Q1. The arithmetic mean of the following numbers is
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7
(a) 4
(b) 5
(c) 14
(d) 20
Q2. If the average of 6 consecutive even numbers is 25, the difference between the largest and the smallest number is:
(a) 18
(b) 10
(c) 12
(d) 14
Q3. The average age of the family of 5 members is 24. If the present age of youngest member is 8 years, then what was the average age of the family just before the birth of the youngest member?
(a) 20 years
(b) 16 years
(c) 12 years
(d) 18 years
Q4. The difference between the simple and compound interest on a certain sum of money for 2 years at 4% per annum is Rs. 1. The sum is:
(a) Rs. 676
(b) Rs. 675
(c) Rs. 625
(d) Rs. 700
Q5. The simple interest accrued on an amount of Rs. 15500 at the end of three years is Rs. 5580. What would be the compound interest accrued on the same amount at the same rate in the same period?
(a) Rs. 6726.348
(b) Rs. 6276.384
(c) Rs. 6267.834
(d) Rs. 6627.438
Q6. If logx/(a^2+ab+b^2 )=logy/(b^2+bc+c^2 )=logz/(c^2+ca+a^2 ), then x^(a-b).y^(b-c).z^(c-a) =
(a) 0
(b) – 1
(c) 1
(d) 2
Q7. If x = 11, then the value of x^5-12x^4+12x^3-12x^2+12x-1 is:
(a) 5
(b) 10
(c) 15
(d) 20
Q8. If (x^(3/2)-(xy)^(1/2)+x^(1/2)(y)-y^(3/2) ) is divided by (x^(1/2)-y^(1/2) ), then the quotient is:
(a) x + y
(b) x – y
(c) x^(1/2)+y^(1/2)
(d) x^2-y^2
Q9. The product of two non-zero expressions is (x + y + z)p^3. If their H.C.F. is p^2, their L.C.M. is:
(a) (x + y)p
(b) (y + 2)p
(c) (z + x)p
(d) (x + y + z)p
Q10. There are some parrots and some tigers in a forest. If the total number of animal heads in the forest are 858 and total number of animal legs are 1746, what is the number of parrots in the forest?
(a) 845
(b) 843
(c) 800
(d) None of these
Solutions
S1. Ans.(b)
Sol. required mean
=(1×1+2×2+3×3+4×4+5×5+6×6+7×7)/(1+2+3+4+5+6+7)
=(1+4+9+16+25+36+49)/28
=140/28=5
S2. Ans.(b)
Sol. Let, the numbers be x, x + 2, …, x + 10
∴ Required difference = x + 10 – x = 10
S3. Ans.(a)
Sol. Total age of the family of five numbers
= 24 × 5 = 120
Total age of the family of 5 members before 8 years
= 120 – 5 × 8
= 120 – 40 = 80
So, the required average age = 80/4 = 20 years.
S4. Ans.(c)
Sol. Sum = Difference (100/R)^2
∴ Sum = 1(100/R)^2 = Rs. 625.
S5. Ans.(b)
Sol. Rate of interest = (5580 × 100)/(15500 × 3) = 12%
After compounding 12% for 3 years, the equivalent rate of simple interest = 40.4928%.
Now, (12 × 3) = 36% = 5580
∴ 40.4918% = 5580/36 × 40.4928 = Rs. 6276.384
S6. Ans.(c)
Sol. Each ratio = k ⇒ log x=k(a^2+ab+b^2 )
⇒(a-b)logx=k(a^3-b^3)
⇒logx^(a-b)=k(a^3-b^3 )⇒x^(a-b)=e^k(a^3-b^3 )
Similarly, y^(b-c) = e^k(b^3-c^3 ) ,z^(c-a)=e^k(c^3-a^3 )
∴x^(a-b).y^(b-c).z^(c-a)=e^0=1.
S7. Ans.(b)
Sol. x = 11 (Given)
∴x^5-12x^4+12x^3-12x^2+12x-1
=x^5-(11+1) x^4+(11+1) x^3-(11+1) x^2+(11+1)x-1
=x^5-11x^4-x^4+11x^3+x^3-11x^2-x^2+11x+x-1
When x = 11,
=(11)^5-(11)^5-(11)^4+(11)^4+(11)^3-(11)^3-(11)^2+(11)^2+11-1
= 10
S8. Ans.(a)
Sol. x^(3/2)-(xy)^(1/2)+x^(1/2) y-y^(3/2)
=x(x^(1/2)-y^(1/2) )+y(x^(1/2)-y^(1/2) )
= (x + y) (x^(1/2)-y^(1/2 ) )
∴(x^(3/2)-(xy)^(1/2)+x^(1/2) y-y^(3/2))/(x^(1/2)-y^(1/2) )
=(x+y).
S9. Ans. (d)
Sol. L.C.M. = Product/(H.C.F.)=((x+y+z) p^3)/p^2
= (x + y + z)p.
S10. Ans.(b)
Let total no. of parrots and tigers in the forest are p and t respectively
A.T.Q.
P+t=858
2p+4t=1746
On solving these two equations
t= 15 and p= 843
