Grand Test : Mathematics 1A
Q1. The LCM of two numbers is 5040 and their HCF is 12. If one number is 168, the other number is:
Q2. (−7/9) × (5/14) × (−18/25) × (21/10) = ?
Q3. If 63% of a number is 252, then 17% of the same number is:
Q4. A sum of money amounts to ₹17,640 in 2 years at 8% p.a. compound interest. The sum is:
Q5. In a quadrilateral ABCD, diagonals AC and BD intersect at O such that AO/OC = 3/5 and BO/OD = 2/3. The ratio of area of △AOB : area of △COD is:
Q6. The number of vertices of a polyhedron having 12 faces and 30 edges is:
Q7. If x + 1/x = 5, then the value of (x² + 1/x²) is:
Q8. Factorise: 12x² + 37xy + 21y²
Q9. A cylindrical vessel of radius 28 cm is filled with water. If a solid cone of radius 21 cm and height 40 cm is completely immersed in it, the rise in water level is:
Q10. If the angles of a triangle are in the ratio 2:3:7, then the triangle is:
Q11. The value of (256)^0.16 × (256)^0.09 is:
Q12. Three numbers are in the ratio 3:4:5 and their LCM is 2520. The smallest number is:
Q13. If 5^x−2 × 3^2x−5 = 45, then x =
Q14. The mean of 11 observations is 50. If one observation 40 is replaced by 70, the new mean is:
Q15. A shopkeeper marks his goods 40% above cost price and gives 15% discount. If he still gains 10%, the percentage he marked above cost price is actually:
Q16. If a + b + c = 0, then the value of a³ + b³ + c³ is:
Q17. The perimeter of a rhombus is 148 cm and the length of one diagonal is 40 cm. The area of the rhombus is:
Q18. If √(1 + x/900) = 11/10, then x =
Q19. The probability of getting a number greater than 3 when a die is thrown twice and numbers are added is:
Q20. If (x – 2) is a factor of x³ – 6x² + ax + b and a + b = 6, then the values of a and b are:
Q21. The value of k for which the system 2x + 3y = 7 and 4x + ky = 17 has no solution is:
Q22. If 9^2x+1 ÷ 3^3x = 27^x, then x =
Q23. The volume of the largest cube that can be cut from a wooden sphere of diameter 21 cm is:
Q24. In △ABC, DE∥BC, AD = 4 cm, DB = 6 cm, AE = 5 cm. Then EC =
Q25. The value of 0.3¯ + 0.23¯ is:
Q26. If the radius of a cylinder is doubled and height is halved, the volume becomes:
Q27. The number 3.7272… in p/q form is:
Q28. If the selling price of 40 articles is equal to cost price of 48 articles, the percentage loss is:
Q29. A person travels 48 km at 8 km/h, 60 km at 10 km/h and 72 km at 12 km/h. His average speed for the whole journey is:
Q30. If (a + b + c) = 9 and ab + bc + ca = 26, then a³ + b³ + c³ – 3abc =