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Class 11 || Basic of Coordinate Geometry || IIT-JEE || Board Exams

If 10^n+3xx4^(n+2)+lambda is divisible by 9 or all n N , then the least positive integral value of lambda is a. 5 b. 3 c. 7 d. 1

Show that the relation R defined in the set A of all triangles as R={(T_1,T_2): T_1( i s s i m i l a r t o T)_2} , is equivalence relation. Consider three right angle triangles T_1 with sides 3, 4, 5, T_2 with sides 5, 12, 13 and T_3 w

If all the letters of the word IIT-JEE are written at random in a row, then the probability that both I's come before T, is (a)1/5 (b) 1/(30) (c) 1/(10) (d) 1/3

If all the letters of the word IIT-JEE are written at random in a row, then the probability that both I's come before T, is 1/(15) b. 1/(30) c. 1/(10) d. 1/3

Show that the relation R defined on the set A of all triangles in a plane as R={(T_1,\ T_2): T_1 is similar to T_2) is an equivalence relation. Consider three right angle triangle T_1 with sides 3,\ 4,\ 5; T_2 with sides 5,\ 12 ,\ 13 and T_3 with sides 6, 8, 10. Which triangles among T_1,\ T_2 and T_3 are related?

Consider the quadratic equation (c - 5)x^(2) - 2cx + (c - 4) = 0, c ne 5 . Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is a. 11 b. 18 c. 10 d. 12

Probability that a student will succeed in I.I.T. Entrance test is 0.2 and that he will succeed in Roorkee entrance test is 0.5. If the probability that he will be successful at both the places is 0.3, then the probability that he does not succeed at both the places, is

An investigator interviewed 100 students to determine their preferences for the three drinks, milk (M), coffee (C ) and tea (T). He reported the following: 10 students has all three drinks M, C, T, 20 had M and C, 30 had C and T, 25 had M and T, 12 had M only, 5 had C only and 8 had T only. Using a Venn diagram, find how many did not take any of the three drinks?