JMMC RAMANUJAN MEMORIAL MTSE SAMPLE QUESTIONS CLASS - IX

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CLASS - IX. What is the value of 0 a? 0 undefined ( or (. If a + b + c =, ab + bc + ca = and abc = 3 then? a bc b ca c ab - - 0 3.

1 CLASS - IX. What is the value of 0 a? 0 undefined ( or (. If a + b + c =, ab + bc + ca = and abc = 3 then? a bc b ca c ab Express (a + b ) as a sum of three square number :- (a b ) + (a (a + b ) (a (a b ) + (a. Ratio of two numbers is : 3 and the difference between the square of this two numbers is 8. Numbers are 8,6 8,6 ; -8,-6-8,-6 5. a b = 5 and a + b = 3, then ab =? 3 6. What is the relation between 5 3 & What is the equation of parallel axis of x axis? x =a, where a is constant y = b where b in comtent x = a, y = a where a in constant 8. In the adjoining figure, DE BC Given AD = 3, DB = 5 and AC =.8 then AE =? A D E B C. O is a point inside ΔABC, then which of the followings is /are correct? (OA + OB + OC) = (AB + BC + AC) (OA + OB + OC) < (AB + BC + AC) (OA + OB + OC) > (AB + BC + AC) 0. Arrange in increasing order (3 : 5),( : ),(5 : ) and ( : 3) (3 : 5) > ( : ) > (5 : ) > ( : 3) ( : ) < (3 : 5) < ( : 3) < (5 : ) ( : 3) > (3 : 5) > (5 : ) > ( : ) ( : ) < (5 : ) < (3 : 5) < ( : 3). If (a + : (a - b ) = : 5, then (a - b ) : (a + b ) =? : 3 3 : 5 : 3 3 : 5

2 . In a filled container ther is 3 parts of water and part of milk mixed together. What part of the mixture is replaced with that part of milk so that the content of milk and water is equal in the container? 3 part part part 6 3. A(-3, ), B(p, q) and C(, 3) are three vertices of an isosceles triangle. Which of the following is/are correct when AB = BC. p = + q p + q = p = q - + x =? + x + x - x + x + x + x Difference between in-circle and circum-circle of a square is a. Find perimeter of that square? (circum-circle goes through the vertices of the square) a a a None of these. 6. In an exam, % and 8% of examinees passed in mathematies and Bengali. If no examinees have failed in both the subjects then what percentage of the examinees passed in both the subject? 35% 0% 5% 50%. AD,BE and CF are three medians of ΔABC. Which one is correct? BC = 8CF 8BE + AD BC = 8CF + 8BE + AD BC = 8CF + 8BE AD 8. By adding what value to 3 : 5 will it become 5 : 6? 5. Given A = 3B = C, then A : B : C =? : 3 : : 3 : 6 : : 3 3 : : a a a 5a a? 0 5 a (a + )(a + )(a + )(a + 5) 0 a (a + )(a + )(a + 3)(a + ) 0 a (a + )(a + 3)(a + )(a + 5) 0. Chord of a circle with radius makes a right-angle with the centre of the circle. Find area of the shaded region. O A B

3 Find G.C.M (-33) JMMC RAMANUJAN MEMORIAL MTSE SAMPLE QUESTIONS. x x & x + 8x + 3 (x ) (x + ) x 3. (x - y ) & (x 6 y 6 ) x + y x y x y. If ab + bc + ca = 0, then find H.C.F of (a + b + 3 and a 3 + b 3 + c 3 3abc (a + b + (a + b + (a + b If (x ) is the H.C.F of x x and x mx 8 then m =? 0 6. H.C.F. and L.C.M of two expressions are (x + 3) and m 3 x + 6 respectively. If one of the expression is (x + x 3) then the other expression is x + x + 6 x + x + 6 x x + 6 x + x 6. L.C.M of (a 6 ),(a m) & a + a + is (a + ) (a ) (a + a +) (a a + ), then m =? 3 8. Factorise- x 3 + x x (x + )(x + )(x 3) (x 3)(x + )(x ) (x 3)(x + 3x ) (x 3)(x + x + )? ()() a b b c a c b a c a c b. Given, a + b + c = Express (x + )(x + )(x + 6)(x + ) + (x + ) as a square number. (x + 8x +0) (x + 8x 0) (x + 8x +0) (x + 8x 0) 3. (x (x (x...(x z) =? 0 x 6 + abc...z If A= {a,b}, B = {c,d}and A B = {(a,,(a,,(b,,(b, }then find A B when A = {3, 5}, B = {5, }a b c d {(3,5),(3,),(5,5),(,5)} {(3,5),(3,),(,5),(5,5)} {(3,5),(3,),(5,5),(5,)} {(5,3),(5,5),(,3),(,5)} 33. In figure-, shaded region is A B. Then what will be the shaded region in figure? A B A B A + B A B A B A B A B 3. What is the lowest value of (x )(x 3)(x )(x 6) + 0? The ratio of the sum of the ages of father and mother to that of their two sons are : 3 :. Elder brother is 6 year older than younger brother. The ratio age of father & mother is :. Then what is the age of two sons, father & mother? Father - 0, Mother -3, elder brother-, younger brother- F-38, M-3, EB-8, YB-3 F-0, M-3, EB-, YB-3

4 x a x b x 3a 3b 36. Solve :- 0 b a a b x = a x = b x = a-b x = a + b Passage for question number 3 to. x y expresses both the parts of x and y (excluding all repeatations) and x y expresses the common parts between both x and y. If A = {,,3,}, B = {,5,}, C ={,,,} the answeer the following A B C 3.? A B A C 38. A B C? A B C A B C A B A C A B AC 3. A B C =? A B C A B C A B A C 0. A B? B A B A A B. A C? {,} {} {}. For what value of n, O n is undefined For which condition (a + (b + (c = 0 a b = 0,b c = 0,c a =0 a =b = c ( and ( both are correct. Express (p + q)(p + q) as the difference of two square (3p + 3q) + (p q) (3p 3q) (p q) (3p + 3q) (p + q) (3p + 3q) (p q) 3 5. If x 3 x x,then find x? x 3 6. The ratio of principal and annual amout is 8 :. The annual rate of interest is - % 3 % 3 3 % %. In mixed ore the ratio of copper, xinc, and nickel is : 3 : 5. What is the percentage of zinc. % 5% 6% % 8. In a mathematics exam in the first paper a student scored 30% out of 80. What percentage should he score in the second paper of 50 marks so that he score 50% in the overall. 3 5

5 n a n i s s o s c e l e s t r i a n g l e t h e v e r t i c a l a n g l e i s 5 JMMC RAMANUJAN MEMORIAL MTSE SAMPLE QUESTIONS. Two circles passes through the centre of both the each other, O and Q are the centre of two circles. Find the area of the shaded portion if OQ = a. O Q 50. I 3 3 b and the base is b, the area is - b b 5. In an equilateral triangle, semiperimeter is S and if the hypotenulse is x then the area of the triangle is - s(s + x) s(s x) s x 5. The point of intersection of three median of three sides of a triangle is called Centroid Centre of gravity incentre 53. In a triangle ABC the three medians interesects at D, if E and F are mid points of BD and CD respectively the DEF ΔABC ΔABC ΔABC 3 ΔABC 5. The ratio of areas of an equilateral triangle and a square is 3 :. The diagonal of a square is 60, then the perimeter of the triangle is If an angle of a triangle is equal to the sum of other two angles then the triangle is Right angled triangle Equilateral triangle Isosceles triangle Impossible to determine. 56. In an isosceles triangle which of the following conditions holds:- It can be acute angled triangel It can be right angle triangle it can be obtuse angled triangle (, ( & (all are correct. 5. In a triangle if two angles are equal then the triangle is Isosceles equilateral right angled scalene 58. The lenght of a diagonal of a rhombus is twice the other. The area of the rhombus is 6 sq. Find the length of the diagonals., 8 8, 6, 6, 5. In a trapezium the length of the parallel sides are 6 &. If the distance between them be 0 find the are of the trapezium. 0sq sq sq 60. Factoirse : a b a b + (b + )(b )(a ) (b )(a ) (b )(a )

[BIT Ranchi 1992] (a) 2 (b) 3 (c) 4 (d) 5. (d) None of these. then the direction cosine of AB along y-axis is [MNR 1989]

[BIT Ranchi 1992] (a) 2 (b) 3 (c) 4 (d) 5. (d) None of these. then the direction cosine of AB along y-axis is [MNR 1989] VECTOR ALGEBRA o. Let a i be a vector which makes an angle of 0 with a unit vector b. Then the unit vector ( a b) is [MP PET 99]. The perimeter of the triangle whose vertices have the position vectors