SSC Mathematics Model Test-6

SSC Mathematics Model Test-6

Time: 03 hours.                                                                                Full marks- 100

	[N.B.- The figures in the right margin indicate full marks.]
1.	If A = {a, b}, B = {2, 3}, C = {3, 4}, then find A × ( ) and .	4
	Or,
	Determine the set in Roster method.
	{ and x is a multiple of 3}
2.	Solve and show the solution set in a number line:	4
3.	Answer any three of the following:-                                                                  5 × 3 =	15
	(a)   If + then find the value of
	(b) If x + y + z =15 and  than show that the value of xy + yz + zx =71.
	(c)   Resolve into factors any two of the followings:
	(i)
	(ii)
	(iii)
	(d)   Determine the L.C.M of
	(e)   The salary of the brother is y% more than that of the sister; as a result, the
	salary of The sister is x% less than that of the brother. Express x as a function of y.
4.	Simplify:-	5
	Or,
	Simplify:- log2 + 2log5 –log3-2log7.
5.	The perimeter of a triangle is 18cm. If the ratio of length of the sides is 3:4:5, Then	5
	find The length of each side.
	Or,
	If ax = by = cz, Then show that,
6.	Find the solution of .	4
	Or,
	The hypotenuse of right-angled triangle is 13cm and its perimeter is 30cm. What is
	the area of triangular region?
7.	If  and then show that,	4
	Or,
	Sketch the graph of the equation  Find the length of the
	segment of the graph cut by the anes.
8.	Solve:    ax – by = ab	4
	bx – ay = ab
	Or,
	A boat goes 15km per hour when rowed in favour of the current and it goes 5km per
	hour against the current. Find the speed of the current.
9.	In a certain arithmetic series, if the m-th term is  and the n-th term is What is	5
	the (m + n) th term?
	Or,
	If 5 + x + y + 135 is a geometric series, find the value of x and y.
10	Prove that, if the square on one side of a triangle is equal to the sum of the squares	6
	on the Other two sides, the angle contained by these two sides is a right angle.
	Or,
	Prove that Standing on the same arc the angle at the circumference is half the angle
	at the Centre.

11	Prove that, Angles is the same segment of a circle  are equal.
	Or,
	Prove that, the angle made by a tangent to a circle with any chord drawn from the
	point of contact is equal to any angle in the alternative segment of the circle.
12	The bisector of the angles
	90º
	Or,
	Prove that, Three bisectors of the angles of a triangle are concurrent.
13	A chord AB of one of the two concentric circles intersects the other cirele at points
	C and D. prove that, AC = BD.
	Or,
	AB is a diameter of a circle and BC is chord equal to its radius. If the tangents
	drawn at A and C meet each other at the point D. Then prove that ACD is an
	equilateral triangle.
14	Answer any one of the followings:-                                                                   1 × 5 =	5
	[The sign and description of the construction are essential]
	(a)   If two sides and an angle (acute) opposite to one of them are given, Then the
	triangle is to be constructed. [The sign and description of the construction are essential]
	(b) The length of two line segments are a and b respectively. To find the line segment of
	Length C, such that ab = . [The sign and description of the construction are essential]
	(c)   To draw a direct common tangent to two circles of unequal radii .
	[The sign and description of the construction are essential]
15	Answer any one of the followings:                                                                   1 × 5 =	5
	[The sign and description of the construction are essential]
	(a)   Construct a triangle when an angle adjacent to the base, the altitude and the sum
	of the Other two sides are given.
	(b)   Draw a tangent to a circle which is parallel to a given straight line.
16	(a)   If   then show that,	4
	Or,
	If  tan A + sin A = m and tan A – sin A = n, Prove that,
	(b)   Solve:  0	4
	Or,
	If, cot (A+B) =1 and cot (A-B) = Then find value of A & B. When A & B are
	both Acute angle.
	(c)   If the angle of elevation at the top of the minar is from 45° to 60°, from a point	4
	on moving 60 metres towards the minar, find the height of the minar.
	Or,
	A ladder 18 metre long touches the root of a wall and makes an angle 45° with
	hovizon.What is the height of the wall?
17	The lengths of the sides of a parallelogram are 30cm and 26cm. If one of its	4
	diagonals is 28cm, find the length of the other diagonal.
	Or,
	A horse moves for 1.5 minute at the rate of 66 metre per minute in a circular field.
	Find the diameter of that circular field.
18	The area of the whole surface of a cube is 48 square metres. Find the length of its	4
	diagonals.
	Or,
	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

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