SSC Mathematics Model Question-10

Class: X

Subject: Mathematics (Compulsory)

Time: 3 hrs                                                                                                                                          Marks: 100

1.         Determine the following set into roaster method :{ xÎN; x> 15 and x< 225}                            4

Or

I           f A= {a, b}, B= {2, 3} and C= {3, 4} then find A× (B C) and A× (B C)

2.         Show that if the square of an odd natural number is divided by 8 then in each case the remainder will be 1.                                                                                                                                             

3.         Answer any three of the following questions :                                                                       5×3=15

            a)         If a +Ö3 then find the value of   a +.

            b)         If x +y =2 and x+y=4, find the value of x+ y .

            c)         Resolve into factor (Any two)

                         i. x+x –(a+1)(a+2)             ii.(a x-y)+4abxy                          iii. x -21x -20

            d.         If (x+ a) is the H.C.F. of x+p x+ q and x+ m x +n then prove that (p-m) a=q-n

            e.         A boatman man can go d km. against the current in t hours. It takes thours to cover the

            same distance in the direction of current. Find the speed of the current and of the boat.

4.         Simplify:                                                                                                     5

Or 

            (i)         If log then x=?             (ii)        If log find the value of a.

5.         If  then prove that a = c   or   a +b +c +d=0                                                                           5

Or,

            The area of a plot of land is 588 sq. meter. The ratio of length and breadth of a second plot of land with that of the former plot of land is 3:4 and 2:3 respectively. Find the area of the later plot of land.

6.   Solve the equation:                                                                                                4

Or

            The length of the perpendicular drown from the center of a circle to a chord is 2 cm. less than half            the length of the chord. If the radius of the circle is 10 cm. then what is the length of the chord?                              

7.         If A={2,5},B={3,6}and we consider the condition x   xÎA  and yÎB, Find the relation.                                                                                                                                               4

Or,       

             If   x a y, prove that x- ya x y  

8.         Solve with the help of the rule of cross-multification:     a x – c y = 0                                               4

                                                                                                       ay – c x = a - c

            Or   

            If a two digits number is divided by the product of its digits, the quotient is 3.When 18 is added to         the number, the digits of the number change their places. Find the number.

9.         Which term of   8+11+14+ !7 +………………………..is 392?                                                     5

            Or

            If   5+a+b+135 is in geometric series, find the value of a   and   b

10.       If the square of one side of a triangle is equal to the sum of the squares on the other two sides, the angle contained by these two sides is a right angle. Prove it.                                                                                  6

Or

            Prove that the perpendicular drawn from the centre of a circle on any chord other than the            diameter bisects the chord.

11.       Prove that if two tangents are drawn to a circle from an external point, the distances of points of the contact from that point are equal.                                                                                                                    6

            Or

.           Prove that equal chords in equal circles cut off equal arcs.

12.       ABC is an equilateral triangle and AD is the perpendicular to BC .Prove that, 4AD=3AB        4

            Or

             In   DPQR, M and N are the middle points of   PQ and PR respectively, then prove that MN is    parallel to QR and QR=2MN.

13. The chord AB and CD of  a circle with  centre O  meet  at right angles at some point within the circle, prove that  ÐAOD+ÐBOC=2 right angles.                                                                                                          4

            Or

            Given that two circles touch externally at the point A the tangent TT touches the two circles at P            and Q .Prove that ÐPAQ=90

14.       Answer any one of the following.                                                                                                      5

a) The intercepted parts of two diagonals and an interior angle of two diagonals of a quadrilateral are given, Construct the quadrilateral (The sign of drawing and description are essential)

b) To draw a parallelogram whose one angle is equal to a given angle and the region bounded by it is equal to a triangular region. (The sign of drawing and description are essential)

c) To draw a direct common tangent to two circles of unequal radii. (The sign of drawing and description are essential)

15.       Construct a square when its perimeter is given.

            (The sign of drawing and description are essential)                                                                           5

            Or

            Draw a circle which touches a given circle and a given straight line at a given point

            (The sign of drawing and description are essential)

16.       a) Prove that                                                                                     4

            Or

            Prove that       

            b) Find the trigonometrical ratios of angle 30geometrically.                                                          4

Or

            Solve:  sinq+ cosq =1;  where   0 £ q £ 90 

c) A ladder of 18 meters long touches the roof of a wall and makes an angle 45with the horizon. What is the height of the wall?

Or

A tree is broken by storm in such a way that the broken part makes on angle of 30 with the other part and touches the ground at a distance of 10 meters from it. Find the length of the tree. 

17.       a) The diameter of a wheel is 4.2metres.How many times will the wheel move to describe a distance of 330 meters.                                                                                                                                              4 

Or 

            The lengths of the sides of a parallelogram are 30 cm. and 26 cm. If one of its diagonal is 28 cm. Find the length of the other diagonal.

b) The height of a right circular cylinder and a cone is h and they stand on the same base. If the areas of their curved surfaces are in the ratio 4:3, show that the radius of the base is.                         4

Or

            The area of the whole surface of a cube is 48 sq, meters; Find the length of its diagonal.