Inequalities L-2 | Intervals | By Naman Agarwal | JEE Mains and Advanced | CBSE

Let complex number 'z' satisfy the inequality 2 le | x| le 4 . A point P is selected in this region at random. The probability that argument of P lies in the interval [-pi/4,pi/4] is 1/K , then K =

Dinitrogen pentoxide decomposes to NO_(2) and O_(2) following first order kinetics N_(2)O_(5)(g) rarr 2NO_(2)+O_(2)(g) 0.2 mole of N_(2)O_(5) was taken in 2L vessel and heated at 200K. The concentrated of N_(2)O_(5) is measured at different intervals . Following graphs A and B were obtained from the data. Slope of straight line in graph 'A' is -1 .2 xx 10^(2) sec^(-1) . What is half life of the reaction ?

Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0):} where a is a positive constant . The interval in which f '(x) is increasing is [(k)/(a ),(a)/(l)], Then k +l is equal to ______

The reaction between Cr_(2)O_(7)^(2-) and HNO_(2) in an acidic medium is Cr_(2)O_(7)^(2-) + 5H^(o+) + 3HNO_(2) rarr 2Cr^(3+) + 3NO_(3)^(ɵ) + 4H_(2)O . The rate of disappearance of Cr_(2)O_(7)^(2-) is found to be 2.4 xx 10^(-4) mol L^(-1) s^(-1) during measured time interval. What will be the rate of disappearance of HNO_(2) during the same time interval? (a) 2.4xx10^(-4) (b) 7.2xx10^(-4) (c) 4.8xx10^(-4) (d) 0.8xx10^(-4)

The set of values of a for which the inequality, x^2 + ax + a^2 + 6a < 0 is satisfied for all x belongs (1, 2) lies in the interval:

Let l be the lower class limit of a class-interval in a frequency distribution and m be the mid-point of the class. Then, the upper class limit of the class is (a) m+(l+m)/2 (b) l+(m+1)/2 (c) 2m-l (d) (m-2l)

It is stated in the previous problem that a pilse travels from the bottom to the top of a hanging rope of length L in the time interval Delta=2sqrt(L/g) . Use this result to answer the following question. (It is not neccesary to set up any new integrations.) (a) over what time interval does a pulse travel halfway up the rope? Give your answer as a fraction of the quantity 2sqrt(L/g) . (b) A pulse starts travelling up the rope. how far it travelled after a time interval sqrtL/g) ?

Two particle are initially moving with angular momentum vec(L)_(1) and vec(L)_(2) in a region of space with no external torque. A constant external torque vec( tau) then acts on one particle, but not on the other particle, for a time interval Delta t . What is the change in the total angular momentum of the two particles ?

Let S be the set of all non-zero real numbers such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1a n dx_2 satisfying the inequality |x_1-x_2|<1. Which of the following intervals is (are) a subset (s) of S ? (1/2,1/(sqrt(5))) b. (1/(sqrt(5)),0) c. (0,1/(sqrt(5))) d. (1/(sqrt(5)),1/2)