JEE Advanced 2016 Question Paper

Area of the region (x,y)∈ℝ2:y≥x+3,5y≤x+9≤15is equal to

A transparent slab of thickness d has a refractive index n (z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2 (> n1 ), as shown in the figure. A ray of light is incident with angle θi from medium 1 and emerges in medium 2 with refraction angle  θf with a lateral displacement l. Which of the following statement (s) is (are) true?

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30 0C and the entire stored 120 litres of water is initially cooled to 10 0C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is (Specific heat of water is 4.2 kJ kg-1 K-1 and the density of water is 1000 kg m-3 )

In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is T=2π7(R-r)5g.The values of R and r are measured to be (60±1) mm and (10±1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?