Two numbers when divided by a certain divisor give remainder 437 and 298. When their sum is divided by the same divisor, the remainder is 236. Find the divisor. a) 486 b) 499 c) 577 d) 481 Sol: Required divisor = (437+ 298 – 236) = 499

When 200 is divided by a positive integer x, the remainder is 8. How many values of x are there?  (a) 7 (b) 5 (c) 8 (d) 6 Sol: When 200 is divided by x remainder is 8. So, the number exactly divisible by x is 192. Multiples of 192 = 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, ...

If p and q are the lengths of perpendicular from the origin to the lines x cos θ−y sin θ=k cos 2θ and x sec θ+y cosec θ=k, respectively. Prove that p2+4q2=k2 Ans:

Working alone A can do the task in 27 hours and B can do it in 54 hours. Find share if A, B and C get paid Rs. 4,320 for completing the task in 12 hours on which they worked together? a) 1440 Rs. b) 960 Rs. c) 1920 Rs. d) 1280 Rs. Sol: Let’s take Total task = 108 units (LCM of 27, 54 and 12)  ⇒ ...

Which of the following is largest 14/15, 23/24, 27/26, 440/441, 51/53 a) 14/15 b) 51/53 c)  27/26 d)  440/441

If x(x-5)=-1, then the value of x3(x3-110)=? a)            1 b)            -1 c)            2 d)            -2 Sol:

Q. If p and q are the lengths of the perpendiculars from the origin on the lines, x cosecα−ysecα=kcot2α and xsinα+ycosα=ksin2α respectively, then k2 is equal to : Sol: Given lines arex cosecα−ysecα=kcot2α and xsinα+ycosα=ksin2αDistance from ...

The ratio of income of A, B and C is 3 : 4 : 5 and there expenses are in the ratio 4 : 5 : 6. If savings of A   of his income. Then find the ratio of their savings. a) 12 : 19 : 26 b) 13 : 20 : 27 c) 19 : 12 : 26 d) 14 : 21 : 29  Sol: Saving ratio = 12 : 19 : 26

A cylindrical vessel of radius 13.5m is to be filled with petrol. How many liters of petrol will increase the height of the liquid in the vessel by 10.5cm a)            60250 liter ...

Let x = 224 and, y = 322. If the highest common factor of 23x and axy is divisible by x and y, then what can be the possible value of a? a)            18 b)            16 c)            19 d)            20 Sol: Given:  x = 224, y = 322  Calculation:  HCF(Highest Common Factor) of a and b is the ...