NUmerical ability and enchancement skills sem 2 kuk pyq 2024

Based on the provided document, here are the questions: **Compulsory Question (Unit-I)** * (i) Evaluate $70 \\div 14 \\times 3 - 45 \\div 9$. * (ii) If $x:y=2:3$ and $y:z=4:5$, find $x:y:z$. * (iii) Find the $6^{th}$ term of the sequence $1, -\\frac{1}{2}, \\frac{1}{4}, -\\frac{1}{8}, \\dots$ * (iv) Find the average of all prime numbers between 30 and 50. * (v) Today is Monday. After 61 days what will be the day of the week? * (vi) Find the characteristic of log 8954. * (vii) Find the square root of 1369. **Unit-II** * **2.** (a) Prove that $\\sqrt{2}$ is not a rational number. (b) If $x=3+2\\sqrt{2}$, find the value of $\\sqrt{x}-\\frac{1}{\\sqrt{x}}$. * **3.** (a) Evaluate $\\sqrt\[3\]{\\frac{125}{216}}$. (b) Prove that $(\\frac{x^{a}}{x^{b}})^{a+b}(\\frac{x^{b}}{x^{c}})^{b+c}(\\frac{x^{c}}{x^{a}})^{c+a}=1$. **Unit-III** * **4.** (a) Find the smallest 5 digit number which is divisible by 21, 28, 36, 45. (b) The ratio of present ages of Supriya and her mother is 2:9. Mother's age at the time of birth of Supriya was 28 years. Find their present ages. * **5.** (a) Which number should be subtracted from each of 11, 23 and 53 in order that the remainders would be in continued proportion? (b) The sum of three numbers in A.P. is 24 and their product is 440. Find the numbers. **Unit-IV** * **6.** (a) A medical student has to secure 40% marks to pass. He gets 80 marks and fails by 60 marks. Find the maximum marks. (b) The cost of one type of rice is 85 per kg and cost of other type of rice is 125 per kg. If both types of rice are mixed in the ratio 2:3, then find the price per kg of mixed rice. * **7.** (a) A dealer sold two coolers at 2,970 each. On selling one cooler he gained 10% and on selling the other he lost 10%. Find the dealer's gain or loss percent. (b) Shivam travels from A to B a distance of 250 km in $5\\frac{1}{2}$ hours. He returns to A in $4\\frac{1}{2}$ hours. Find his average speed. **Unit-V** * **8.** (a) Solve for $x$: $\\log(10x+5)-\\log(x+4)=\\log 2$. (b) A rectangular grassy plot is 124 m long and 96 m broad. It has a path 3.2 m wide all around it outside the plot. Find the area of the path and the cost of constructing it at the rate of 17.50 per square meter. * **9.** (a) Solve the equation $11^{4x-5}\\times3^{2x}=5^{3-x}\\times7^{x}$. (b) A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone with a radius of its base as 1.2 cm. Find the height of the new one.