6. The number of (staircase) paths in the xy-plane from (0, 0) to (7, 5) where...

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6. The number of (staircase) paths in the xy-plane from (0, 0) to (7, 5) where each such path is made up of individual steps going one unit upward (U) or one unit to the right (R). (a) 12C5 (b) 12! (c) 5! 7! (d) 12P5 7. The number of integral solutions of x+y+z=0 with x-5, y 5, z5 is: 8. 9. (a) 134 (b) 136 (c) 138 (d) 140 There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is : (a) 6 (b) 7 (c) 8 (d) 9 Kunal Gaba has n objects, each of weight w. He weighs them in pairs and finds the sum of the weights of all possible pairs is 120 g. When his friend Rakshit weighs them in triplets, the sum of all possible weights is 240 g. The value of n is: (a) 7 (b) 6 (c) 5 (d) 10 1 10. If ||=2, then the set of points x+iy =w== lie on: @ (a) circle (b) ellipse (c) parabola (d) hyoperbola 6. The number of (staircase) paths in the xy-plane from (0, 0) to (7, 5) where each such path is made up of individual steps going one unit upward (U) or one unit to the right (R). (a) 12C5 (b) 12! (c) 5! 7! (d) 12P5 7. The number of integral solutions of x+y+z=0 with x-5, y 5, z5 is: 8. 9. (a) 134 (b) 136 (c) 138 (d) 140 There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is : (a) 6 (b) 7 (c) 8 (d) 9 Kunal Gaba has n objects, each of weight w. He weighs them in pairs and finds the sum of the weights of all possible pairs is 120 g. When his friend Rakshit weighs them in triplets, the sum of all possible weights is 240 g. The value of n is: (a) 7 (b) 6 (c) 5 (d) 10 1 10. If ||=2, then the set of points x+iy =w== lie on: @ (a) circle (b) ellipse (c) parabola (d) hyoperbola