Mathematics Questions Test – 1

 

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#1. The area of a right-angled isosceles triangle having hypotenuse 16√2 cm is

#2. The ratio of the monthly incomes of X and Y is 5: 4 and that of their monthly expenditures is 9: 7. If the income of Y is equal to the expenditure of X, then what is the ratio of the savings of X and Y?

#3. The sides of a triangle are in the ratio 2 : 3 : 4. The perimeter of the triangle is 18 cm. The area (in cm2) of the triangle is

#4. if a+b+c=7 and a3+b3+c3-3abc=175, then what is the value of (ab+bc+ca)?

#5. In △ABC, M and N are the points on side BC such that AM ⊥ BC, AN is the bisector of ∠A, and M lies between B and N. If ∠B = 68°, and ∠C=26°, then the measure of ∠MAN is:

#6. LCM of two numbers is 56 times their HCF, with the sum of their HCF and LCM being 1710. If one of the two numbers is 240, then what is the other number?

#7. The greatest four digit number which is exactly divisible by each one of the numbers 12, 18, 21 and 28.

#8. The LCM of four consecutive numbers is 60 The sum of the first two numbers is equal to the fourth number. What is the sum of four numbers?

#9. Let x be the greatest number which when divides 955, 1027, 1075, the remainder in each case is the same. Which of the following is NOT a factor of x?

#10. In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer. I. x2- 12x + 35 = 0 II. y2- 25y + 126 = 0

#11. In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer. I. x2– 35x + 294 = 0 II. y2– 68y + 1140 = 0

#12. A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is:

#13. The area of two equilateral triangles are in the ratio 25 : 36. Their altitudes will be in the ratio :

#14. The diagonal of a right angle isosceles triangle is 5 cm. Its area will be

#15. The number between 4000 and 5000 that is divisible by each of 12, 18, 21 and 32 is

#16. A and B start moving from places X and Y and Y to X, respectively, at the same time on the same day. After crossing each other, A and B take 54/9 hours and 9 hours, respectively, to reach their respective destinations. If the speed of A is 33 km/h, then the speed (in km/h) of B is:

#17. In △PQR, ∠P = 90°. S and T are the mid points of sides PR and PQ, respectively. What is the value of RQ2/(QS2+ RT2)?

#18. In △ABC, D and E are points on the sides AB and AC, respectively, such that DE || BC and DE: BC=6:7. (Area of △ ADE): (Area of trapezium BCED) = ?

#19. Pipes A and B can fill a tank in 12 minutes and 15 minutes, respectively. The tank when full can be emptied by pipe C in x minutes. When all the three pipes are opened simultaneously, the tank is full in 10 minutes. The value of x is:

#20. irection: In the following questions two equations numbered I and II are given. You have to solve both the equations and find relation between x and y. I. x2+ 14x + 48 = 0 II. y2+ 12y + 32 =0

#21. If x2+4y2=17 and xy=2, where x>0,y>0, then what is the value of x3+8y3?

#22. If the numerical value of thes perimeter of an equilateral triangle is √3 times the area of it, then the length of each side of the triangle is

#23. The LCM of 1.2 and 2.7 is:

#24. In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer. I. x2– 37x + 330 = 0 II. y2– 28y + 195 = 0

#25. Each side of an equilateral triangle is 6 cm. Find its area.

#26. From a point in the interior of an equilateral triangle, the length of the perpendiculars to the three sides are 6 cm, 8 cm and 10 cm respectively. The area of the triangle is

#27. Two pipes of length 1.5 m and 1.2 m are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of same size which can be cut from these two lengths will be

#28. In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer. I. 16×2– 32x + 15 = 0 II. 16y2– 48y + 35 = 0

#29. The graphs of the linear equations 3x-2y=8 and 4x+3y=5 interest at the point P(α, β). What is the value of (2 α – β)?

#30. In a quadrilateral ABCD, E is a point in the interior of the quadrilateral such that DE and CE are the bisectors of ∠D and ∠C, respectively. If ∠B = 82° and ∠DEC = 80°, then ∠A = ?

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