  # IIFT 2018

Instructions

For the following questions answer them individually

Question 101

# The roots of quadratic equation $$y^2 -8y + 14$$ are $$\alpha$$ and $$\beta$$. Find the value of $$(1 + \alpha + \beta^2)(1 + \beta + \alpha^2)$$ Question 102

# $$\frac{1}{\log_x yz + 1} + \frac{1}{\log_y xz + 1} + \frac{1}{\log_z xy + 1}$$ = ? Question 103

# Ram, Ravi and Ratan can alone finish an assignment in 9 days, 12 days and 15 days respectively. They decide to complete a work by working in turns. Ram works alone on Monday, Ravi does the work alone on Tuesday, followed by Ratan working alone on Wednesday & so on. What proportion of the complete work is done by Ravi? Question 104

# Let $$S_1$$ be a square of side 4 cm. Circle $$C_1$$ circumscribes the square $$S_1$$ such that all its corners are on $$C_1$$. Another square $$S_2$$ circumscribes the circle $$C_1$$. Circle $$C_2$$ circumscribes the square $$S_2$$, and square $$S_3$$ circumscribes circle $$C_2$$, & so on. If $$A_N$$ is the area between the square $$S_N$$ and the circle $$C_N$$, where N is the natural number. then the ratio of sum of all $$A_N$$ to $$A_l$$ is Question 105

# Joseph diametrically crosses a semi-circular playground and takes 48 seconds less than if he crosses the playground along the semi-circular path. If he walks 50 metres in one minute, the diameter of playground is Question 106

# Garima had only Rs. 200. Rs. 500 and Rs. 2000 notes in her wallet. She goes to Shoppers Stop. purchases some dresses and gives half of her Rs. 2000 notes & in turn receives same number of Rs. 200 notes. She then goes to a restaurant and gives all her Rs. 500 notes and receives thirty Rs. 2000 notes, which increases the number of Rs. 2000 notes she had by. 75%.- If now she has fifty Rs. 200 notes. what were the original number of Rs. 2000 and Rs. 200 notes she had at the start? Question 107

# A metallic solid is made up of a solid cylindrical base with a solid cone on its top. The radius of the base of the cone is 5 cm. and the ratio of the height of the cylinder and the cone is 3:2. A cylindrical hole is drilled through the solid with height equal to 2/$$3^{rd}$$ of the height of solid. What should be the radius (in cm) of the hole so that the volume of the hole is 1/$$3^{rd}$$ of the volume of the metallic solid after drilling? Question 108

# Nitin installed an overhead tank on the roof of his newly constructed house. Three taps are connected to the tank: 2 taps A and B to fill the tank and one tap C to empty it. Tap A alone can fill the tank in 12 hours, while tap B alone takes one and a half times more time than tap A to fill the tank completely. Tap C alone can empty a completely filled tank in 36 hours. Yesterday, to fill the tank, Nitin first opened tap A, and then after 2 hours opened tap B also. However after 6 hours he realised that tap C was open fi-om the very beginning. He quickly closes tap C. What will be the total time required to fill the tank? Question 109

# At the foot of the mountain, the angle of elevation of the summit at the top of the mountain is 45°. After ascending 100 metres, at a slope of 30° up the mountain towards the summit. the angle of elevation of the summit is 60°. Find the height of the summit. Question 110

# Land Cruiser Prado, the latest SUV from Toyota Motors, consumes diesel at the rate of $$\frac{1}{400}\left\{ \frac{1000}{x} + x\right\}$$litres per Km. when travelling at the speed of x km/hr. The diesel costs Rs. 65 per litre and the driver is paid Rs. 50 per hour. Find the steady speed that will minimize the total cost of a 1000 km trip? OR