Practice Test


1) 8 is the solution of the equation


2) If the diagonal of a rectangle is 5 cm and one of its sides is 4 cm, then its area is


3) Divide 56 into two parts such that three times the first part exceeds one-third of the second by 48. Then the two parts are


4) The sum of the digits of a two digit number is 10. If 18 be subtracted from it, the digit in the resulting number will be equal. Then the number is


5) The product of two numbers is 3200 and the quotient, when the larger number is divided by the samller is 2. Then the two numbers are


6) The denominator of a fraction exceeds the numerator by 2. If 5 be added to the numerator, the fraction increases by unity. Then the fraction is


7) Three person A, B and C together have Rs. 51. If B has four-fifth of the money than A has, and C has three-fourth of the money than A has, then they have money as


8) A positive number consists of two digits. The digit in the ten's place is three times the digit in the unit's place. If 54 are subtracted from the number, the digits are reversed. Then the numbers is


9) Hemant is asked to divide one half of a given number by 6 and the other half by 4 and then add the two quantities. Instead, he divides the number by 5. If his number is 4 short of the correct (actual) answer, then the given number is


10) Ten years ago, the age of a father was four times the age of his son. Ten years hence, the age of the father will be twice that of his son. The present ages of the father and the son are


11) Which one of the following equalities is an equation?


12) Which one of the following equalities is an identity?


13) The equation x-7-9x=4x-3-8x is true for


14) what is the number of the solution of the equation 3x+1=(4x-3)-( x-5)?


15) Mary is 24. Ann was half the age Mary is when Mary was the age Ann is now. How old is Ann ?


16) A man's wife is 6 years younger than her husband. One day he said to her " did you know, my dear , that we have been happily married for 22 years now and , since our marriage , the sum of our ages had exactly doubled ? " how old were the man and his wife when they were married ?


17) Divide the number 850 into two parts such that 8% of the first added to 24% of the second is 12% of the whole. Then the two parts are


18) The sum of the digits of a two-digit number is 12. If the digits are interchanged, the number increases by 75%. The given numbers is


19) Monthly income of two persons are in the ratio 4:5, and their monthly expenses are in the ratio 7:9. If each saves Rs.50 per month, then their respective monthly incomes are rupees


20) The age of a person is twice the sum of the ages of his two sons. If, five years ago, his age was thrice the sum of their ages at that time, then his present age is


21) A two digit number is four times the sum of its digits. If 27 be added to the number, its digit get reversed. Then the given number is


22) If x-y=2 and 3x-2y=9, then : x+y =


23) If 2x+y=11 and 3x-y=9, then : x-y =


24) If 15x+23y= -10 and 3x+4y= -2, then 3x+2y+2=


25) If 4x+3y+4= 0 and 6x+5y+7=0, then : 2x+y =


26) If 3(x-2) -2(y+3) = 1 and 2(x-3)+3 ( y+2)=0, then: x-y =


27) If 3(x-4) -4(y+3)=1 and 5(y+3) -4(x-4)=0, then : x-y =


28) If 3x-y=0 and -x+y=0, then : (x,y) =


29) If 0.x+y=0 and 0.x-0.y=0 then


30) If 5x+4y=27 and 4x+5y=18, then the values of (x+y) and (x-y) are respectively


31) If 4x+3y=24 and 3x+4y=25, then the values of (x-y) and (x+y) are respectively


32) If x+y=3, y+z=2 and z+x=1, then x+2y+3z=


33) 5% of one number and 4% of the other together amount to 16. If 6% of the first number and 8% of the second add up to 24, then these number are respectively.


34) If one root of the equation x(x-6)=3k(1-x) is negative of the other, then: k =


35) If the sum of roots of a quadratic equation is 5, and the sum of their square is 27, then the equation is


36) If the sum of the two number is 8 and the sum of their square is 34, then the numbers are


37) If the sum of roots of quadratic equation is 3, and the sum of their cubes is 7, then the equation is


38) Two squares have sides p cm and (p+5)cm. If the sum of their areas is 625 sq.cm, then their sides are


39) The area of a rectangular field is 2000 sq.m and its perimeter is 180 m. the length and breadth of this field are respectively


40) The hypotenuse of a right-angled triangle is 20 cm. if the difference between its other two sides is 4 cm, then they are


41) The three sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively. if the triangle so formed is right-angled, then the sides of the equilateral triangle is


42) The sum of two distinct irrational numbers multiplied by the larger one is 70. if their difference multiplied by the smaller one is 12, then the two numbers are


43) x, x-4 and x+5 are factors of the left-hand side of the equation


44) Co-ordinates of points on x-axis which are at a distance of 10 units from the point (3,-6) are


45) Co-ordinates of points on y-axis which are at a distance of 13 units from the point (5, 4) are


46) If the distance between the point (na, nb) and (a,b) is 4 times the distance between the points (5a,5b) and (a,b), then : n=


47) The four points (0,-1), (-2,3) (6,7) and (8,3) form a quadrilateral which is a


48) If the points (-3, 4), (-14, 12) and (8, k) are collinear then : k =


49) If the triangle whose vertices are A (4, 3), B(6, -2) and C (k, -3) is right-angled at a, then : k=


50) If a line makes equal intercepts on the x- and y- axis, then its slope is


51) If a line has x-intercept a and y-intercept b, then its slope is


52) The equation of the line joining the point (3, 5) to the point of intersection of the lines 4x+y-1=0 and 7x-3y-35=0 is


53) The total cost curve of the number of copies of a particular photograph is linear. If the total costs of 5 and 8 copies of the photograph are Rs.80 and Rs.116 respectively, then the total cost of 10 copies of the same photograph will be


54) A survey shows that there is a linear relation between the population of a country and time. In the year 1980, population was 84 crores and in the year 1990 it was 93 crores. Then the population in the year 2008 would be


55) The point of intersection of the lines 3x+2y=6 and 3x-y=12 lies in


56) The distance from the origin to the point of intersection of the lines 3x-2y=6 and 3x+2y=18 is


57) A right angled triangle is formed by the line 4x+3y=12 with the co-ordinate axes. The length of the perpendicular from the origin to the hypotenuse is


58) The equation of the line passing through the point of intersection of the lines 2x+3y-5=0 and 7x-5y-2=0, and parallel to the line 2x-3y+14=0 is


59) The x-and y- intercepts of the line 4x+5y+9=0 are respectively


60) The equation of the line which passes through the point (4, 1) and whose x-intercept is double its y-intercept is


61) If a line passing through the point (1, 2) makes equal intercepts on the X- and Y- axis, then each intercept is


62) If (2, 3) is the mid-point of the portion of a line intercepted between the co-ordinate axes, then the x- and y- intercepts of the line are respectively


63) The equation of the line having y-intercept = -7, and parallel to the line joining the points (2, 3) and (-3, 7), is


64) If the line Kx+4y=6 passes through the point of intersection of the lines 3x+4y=5 and 2x+3y=4 , then : K=


65) If a line passing through the point of intersection of the lines 3x-y+11=0 and 2x-y+9=0 , makes equal intercepts on the co-ordinate axes, then its equation is


66) The equation of the line whose x- and y-intercepts are respectively twice and thrice of those of the line 3x+4y=12 is


67) If the three line 2x-3y+K=0, 3x-4y-13=0 and 8x-11y-33=0 are concurrent, then : K=


68) A line passes through the point (2, 2) and is perpendicular to the line 3x+y=3. Its y-intercept is


69) The cost of a bus ticket depends linearly on the distance travelled. A journey of 2 miles costs 40 paise while a journey of 6 miles costs 60 paise. Then, a journey of x miles will cost y rupees, where


70) The cost of manufacturing 10 typewriters is Rs.350 while it costs Rs.600 to produce 20 typewriters. Assuming a linear cost model, the total cost y rupees of producing x typewriters is


71) It is known that 30 % of the population was educated in the year 1963; and 55 % in 1983. if the educated population depends linearly upon the year, then the estimated educated population in the year 2003 is


72) The life expectancy of males in 1987 in a country is 70 years. In 1962 it was 60 years. Assuming the life expectancy to be a linear function of time, the life expectancy of males in that country in the year 1997 is


73) If x+4x-3x+8=0, then x


74) If 2x+y=y+14, then x


75) If 2x+5=-25 and -3y -6=48, then xy


76) If 6 = 2x+4y, what is the value of x+2y is


77) If xy+z=y, what is x in terms of y and z?


78) If 2x + y = y + 14, then x


79) A linear equation has


80) When the system is inconsistent, there is


81) Which one is a linear equation?


82) There are two families A and B. In family A, there are 4 men, 6 women and 2 children and in family B, there are 2 men, 2 women and 4 children. The recommended daily requirement for calories is.
Men 2,400, women 1,900, children 1,800 and for protein is.., Men 55 gm., women 45 gm., children 33 gm.
Calculate the total requirements of calories and proteins for each of the two families using matrix method.


83) In a certain city, there are 5 Colleges and 120 Schools. Each school has 3 peons, 1 clerk and 1 head clerk, whereas College has 5 peons, 3 clerks, 1 head clerk and an additional staff as a caretaker. The monthly salary of each of them is as follows.
Peon = Rs. 1,100
Clerk = Rs. 1,700
Head Clerk = Rs. 3,000
Caretaker = Rs. 2,500
Using matrix method, find the total monthly salary bill of each School and College.


84) Three firms A, B and C supplied 40, 35 and 25 truck loads of stones and 10, 5, 8 truck loads of sand respectively to a contractor. If the cost of stone and sand are Rs. 1,200 and Rs. 500 per truck load respectively, find the total amount paid by the contractor to each of these firms, by using matrix method.


85) Define elementary column operations on a matrix.


86) There are two families X and Y. Family X has 2 men, 3 women and one child, while family Y has one man, and two children. Their individual daily requirements are as follows.
Man: 2,400 calories and 55 gms. Protein, Woman: 1,900 calories and 45 gms protein, Child 1,800 calories and 33 gms protein.
Present the above information in the form of matrices. Using matrix multiplication, calculate the total daily requirements of calories and protein for each of the two families.


87) A student has 4 places where he can have his lunch. The College Canteen charges Rs. 9 for a cold drink, Rs. 6 for a cutlet and Rs. 5 for a sandwich. The Coffee House charges Rs. 10, Rs. 8 and Rs. 9 for the same items, while fast food joint charges Rs. 12, Rs.15, Rs. 15, and the Restaurant charges Rs. 15, Rs. 25 and Rs. 20 for the above items respectively. The student wants to have one cold drink, two cutlets and one sandwich. Where should he have his lunch so that the lunch costs him the least?


88) A company manufactures two types of T.V. sets, which are assembled and finished in two workshops W1 and W2. Each type takes 20 hours and 10 hours for assembly and 5 hours and 3 hours for finishing in the respective workshops. If total number of hours available are 450 and 230 in workshops w1 and w2 respectively, calculate the number of units of each type be produced, using matrix method only.


89) The age of a man is three times the sum of the ages of his two sons and 5 years hence his age will be double the sum of their ages. Find the present age of the man?


90) The average age of a group of eight is same as it was 3 years ago, when a young member is substituted for an old member, the incoming member is younger to the outgoing member by


91) A school has 20 teachers, one of them retires at the age of 60 years and a new teacher replaces him, this change reduces the average age of the staff by 2 years, the age of new teacher is -


92) If thrice of A's age 6 years ago be subtracted from twice his present age the result would be equal to his present age. Find A's present age.


93) Y is older than X by 7 years. 15 years back, the ratio of their ages was 3:4. Their present ages are


94) If the sum of a number and the original number increased by 5 is greater than 11, which could be a possible value of the number?


95) If the difference of the squares of two numbers is 45, the square of the smaller number is 4 times the larger number, then the numbers are


96) A number between 10 and 100 is five times the sum of its digits. If 9 be added to it the digits are reversed, find the number.


97) The sum of two numbers is 52 and their difference is 2. The numbers are


98) The sum of numerator and denominator of a fraction is 8. If 3 is added to both the numerator and the denominator then the fraction becomes 3/4. Then the fraction is


99) The denominator of a fraction exceeds the numerator by 5 and if 3 be added to both the fraction becomes 3/4 . Find the fraction.


100) Difference between a number and its positive square root is 12; find the numbers.


101) The ratio between a two digit number and the sum of digits of that number is 4:1. If the digit in the unit place is 3 more than the digit in the tenth place, what is that number?


102) The sum of two irrational numbers multiplied by the larger one is 70 and their difference is multiplied by the smaller one is 12; the two numbers are


103) The sum of two numbers is 45 and the mean proportional between them is 18. The numbers are


104) There are two consecutive numbers such that the difference of their reciprocals is 1/240. The numbers are


105) The difference of two positive integers is 3 and the sum of their squares is 89. The integers are


106) A number consists of three digits of which the middle one is zero and the sum of the other digits is 9. The number formed by interchanging the first and third digit is more than the original number by 297. Find the number.


107) A number consists of two digits. The digit in the ten's place is twice the digit in the unit's place. If 18 be subtracted from the number the digits are reversed. Find the number.


108) The sum of the digits in a three digit number is 12. If the digits are reversed the number is increased by 495 but reversing only of the tens and unit digits increases the number by 36. The number is


109) Two numbers are such that thrice the smaller number exceeds twice the greater one by 18 and 1/3 of the smaller and 1/5 of the greater number are together 21. The numbers are -


110) On two numbers 1/5th of the greater is equal to 1/3rd of the smaller and their sum is 16. The numbers are


111) A number consisting of two digits is four times the sum of its digits and if 27 be added to it the digits are reversed. The number is


112) Find the fraction which is equal to 1/2 when both its numerator and denominator are increased by 2. It is equal to 3/4 when both are increased by 12.


113) If a number of which the half is greater than 1/5th of the number by 15 then the number is


114) The sum of the digits of a two digit number is 10. If 18 be subtracted from it the digits in the resulting number will be equal. The number is -


115) The fourth part of a number exceeds the sixth part by 4. The number is -


116) The product of two numbers is 3200 and the quotient when the larger number is divided by the smaller is 2. The numbers are -


117) Rs.14 is divided between A and B such that half of the share of A is equal to two thirds of the share of B, the share of A is


118) The number of kilograms of corn needed to feed 5,000 chickens is 30 less than twice the number of kilograms needed to feed 2,800 chickens. How many kilograms of corn are needed to feed 2800 chickens?


119) Divide 25 into two parts so that sum of their reciprocals is 1/6 .


120) Divide 50 into two parts such that the sum of their reciprocals is 1/12. The numbers are


121) A piece of string is 40 cms long. It is cut into three pieces. The longest piece is 3 times as long as the middle-sized and the shortest pieces are 23 cms shorter than the longest piece. The length of the shortest piece (in cm) is


122) The hypotenuse of a right-angled triangle is 20 cm. The difference between its other two sides is 4cm. The sides are


123) The sides of an equilateral triangle are shortened by 12 units 13 units and 14 units respectively and a right angle triangle is formed. The side of the equilateral triangle is


124) Two squares have sides p cm and (p + 5) cms. The sum of their squares is 625 sq.cm. The sides of the squares are


125) The area of a rectangular field is 2000 sq.m and its perimeter is 180 m. The 000000length and breadth are


126) A piece of iron rod costs Rs. 60. If the rod was 2 metre shorter and each metre costs Rs. 1.00 more, the cost would remain unchanged. What is the length of the rod?


127) The diagonal of a rectangle is 5cm and one of at sides is 4 cm. Its area is


128) A train travels first 300 kms at an average rate of 30 Km per hour and further travels the same distance at an average rate of 60 Km per hour then the average speed over the whole distance is


129) If a car is traveling at a constant rate of 45 miles per hour, how many miles does it travel from 10:40 a.m. to 1:00 p.m. of the same day?


130) A motor boat traveling at 18 miles per hour traveled the length of a lake in one quarter of an hour less time than it took when traveling at 12 miles per hour. What was the length in miles of the lake?


131) A freight train and a passenger train start towards each other at the same time from two towns that are 500 miles apart. After 3 hours the trains are still 80 miles apart. If the average rate of speed of the passenger train is 20 miles per hour faster than the average rate of speed of the freight trains, what is the average rate of speed, in miles per hour, of the freight train?


132) If four pens cost Rs. 1.96, what is the greatest number of pens that can be purchased for Rs. 29.40?


133) The total cost curve of the number of copies photograph is linear. The total cost of 5 and 18 copies of photographs are Rs. 80 and Rs. 106 respectively. Then the cost for 10 copies of the photograph is


134) Particular company produces some articles on a day. The cost of production per article is Rs. 2 more than thrice the number of articles and the total cost of production is Rs. 800 on a day then the number of articles is


135) A factory produces 300 units and 900 units at a total cost of Rs. 6800/- and Rs. 10400/- respectively. The linear equation of the total cost line is


136) The total cost curve of the number of copies photograph is linear. the selling price is Rs. 8 per unit the break even point will arise at the level of


137) The total cost curve of the number of copies photograph is linear. if a profit of Rs. 2000/- is to be earned sale and production levels have to be elevated to


138) The total cost curve of the number of copies photograph is linear. if a loss of Rs. 3,000/- is budgeted the factory may maintain production level at


139) A factory produces 200 bulbs for a total cost of Rs. 800/- and 400 bulbs for Rs. 1200/-. The equation of the total cost line is


140) A factory produces 200 bulbs for a total cost of Rs. 800/- the factory intends to produce 1000 bulbs the total cost would be


141) A manufacturer produces 80 T.V. sets at a cost of Rs. 2,20,000 and 125 T.V. sets at a cost of Rs. 2,87,500. Assuming the cost curve to be linear, find the equation of the line and then use it to estimate the cost of 95 sets.


142) If an investment of Rs. 1,000 and Rs. 100 yield an income of Rs. 90 and Rs. 20 respectively. For earning Rs. 50, investment required will be


143) The equation in terms of If an investment of Rs. 1,000 and Rs. 100 yield an income of Rs. 90 and Rs. 20 respectively. For earning Rs. 50, investment required will be


144) If an investment of Rs. 60,000 and Rs. 70,000 respectively yields an income of Rs. 5,750 Rs. 6,500 an investment of Rs. 90,000 would yield income of


145) If an investment of Rs. 60,000 and Rs. 70,000 respectively yields an income of Rs. 5,750 Rs. 6,500 an investment of Rs. 50,000 would yield income of


146) If an investment of Rs. 60,000 and Rs. 70,000 respectively yields an income of Rs. 5,750 Rs. 6,500 an investment of Rs. 90,000 would yield income of


147) One machine can seal 360 packages per hour, and an older machine can seal 140 packages per hour.How many minutes will the two machines working together take to seal a total of 700 packages?


148) If x people working together at the same rate can complete a job in h hours, what part of the same job can one person working along complete in k hours?


149) The wages of 8 men and 6 boys amount to Rs. 33. if 4 men earn Rs. 4.50 more than 5 boys determine the wages of each man and boy.


150) One student is asked to divide a half of a number by 6 and other half by 4 and then to add the two quantities. Instead of doing so the student divides the given number by 5. If the answer is 4 short of the correct answer then the actual answer is -


151) The age of a person is 8 years more than thrice theage of the sum of his two grandsons who were twins. After 8 years his age will be 10 years more then twice the sum of the ages of his grandsons. Then the age of the person when twins born is_______ :


152) The equation of the line passing through points (1, -1) and (-2, 3) is given by


153) In the Co-ordinate Plane, if the points (1,3), (-2, 1) and (k, -1) are Collinear then the value of 'k' is


154) The line joining (-8, 3) and (2, 1) and the line joining (6, 0) and (11, -1) are


155) The line joining (-1, 1) and (2, -2) and the line joining (1, 2) and (2, k) are parallel to each other for the following value of k.


156) The line joining (-1, 1) and (2, -2) and the line joining (1, 2) and (2, k) are perpendicular to each other for the following value of k.


157) The equation of the straight line passing through the points (-5, 2) and (6, -4) is


158) The equation of the line through (-1, 3) and parallel to the line joining (6, 3) and (2, -3) is


159) The equation of a straight line passing through the point (-2, 3) and making intercepts of equal length on the ones is


160) If the three points (3, 1), (5, -5), and (-1, 13) are collinear, then find the equation of the line through these three points


161) Find the equation of the line parallel to the line joining (7,5) and (2,9) and passing through (3,-4)


162) The graph of Y = X is a straight line passing through the point


163) The equation of a straight line is


164) If the graphs of both the equations are same, every point on the graph is a point of intersection then there will be


165) The equation of a straight line in intercept form is


166) The equation of a straight line is


167) 2X - 2 = 0 is a straight line parallel to


168) The equation of line passing through the points (1, -1) and (3, -2) is given by


169) The line joining (-1, 1) and (2, -2) and the line joining (1, 2) and (K, 3) are perpendicular to each other for the value of K.


170) Find the equation of the line with slope -0.25 and (-2, -4) on the line


171) The equation of a line passing through (3, 4) and slope 2 is


172) Find the distance between the pair of points p (-5, 2) and q (-3, -4)


173) The points (-3, 4) (2, 4) and (1, 2) are the vertices of a triangle which is


174) The points (2, 3) (-5, 2) and (-6, -9) are the vertices of a triangle which is


175) The points (2, 3) (-5, 2) and (-4, 9) are the vertices of a triangle which is


176) The points (2,7) (5,3) and (-2,4) are the vertices of a triangle which is


177) The points (2,-1) (-2, 3) (3, 4) and (-3, -2) are the vertices of a


178) The co-ordinates of the circumcentre of a triangle with vertices (3, -2) (-6, 5) and (4, 3) are


179) The centroid of a triangle with vertices (1,-2) (-5, 3) and (7, 2) is given by


180) The ratio in which the point (11, -3) divides the joint of points (3, 4) and (7, 11) is


181) The area of a triangle with vertices (1, 3) (5, 6) and (-3, 4) in terms of square units is


182) The area of a triangle with vertices (0, 0) (1, 2) and (-1, 2) is


183) The area of the triangle with vertices (4, 5) (1, -1) and (2, 1) is


184) The area of the triangle with vertices (-3, 16) (3,-2) and (1, 4) is


185) The area of the triangle with vertices (-1, 1) (-3, 2) and (-5, 4) is


186) The area of the triangle with vertices (pq, r),(qr, p)and(rp, q)is


187) The area of the quadrilateral with vertices (1, 7) (3, -5) (6, -2) and (-4, 2) is


188) The centroid of the triangle with vertices (p - q, p – r)(q - r, q - p) and (r - p, r - q) is located at


189) Points (p, 0) (0 ,q) and (1,1) are collinear if


190) The equation of the line passing through (5 -3) and parallel to the line 2x - 3y +14 = 0 is


191) The points (2, -2) (-1, 1) (8, 4) and (5, 7) are the vertices of a


192) The points (2, 1) (3, 3) (5, 2) and (6, 4) are the vertices of a


193) The equation of the straight line through the point of intersection of x + 2 y - 5 = 0 and x - 3 y - 7 = 0?and passing through the point (1, 0) is:


194) A man sells 6 radios and 4 televisions for Rs. 18,480. If 14 radios and 2 televisions are sold for the same amount, what is the price of a television?


195) The equation of a line which is perpendicular to 5 x - 2 y = 7 and passes through the mid point of the line joining (2, 7) and (4, 1) is:


196) A man starts his job with a certain monthly salary and earns a fixed increment every year. if his salary was Rs. 1,500 after 4 year of service and Rs. 1,800 after 10 years of service, what was his starting salary and what is the annual increment in rupees?


197) The area of a triangle with vertices (1, 3), (5, 6) and (-3, 4) in terms of square units is:


198) The line joining (-1, 1) and (2, -2) and the line joining (1, 2) and (2, k) are perpendicular to each other for the following value of k:


199) The sides of an equilateral triangle are shortened by 12 units. 13 units and 14 units respectively and a right angled triangle is formed. The side of the equilateral triangle is:


200) The value of k for which the points (k, 1), (5, 5) and (10, 7) may be collinear is:


201) A man went to the Reserve Bank of India with Rs. 1,000. He asked the cashier to give him Rs. 5 and Rs. 10 notes only in return. The man got 175 notes in all. Find how many notes of Rs. 5 and Rs. 10 did he received?


202) The centroid of the triangle ABC is at the point (2, 3) A and B are the points (5, 6) and (-1, 4) respectively. The coordinates of C are:


203) A man rowing at the rate of 5 km in an hour in still water takes thrice as much time in going 40 km up the river as in going 40 km down. Find the rate at which the river flows:


204) A straight line passes through the point (3, 2). Find the equation of the striaght line.


205) If the length of a rectangle is 5 cm more than the breadth and if the perimeter of the rectangle is 40 cm, then the length and breadth of the rectangle will be:


206) The point of intersection of the lines 2 x - 5 y = 6 and x + y = 3 is:


207) If arithmetic mean between roots of a quadratic equation is 8 and the geometric mean between them is 5, the equation is _____.


208) Find the point which divides the line joining the points (2, -2) and (-4, 1) in the ration 5 : 2 externally:


209) State the type of Quadrilateral formed by the vertices (1, 1), (4, 4), (4, 8), (1, 5):


210) A seller makes an offer of selling certain articles that can be described by the equation x = 25 - 2 y where 'x' is the price per unit and 'y' denotes the number of unit. The cost price of the article is Rs. 10 per unit. The maximum quantity that can be offered in a single deal to avoid loss is _______.


211) If k x - 4 = (k - 1) x, then which of the following is true?


212) The lines 3 x - 4 y + 5 = 0, 7 x - 8 y + 5 = 0, 4 x + 5 y - 45 = 0 are ___________.


213) The number of students in each section of a school is 36. After admitting 12 new students, four new sections were started. If total number of students in each section now is 30, than the number of sections initially were.


214) A person on a tour has Rs. 9,600 for his expenses. If his tour is extended by 16 days, he has to cut down his daily expenses by Rs. 20, his original duration of tour had been.


215) If 3 x - y = 2, 5 x + a y = 3 and 2 x + y = 3 are concurrent lines, then the value of 'a' is:


216) A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of each article (in Rs.) was 2 more than thrice the number of articles produced on that day. If the total cost of production on that day was Rs. 800, the number of articles produced was


217) If the sides of an equilateral triangle are shortened by 3 units, 4 units and 5 units respectively and a right triangle is formed, then the side of an equilateral triangle is:


218) If the sum of two numbers is 13 and the sum of their squares is 85, then the numbers will be:


219) If the line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24) then the value of x is:


220) The value of k for which points (k, 1), (5, 5) and (10, 7) may be collinear is:


221) If A and B are matrices then which from the following is true?


222) Transpose of a rectangular matrix is a


223) A number consist of two digits such that the digit in one's place thrice the digit in ten's place. If 36 be added then the digits are reversed. Find the number_________.


224) The cost of 2 oranges and 3 apples is Rs. 28. If the cost of an apple is doubled then the cost of 3 oranges and 5 apples is Rs. 75. The original cost of 7 oranges and 4 apples (in Rs.) is:


225) The sum of square of any real positive quantity and its reciprocal is never less than:


226) If one root is half of the other of a quadratic equation and difference in roots is a then the equation is


227) In a multiple choice question paper consisting of 100 questions of 1 mark each, a candidate gets 60% marks. If the candidate attempt all questions and there was a penalty of 0.25 marks for wrong answer, the difference between number of right answers and wrong answer is:


228) If the square of a number exceeds twice of the number by 15, then number that satisfies the condition is