SOLUTION
  • Question 6
    If 3x+75y+12-3x=1y-28 8, then the value of x and y respectively are:

    (a) –2, 7

    (b) -13, 7

    (c) -13, -23

    (d) 2, –7 VIEW SOLUTION
  • Question 7
    The centroid of the triangle with vertices at (–2, –5), (–2, 12) and (10, –1) is :

    (a) (6, 6)

    (b) 4, 4)

    (c) (3, 3)

    (d) (2, 2) VIEW SOLUTION
  • Question 8
    The value of k if the straight lines 3x + 6y + 7 = 0 and 2x + ky = 5 are perpendicular is:

    (a) 1

    (b) – 1

    (c) 2

    (d) 12 VIEW SOLUTION
  • Question 9
    If the sides of two similar triangles are in the ratio 2 : 3, then their areas are in the ratio:

    (a) 9 : 4

    (b) 4 : 9

    (c) 2 : 3

    (d) 3  : 2 VIEW SOLUTION
  • Question 10
    If the tangents PA and PB from an external point P to a circle with centre O are inclined to each other at an angle of 40° then ∠POA =

    (a) 70°

    (b) 80°

    (c) 50°

    (d) 60° VIEW SOLUTION
  • Question 11
    If x = a sec θ, y = b tan θ, then the value of x2a2-y2b2=:

    (a) 1

    (b) –1

    (c) tan2θ

    (d) cosec2θ VIEW SOLUTION
  • Question 12
    (cos2 θ – 1) (cot2 θ + 1) + 1 =

    (a) 1

    (b) –1

    (c) 2

    (d) 0 VIEW SOLUTION
  • Question 13
    The ratios of the respective heights and the respective radii to two cylinders are 1 : 2 and 2 : 1 respectively. Then their respective volumes are in the ratio:

    (a) 4 : 1

    (b) 1 : 4

    (c) 2 : 1

    (d) 1 : 2 VIEW SOLUTION
  • Question 14
    The variance of  10, 10, 10, 10, 10, is:

    (a) 10

    (b) 10

    (c) 0

    (d) 5 VIEW SOLUTION
  • Question 15
    Probability of getting 3 heads and 3 tails in tossing a coin 3 times is :

    (a) 18

    (b) 14

    (c) 38

    (d) 12 VIEW SOLUTION
  • Question 17
    Let A = {1, 2, 3, 4, 5}, B = N and f : A → B be defined by f(x) = x2. Find the range of f. Identify the type of function. VIEW SOLUTION
  • Question 18
    Find the first term and common difference of the A.P. 12, 56, 76, 32, ..........., 176 VIEW SOLUTION
  • Question 20
    If α and β are the roots of 3x2 – 5x + 2 = 0, then find the value of αβ+βα. VIEW SOLUTION
  • Question 21
    A=8   521-34 then find AT and (AT)T. VIEW SOLUTION
  • Question 22
    If A=   23-95-1  57-1 then find the additive inverse of A. VIEW SOLUTION
  • Question 23
    The centre of a circle is at (–6, 4). If one end of a diameter of the circle is at the origin, then find the other end. VIEW SOLUTION
  • Question 24
    Find the slope and y-intercept of the line whose equation is 4x – 2y + 1 = 0. VIEW SOLUTION
  • Question 26
    A ramp for unloading a moving truck has an angle of elevation of 30°. If the top of the ramp is 0.9 m. above the ground level, then find the length of the ramp. VIEW SOLUTION
  • Question 27
    If the circumference of the base of a solid right circular cylinder is 154 cm and its height is 16 cm, find its curved surface area. VIEW SOLUTION
  • Question 28
    Find the range and the coefficient of range of 43, 24, 38, 56, 22, 39, 45. VIEW SOLUTION
  • Question 29
    A bag contains 6 white balls numbered from 1 to 6 and 4 red balls numbered from 7 to 10.
    A ball is drawn at random. Find the probability of getting:
    (i) an even numbered ball.
    (ii) a white ball. VIEW SOLUTION
  • Question 30
    (a) Prove the following identity. sec2 θ+cosec2 θ=tan θ+cot θ
     
    OR
     
    (b) The thickness of a hemispherical bowl is 0.25 cm. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl Take π=227. VIEW SOLUTION
  • Question 31
    Use Venn diagrams to verify De Morgan's law of complementation (A ⋃ B)' = A' ⋂ B'. VIEW SOLUTION
  • Question 32
    Let A = {4, 6, 8, 10} and B = {3, 4, 5, 6, 7} and f : A → B be defined by fx=12 x+1, then represent f by
    (i) an arrow diagram
    (ii) a set of ordered pairs and
    (iii) a table VIEW SOLUTION
  • Question 33
    Find the sum of first n terms of the series 6 + 66 + 666 + .............. VIEW SOLUTION
  • Question 34
    The sum of four consecutive terms of an A.P is 20 and the sum of their squares is 120. Find those numbers. VIEW SOLUTION
  • Question 36
    Find the square root of : 4+25x2-12x-24x3+16x4 VIEW SOLUTION
  • Question 37
    If A=5273 and B=2-1-1   1 verify that (AB)T = BTAT. VIEW SOLUTION
  • Question 38
    Prove that (0, 5) (–2, –2), (5, 0) and (7, 7) are the vertices of a rhombus. VIEW SOLUTION
  • Question 39
    If all sides of a parallelogram touch a circle, show that the parallelogram is a rhombus. VIEW SOLUTION
  • Question 40
    If tan θ + sin θ = m, tan θ – sin θ  = n and m ≠ n, then show that m2-n2=4mn. VIEW SOLUTION
  • Question 41
    A sector containing an angle of 120° is cut off from a circle of radius 21 cm. and folded into a cone by joining the radii. Find the curved surface area of the cone. π=227 VIEW SOLUTION
  • Question 42
    An iron right circular cone of diameter 8 cm and height 12 cm is melted and recast into spherical lead shots each of radius 4 mm. How many lead shots can be made? VIEW SOLUTION
  • Question 43
    The following table shows the marks obtained by 48 students in a quiz competition in mathematics. Calculate the standard deviation.
     
    Data x 6 7 8 9 10 11 12
    Frequency f 3 6 9 13 8 5 4
    VIEW SOLUTION
  • Question 44
    The probability that a new car will get an award for its design is 0.25, the probability that it will get an award for efficient use of fuel is 0.35  and the probability that it will get both the awards is 0.15. Find the probability that :
    (i) it will get at least one of the two awards.
    (ii) it will get only one of the awards. VIEW SOLUTION
  • Question 45
    Find the L.C.M. [Least Common Multiple] of the following:
    x3+y3, x3-y3, x4+x2y2+y4
    OR
    Find the equation of the line whose gradient is 32 and which passes through P, where P divides the line segment joining A(–2, 6) and B(3, –4) in the ratio 2 : 3 internally. VIEW SOLUTION
  • Question 46
    (a) Draw a circle of diameter 10 cm. From a point P, 13 cm. away from its centre, draw the two tangents PA and PB to the circle and measure their lengths.
    OR
    (b) Construct a ΔABC in which the base BC = 5 cm, ∠BAC = 40° and the median from A to BC is 6 cm. Also measure the length of the altitude from A. VIEW SOLUTION
  • Question 47
    (a) Draw the graph of y = x2 + 2x  – 3 and hence find the roots of x2x – 6 = 0.
     
    OR

    (b) A bank gives 10% S.I (Simple Interest) on deposits for senior citizens.
    Draw the graph for the relation between the sum deposited and the interest earned for one year.
    Hence find
    (i) The interest on the deposit of Rs 650
    (ii) The amount to be deposited to earn an interest of Rs 45.
    VIEW SOLUTION
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