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### Mathematical Skills | Simple Equations

 Q. No. 1: If x3 - 6x2 + px + q is exactly divisible by x2 -3x +2, then A : p+q>0 and pq>0 B : p+q>0 and pq<0 C : p+q<0 and pq<0 D : p+q<0 and pq>0 Solution
 Q. No. 2: The sequences x1, x2.... and y1, y2........ are in arithmetic progressions such that x1+y1 = 100 and x22-x21 = y99 - y100. Find the sum of the first 100 terms of the progression, (x1+y1), (x2+y2)........... A : 0 B : 9900 C : 10,000 D : 11,000 Solution
P divides his property among his four sons A, B,C and D after donating Rs 20,000 and 10% of his remaining property. The amounts received by the last three sons are in A.P and the amount received by the fourth son is equal to the total amount donated. The first son receives as his share Rs 20,000 more than the share of second son. The last son received Rs 1 lakh less than the eldest son.
 Q. No. 1: What is the total donation made by P? A : Rs 55,000 B : Rs 65,000 C : Rs 75,000 D : Rs 80,000 Solution
 Q. No. 2: Find the share of the third son. A : Rs 80,000 B : Rs 1,00,000 C : Rs 1,20,000 D : Rs 1,50,000 Solution
 Q. No. 4: When  the index  of an exponential expression with a positive base is doubled, then the expression increases by 700%. If one of the values that the base can not have is X which of the following is not a possible value of P? A : 4 B : 8 C : 5 D : 1 Solution
 Q. No. 5: Abhishek had a certain number of Re1 coins, Rs 2 coins and Rs 10 coins. If the number of Re 1 coins he had is six times the number of Rs 2 coins Abhishek had, and the total worth of his coins is Rs 160, find the maximum number of Rs 10 coins Abhishek could have had. A : 12 B : 10 C : 8 D : 6 Solution
 Q. No. 6: In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P. A : 162 B : 144 C : 156 D : 136 Solution
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