RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION / STD - VIII / QP + SOLUTIONS JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS GANIT PRABHUTWA EXAMINATION

Size: px

Start display at page:

Download "RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION / STD - VIII / QP + SOLUTIONS JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS GANIT PRABHUTWA EXAMINATION"

Benedict Benson
5 years ago
Views:

JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS GANIT PRABHUTWA EXAMINATION Date : 0 - - 07 Std - VIII Total Marks : 00 Time : Hours Q.

1 JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS GANIT PRABHUTWA EXAMINATION Date : Std - VIII Total Marks : 00 Time : Hours Q. A) Choose the correct alternative and write it against the correct sub question number. (0) ) Ray PQ and ray PS are opposite rays. How many points are common to the two rays? (A) 0 (B) (C) (D) Sol. (B) Common point is P Q S P Topic : Lines / Sub Topic : Rays / Level : Easy / Ganit Prabhutwa Eamination ) What is the decimal form of 6? 90 (A) 4.0 (B) 4.0 (C) (D) 4.0 Sol. (D) Topic : Number System / Sub Topic : Decimals / Level : Moderate / Ganit Prabhutwa Eamination ) The centre of the circle passing through all the three vertices of PQR lies on the side PQ. What type of angle is P? (A) acute angle (B) obtuse angle (C) right angle (D) can not be decided Sol. (A) Since angle R must be right angle, P must be acute angle P C R Q Topic :Circles, Triangles / Sub Topic : Circles / Level :Moderate / Ganit Prabhutwa Eamination Website : Rao IIT Academy

2 4) A money lender charges Rs. 6 as interest for 6 months on Rs. 40. What is the rate of interest p.c.p.a? Sol. (C) (A) % (B) % (C) 0 % (D) 0 % Time = 6 months = 6 yr yr SI P R T R R 0 0% Topic :Percentages / Sub Topic : Simple Interest / Level : Moderate / Ganit Prabhutwa Eamination 5) A shopkeeper sells an article for Rs. 40, and suffers a loss of 4 %. What should be the selling price of that article to gain a profit of %? Sol. (D) (A) 5 (B) 6 (C) 6 (D) 80 Let CP 00 After loss of 4 % SP = 96 = so, C.P = 50 S.P. after % profit = % of = 80 Topic :Profit & Loss / Sub Topic : Profit and loss / Level : Moderate / Ganit Prabhutwa Eamination Website : Rao IIT Academy

3 6) What is the averages of the numbers Sol. (B) 7,,0,,? 4 (A) 4 (B).4 (C) (D) =.4 Topic : Data Handling / Sub Topic :Averages / Level :Moderate / Ganit Prabhutwa Eamination 7) What should be added to Sol. (B) 5? so that the sum will be divisible by (A) 4 (B) 4 (C) (D) k a 5 k a a 5a a, k 5 k 4 as well as by Topic : Quadratic Equations / Sub Topic :Factorization / Level : Moderate / Ganit Prabhutwa Eamination 8) If y and 5y 6z find the ratio : z Sol. (B) (A) : (B) 9 : 5 (C) 5 : 9 (D) : 5 y 5y 6z y y 6 z 5 y 6 9 Multiply the two ratios to get so, y z z 5 5 Topic : Ratios & Proportions / Sub Topic : Ratios / Level : Easy / Ganit Prabhutwa Eamination Website : Rao IIT Academy

4 9) Area of a circle is 86 sq.cm. Find its diameter. Sol. (A) (A) 4 cm (B) cm (C) cm (D) 84 cm 7 r 86 r r r r 6 7 Diameter = r 4cm Topic :Mensuration / Sub Topic :Area of circles / Level :Easy / Ganit Prabhutwa Eamination 0) If 8 then find. (A) 4 (B) 4 (C) 4 (D) 4 Sol. (D) Topic : Eponents & Powers/ Sub Topic : Eponents / Level : Easy / Ganit Prabhutwa Eamination 4 Website : Rao IIT Academy 4

5 Q. B) Write only answers of each of the following sub-questions. (0) ) Area of a trapezium is 84 cm. Length of one of its parallel sides is 0 cm and its height is 6 cm. What is the length of the other parallel side? Sol. A = 84 cm a h = 6 b 84 a b h 84 0 b 6 0 b 8 b 8cm Topic : Mensuration / Sub Topic : Trapezium area / Level : easy / Ganit Prabhutwa Eamination ) Two numbers differ by 0. One third of the greater number is half of the smaller number. Find the numbers. Sol. a b 0...() a b a b 0...() a b 40 a b 0 b 40 b 40 a 40 0 a 60 Topic : Linear Equation in one/two variable / Sub Topic : Linear Equation in one/two variable/ Level : Easy / Ganit Prabhutwa Eamination 5 Website : Rao IIT Academy 5

6 ) In the adjoining figure, line l line m. Line n is a transversal. Find values of and y. n y + 0 y 0 l m Sol. y 0 80 [Linear pair] y 70...() y 0 y 0 [Corresponding angles] 40 y n y + 0 y 0 l m Topic : Parallel lines / Sub Topic : Crossponding angles, supplementary length of chord / Level : Easy / Ganit Prabhutwa Eamination 4) In a circle of diameter 0 cm, a chord is at a distance of 6 cm from the centre. Find the length of the chord. Sol. Not possible to solve using diameter as 0 cm. Hence we assume 0 cm is given as the radius and not diameter. A 6 O 0 B In OAB, OB OA AB 0 6 AB AB 00 6 AB 64 AB 8cm Hence length of chord = AB 6cm Topic : Circles / Sub Topic :Length of chord / Level :Moderate / Ganit Prabhutwa Eamination 6 Website : Rao IIT Academy 6

7 5) Find the condition on the values of, so that the triangle of sides 40 cm, 7 cm, and cm can be constructed. Sol. () () 40 7 () 7 40 Using (), () & () Topic : Triangles / Sub Topic :Triangle inequality / Level :Moderate / Ganit Prabhutwa Eamination Q. Solve the following sub-questions. (5) ) Factorize : 8y 4 y 8y Sol. 8y 4 y 8y y 4y y y y y 4y y y y y 4y y y 4y Topic : Factorization / Sub Topic : (a+b) / Level : Moderate / Ganit Prabhutwa Eamination ) Gopal leaves home and by walking at two third of his usual speed reaches his school 0 minutes late. How much time does he take usually to reach the school from home? Sol. D S T D T D T 0 From () & () T T 0 T T 0 T 0 mins Topic :Linear Equation in one variable / Sub Topic : Linear Equation in one variable / Level : Moderate / Ganit Prabhutwa Eamination 7 Website : Rao IIT Academy 7

8 ) Divide the polynomial 6 6 by ( ) and write the remainder. Sol Remainder = 0 p 6 6, then the remainder when divided by ( ) is Alternately if p Topic : Polynomials / Sub Topic : Long division / Remainder theorem / Level : Moderate / Ganit Prabhutwa Eamination 4) Seema purchased 8 chocolates for Rs. 0. How many chocolates should she sell for Rs. 0 to gain a profit of 60 %? Sol. 8chocolates Rs.0 Required profit = 60% 60 SP for 8chocolates 0 6 Rs. 00 Hence SP of one chocolate = Rs. Hence for 0 Rs. number of chocolates to be sold 0 5 chocolates. Topic : Profit and Loss / Sub Topic : Profit and Loss / Level : Moderate / Ganit Prabhutwa Eamination 5) In the adjoining figure, ABCE is a square with side 4 cm. If B, C, D are collinear and l(ed) = 50 cm, find l(bd). A E B C D Rao IIT Academy 8 Website :

9 Sol. A E B 4 C BD In AECD, ED EC CD 50 4 CD CD CD 68 48cm Hence BD BC CD cm D Topic : Pythagorus theorem / Sub Topic : Pythagorus theorem / Level : Moderate / Ganit Prabhutwa Eamination Q. Solve, the following sub-questions. (0) ) If a b c 6, and a b c 9, find the value of ab bc ac. Sol. a b c 6...(i) a b c 9...(ii) a b c 6 a b c ab ac bc Using equation (ii) 9 ab ac bc ab ac bc.5 Topic : Algebraic Identities / Sub Topic : (+y+z) / Level :Moderate / Ganit Prabhutwa Eamination ) Two years before, a machine was purchased for Rs If its price reduces by 0% every year, what is the price of that machine today? Sol. C.P = Rs Price reduces 0% per year. 9 So, it becomes 0 After two years, Price will be Rs. th after every year Topic : Percentages / Sub Topic : Percentages / Level : Moderate / Ganit Prabhutwa Eamination 9 Website : Rao IIT Academy 9

10 ) Mohan bought a bicycle for Rs He paid the amount in the form of notes of Rs. 00, Rs. 50 and Rs. 0. Number of 00 rupee notes was half of 50 rupee notes and number of 0 rupee notes was three times the number of 00 rupee notes. Find the number of notes of each denomination. Sol. Let there be number of 00 rupees notes Hence number of 50 rupees notes = Hence number of 5 rupees notes = Rs.00 4 notes Rs notes Rs.0 4 notes Topic : Linear Equation in one variable / Sub Topic : Linear Equation in one variable / Level : Moderate / Ganit Prabhutwa Eamination 4) In the adjoining figure, ABCD is a trapezium. 5 D -5 P - C Seg. AB seg. DC Find the value of. A B Sol. APB CPD AP PB 5 CP PD A D 5 5 C P B 8 Topic : Geometry / Sub Topic : Geometry of s / Level : Moderate / Ganit Prabhutwa Eamination 0 Website : Rao IIT Academy 0

11 5) / Find the value of. Sol. / / / Topic : Eponents & Powers / Sub Topic : Eponents & Powers / Level : Moderate / Ganit Prabhutwa Eamination Q.4 Solve, the following sub-questions. (0) ) Construct LMN such that l( LM ) 5. cm, l( LN) 5.7 cm, height LT = 4.5 cm. Sol. Step () : First draw any line & draw length LT perpendicular to it of length 4.5 cm. (Drawing perpendicular to a line is a standard procedure) L 4.5 cm T Step () : Take distance L M = 5. in compass & draw an arc with L as centre of cutting the line in M. Similarly take distance LN = 5.7 cm in compass & draw an arc with L as centre & cutting line in N. Note that there will be two possibilities for points M & N as shown. L N M T M N Website : Rao IIT Academy

12 Hence total non-congruent triangles possible as shown. L L M T N Topic : Construction / Sub Topic : Construction of s / Level :Moderate / Ganit Prabhutwa Eamination ) The L.C.M. of two number is fourteen times their G.C.D. The sum of the G.C.D and the L.C.M is 600. Find two pairs of such numbers. Sol. LCM = 4 GCD and LCM + GCD = (GCD) + GCD = 600 GCD = 40 and LCM = 560 As GCD = 5 and LCM = 4 57 One of the numbers must have in the factorization and the other should have 4 as a factor. Both numbers should have 5 in the factorization but only one number should have 7 in the factorization. 4 4 This gives two pairs of numbers as 57, 5 and 5, 57 N M T i.e. 80;80 and 40;560 Topic : LCM & GCD / Sub Topic : LCM & GCD / Level : Moderate_ / Ganit Prabhutwa Eamination ) Perimeters of a rectangle and a square are equal. The ratio of the length and breadth of the rectangle is 5 : 4. Find the ratio of the length of the rectangle to the side of the square. Sol. Take length and breadth of rectangle as 5 and 4 perimeter of rectangle = perimeter of square = 8 side length of square 9 length of rectangle 5 side of square 9 / 0 :9 Topic : Ratio & Proportion / Sub Topic : Rectangles & squares / Level : Moderate / Ganit Prabhutwa Eamination Website : Rao IIT Academy

13 4) Solve,. Sol. Multiply both side by Topic : Linear Equation in one variable / Sub Topic : Linear Equation in one variable / Level : Easy / Ganit Prabhutwa Eamination 5) A train running at a speed 0f 90 km/hr, crosses a bridge in 6 seconds. Another train having length 00 meters less, is running at a speed of 45 km/hr. In how much time will the train cross the same bridge? Sol. Total distance needed to cross a bridge = length of bridge + length of train = speed time 6 km = 900 m 600 for first train, it is for the second train, it will be 00 m less = 800 m = speed time 800 m time required hrs 45 km / hr seconds 64 seconds 450 Topic : Linear Equation in one variable / Sub Topic : Linear Equation in one variable / Level : Moderate / Ganit Prabhutwa Eamination Website : Rao IIT Academy

14 Q.5 Solve the following sub-question. (5) ) ABCD is a rectangle. Prove that seg. AC seg. BD Sol. A B D C ABD CDB by RHS congruency test as hypotenuse BD is common and BAD BCD 90 o Hence AB=CD Now, ABC DCB by SAS congruency test. as AB = CD, BC is the common side and ABC DCB 90 o AC DB Topic : Geometry / Sub Topic : Rectangles / Level : Easy / Ganit Prabhutwa Eamination ) The price of sugar is increased by 0%. By what percent the consumption of sugar be reduced so that ependiture on sugar will remain the same? Sol. If the base price of sugar = 00 Rs/kg then the final increased price Rs / kg 00 Let initial consumption = y kg initial ependiture = 00 y Rs. Since final ependiture = initial ependiture = 00 y Rs. final ependiture 00 y final consumption final price 0 5y kg 6 reduction in consumption 5y y y 6 6 kg % reduction y / % y Topic : Percentages / Sub Topic : Percentages / Level :Moderate / Ganit Prabhutwa Eamination 4 Website : Rao IIT Academy 4

15 ) Factorize : yz y z. Sol. yz y z y yz z = y z y z y z... using a b a ba b z y z y Topic : Factorization / Sub Topic : (a+b) / Level : Moderate / Ganit Prabhutwa Eamination 4) In a terminal eamination Arun scored 8 marks in mathematics. Ajit scored 5 marks less than Amit and Amit scored 4 marks more than the average marks of the class. If the average of marks of Arun, Ajit and Amit is more than the average of marks of the class, find the average of marks of the class. Sol. Let average marks of the class = Amit s marks = + 4 Ajit s marks = 4 5 Average of Arun, Ajit and Amit s marks = more than class average = Topic : Linear Equation in one variable / Sub Topic :Linear Equation in one variable / Level : Moderate / Ganit Prabhutwa Eamination 5 Website : Rao IIT Academy 5

16 5) A copper wire is bent to form a circle whose area is 66 sq. cm. If the same wire is bent to form a square, what will be the area of that square? 7. Sol. r Let the perimeter of the wire p r r p Area p p r 66 cm 4 4 p cm 7 p 88 as p 0 p 88 cm Hence perimeter of the square = 88 cm p side cm 4 p Area of square 484 cm 4 Topic :Mensuration / Sub Topic : Area of circle / square / Level : Easy / Ganit Prabhutwa Eamination 6 Website : Rao IIT Academy 6

Std VIII Ganit Pravinya Exam Dec 2016 Test Paper Solution

Std VIII Ganit Pravinya Exam Dec 2016 Test Paper Solution Std VIII Ganit Pravinya Eam 2016 4 Dec 2016 Test Paper Solution 1. a) Solution - Ratio of length to breath = 1:7 Length = 1 ; Breadth = 7 Area of rectangle = 1 7 = 91 2 Given area =2275 91 2 =2275 2 =