10th Model Question For Maths



Model Questions For Full Syllabus
MARKS: 100                                       MATHEMATICS                                           TIME : 2.30 HRS
I.     Choose the best answer:                                                                                                   15 x 1 = 15
1.     For any three sets A, B and C, A∩(B∪C) is
(a) (A∪B)∪(B∩C) (b) (A∩B)∪(A∩C)       (c) A∪(B∩C)               (d) (A∪B)∩(B∪C)
2.     Ifk+2, 4k-6,3k-2 are the three consecutive terms of A.P, then the value of k is
(a) 2                                   (b) 3                             (c) 4                                         (d) 5
3.     In a G.P ,t2 = and t3  = Than the common  ratio is 
        (a)                                  (b)                (c) 1                                         (d) 5
4.     The system of equations x-4y = 8, 3x-12y = 24
(a) has infinitely many solutions    (b) has no solutions
(c) has a unique solution                (d) may or may not have a solution
5.     If  and  are the two rational expressions, then their product is
        (a)     (b)           (c)           (d)
6.     If  and A+B = 0 then B is
        (a)                     (b)               (c)               (d)
7.     The angle of inclination of a straight line parallel to x-axis is equal to
        (a)                                  (b)                                     (c)                          (d)
8.     The equation of the straight line passing through the origin and perpendicular to the straight line is
        (a)                   (b)                         (c)                 (d)
9.     In is || to BC meeting AB and AC at D and E If AD = 3cm DB=2cm and AE =2.7cm then AC is equal to
a) 6.5cm                (b)4.5cm                      (c) 3.5cm                     (d) 5.5cm
10.   The perimeters of two similar triangles are 24cm and 18cm respectively. If one side of the first triangle is 8cm, then the corresponding side of the other triangle is
        (a) 4cm                              (b)3cm                         (c) 9cm                                    (d) 6cm
11.  
        (a)        (b) (c)  (d)
12.  
        (a)1                                    (b) -1                           (c) 2                             (d) 0
13.   The total surface area of a solid hemisphere of diameter 2 cm is equal to
        (a)               (b)                  (c)                    (d)
14.   If the standard deviation of a set of data is 1.6, then the variance is
        (a) 0.4                                (b)2.56                         (c) 1.96                        (d) 0.04
15.   If  is an impossible event, then
        (a) 1                                   (b)                            (c) 0                             (d)
II.    Answer any 10 questions; Q.NO 30 is compulsory                                                         10 x 2 = 20
16.   If A and B are two sets and U is the universal set such that n (U) = 700, n (A) = 200, n (B) = 300
         And n (AB) = 100, find n (A’  B').
17.   If X = {1, 2, 3, 4, 5}, Y = {1, 3, 5, 7, 9} determine the following relation from A to B is function? Give reason for your answer. f = {(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)}     
18.   If 13 + 23 + 33 + . . .  .+n3 = 36100 ,then find 1+ 2 + 3+ . . . + n
19.    If  are the roots of the equation 3x2–6x+4=0, find the values of
20.   
21.    Find the product of
22.    If the points (a,1) ,(1,2) and (0,b+1) are collinear , then show that
23.    Show that the straight lines 3x – 5y + 7 = 0 and 15x + 9y + 4 = 0 are perpendicular
24.    In  MNO, MP is the external bisector of   , meeting NO produced at P. If MN = 10 cm,           MO = 6 cm , NO = 12 cm then find OP.
25.    A girl of height 150 cm stands in front of a lamp-post and casts a shadow of length 150  cm on the ground. Find the angle of elevation of the top of the lamp-post.
26.    A solid right circular cone  has radius 20cm and height 29 cm. Find its volume.
27.    A solid right circular cylinder has radius of 14 cm and height of 8 cm. Find its total surface area
28.    Calculate the standard deviation of the first 13 natural numbers
29.   Three dice are thrown simultaneously. Find the probability of getting the same number on all the three dice.
30.   Prove the identity = 1 +
( OR )
Solve:3x– =2   
III.  Answer any 9 questions; Q.NO 45 is compulsory                                                           9 x 5 = 45
31.   Use Venn diagrams to verify De Morgan's law for set difference A\(BC)=(A\B)(A \ C)
32.   A function f : [ - 7, 6 )  R is defined as follows
       
       Find                  i) 2 f (4) + 3 f (2)       ii)
33.   Find the sum of first nterms of the series 6 + 66 + 666 + . . . . 
34.   A train covers a distance of 90km at a uniform speed. Had the speed been 15km/hr more, it would have taken 30 minutes less for journey. Find the original speed of the train.
35.   Simplify

36.   Find the G.C.D. of the polynomials x4+3x3–x–3 and x3+x2–5x+3.
37.   If A =  and B =  then prove that (A+B) 2 ≠ A 2 + 2 AB + B 2
38.    Find  the  equation  of  the  straight  line  joining  the point of  intersection  of  the  lines 3x–y + 9 = 0 andx + 2y = 4 and the point of intersection of the lines 2x + y –4 = 0 and x –2y + 3 = 0.
39.    Find the equation of the straight lines passing through the point (–3/10)and the sum of the intercepts is 8.
40.   State and prove the Basic Proportionality (Thales) Theorem
41.   A tent is in the shape of a right circular cylinder surmounted by a cone. The total height and the diameter of the base are 13.5 m and 28 m. If the height of the cylindrical portion is 3 m, find the total surface area           of the tent.
42.   If the curved surface area of a right circular cylinder is 704 sq.cm, and height is 8 cm,find the volume of the cylinder in liters
43.   Calculate the standard deviation of the data 38, 40, 34, 31, 28, 26, 34
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

45.   The sum of three terms of a geometric sequence is  , and their product is 1. Find the common ratio and the terms
(OR)
        A jet fighter at a height of 3000 m from the ground passes directly over another jetfighter at an instance when their angles of elevation from the same observation point are 60 and 45 respectively. Find the distance of the first jet fighter from the second jet at that instant.
IV.  Answer the following questions:                                                                          2 x 10 = 20
46.   Construct a ∆PQR in which the base PQ= 4 cm, and the altitude from R to PQ is 4.5 cm.
(OR)
Draw a circle of radius 3 cm. From an external point P, 7 cm away from its centre, construct the two tangents to the circle and measure their lengths.
47.    Draw the graph of and use it to solve the equation.
(OR)
A cyclist travels from a place A to B along the same route at a uniform speed on different days. The following tables gives the the speed of his travel and the corresponding time he look to cover the distance.
Speed in km/hr
X
2
4
6
10
12
Time in hrs
y
60
30
20
12
10
Draw the speed –time graph and use it to find
(i)                 the number of hours he will take if he travels at a speed of 5km/ hr
(ii)               the speed with which he should travel if he has to cover the distance in 40 hrs.


R.Navaneethakrishnan; M.Sc; B.Ed
P.G.Asst. in Rayar kalvinilayam, Avinashi
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