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 Find the condition for 'a' such that equation |ax - 2y - 3| + |5x + 9| = 0 has the solution (x, y) where x, y have same sign. 


 In ∆ABC , AD ia the altitude from A onto the side BC. If b > c , angle C =23° and AD = abc/(b² - c²) , then angle B is equal to
a. 83°
b. 113°
c. 123°
d. 75°
e. NoT 

  A function f(x) is said to be strictly increasing if f (x1) > f (x2) for x1 > x2. The number of strictly increasing functions that can be defined from set A with 4 positive integers to set B with 6 positive integers is? 

 f(x) be a function for every real x, f(x+1) - f(x) = f(x-2) - f(x-1) and f(3) = 3 then find f(511) ? 

This is an easy question but the idea isn't striking me. Please shower your insights. 


 A polynomial f(x) with positive integer coefficients satisfies f(1) = 12 and f(12) = 2080. Find the last three digits of f(10).  

Find the change in percentage profit for a fruit vendor who, after finding 20% of the fruits rotten, increase his selling price by 10% over and above 15% that he was already charging?

 Q). f(x) + f (1/x) = f(x) f(1/x)
f(4) = 6
Find f(6). 


Please try solving this and let me know the solution.Thanks

Which book to refer if I am weak in QA? Arun Sharma or Sarvesh?

Babu rao goes for a 7-day trip in India . There are four cities A, B, C, and D in the India . Each day Babu visits one city, and he will not visit the same city on two consecutive days. Given that he visits City A on both Day 1 and Day 7, how many different possible itineraries are there for his 7-day trip? 

Please share the detailed approach.

If anyone here has bought Cracku mocks.Can you tell me how many people are giving Cracku Mocks?

Find the remainder when 4^120 is divided by 143.

Find the remainder when 3^666 is divided by 182. Please Explain the procedure.

In a class of 50 students, 25 passed in physics, 27 in maths, 29 in chem, 33 in bio and 35 in geo. What is the max no. of students passed in at least 3 subjects?


a. 49 b. 50 c.25 d.29


Kindly explain the process. Thank you.

  Raju likes the number 17. He likes monic quadratics (they are his favourite) with integer coefficients such that 17 is a root of the quadratic and the roots differ by no more than 17. Compute the sum of the coefficients of all of Raju's favorite polynomials. (A monic quadratic is a quadratic polynomial whose x^2 term has a coefficient of 1.) 


 Find numerically the largest term in the expansion of (2+3x)^9 when x=3/2. 

I have completed Sarvesh Verma. What should I do now ? I have time material with me. Should I do it or go for past mocks.? TIA

Solution pls