Question 1 Roots and Expression Value The roots \( \alpha, \beta \) of the equation \( 3x^2 + \lambda x – 1 = 0 \) satisfy \[ \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15. \] The value of \( (\alpha^3 + \beta^3)^2 \) is: Question 2 Trapezium + Triangles ABCD is a trapezium in which AB is … Read more
Ques 1 When 3^333 is divided by 11, the remainder is Ques 2 A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is 1) 4095 2) 1023 … Read more
Inequality Question All the values of \( x \) satisfying the inequality \( \frac{1}{x + 5} \leq \frac{1}{2x – 3} \) are: 1) \( -5 < x < \frac{3}{2} \) or \( x > \frac{3}{2} \) 2) \( -5 < x < \frac{3}{2} \) or \( \frac{3}{2} < x \leq 8 \) 3) \( x ... Read more
Ages + RatiosWhen Rajesh’s age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima’s age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become 1) 2 : 12) 3 : 23) 4 : 34) 5 : 4 Mixtures … Read more