std 12 itihas | ch 2 | 18મી સદીનો ઉત્તરાર્ધ અને સત્તાપ્રાપ્તિ માટે સંઘર્ષ | part 1 | vijay sir

The roots of equation x^2+2(a-3)x+9=0 lie between -6 and 1 and 2, h_1, h_2, …, h_20 [a] are in H.P., where [a] denotes the integeral part of a and 2,a_1,a_2,..a_20 [a] are in A.P. then a_3h_18= (A) 6 (B) 12 (C) 3 (D) none of these

Median of a distribution is the value of the variable which divides it into equal parts . In case of individual observations x_1,x_2 .. x_n , if the number of observations is odd, then median is the value of ((n+1)/2) th observation when the observations have been arranged in ascending or descending order of magnitude. In case of even number of observations median is the A.M. of the values of (n/2) th and (n/2+1) th observations, arranged in ascending or descending order of magnitude . The mode of distribution is that value of the variable for which the frequency is maximum . Median of the distribution 25,20,11,3,12,18,17 ,9,21,22 is

Median of a distribution is the value of the variable which divides it into equal parts . In case of individual observations x_1,x_2 .. x_n , if the number of observations is odd, then median is the value of ((n+1)/2) th observation when the observations have been arranged in ascending or descending order of magnitude. In case of even number of observations median is the A.M. of the values of (n/2) th and (n/2+1) th observations, arranged in ascending or descending order of magnitude . The mode of distribution is that value of the variable for which the frequency is maximum . The mode of following series is {:("value (x)",40,44,48,52,56,62,64,72,76),("frequency (f)",10,12,14,20,15,19,18,8,4):}

Over the past 200 working days, the number of defective parts produced by a machine is given in the following table : |{:("Number of","0 1 2 3 4 5 6 7 8 9 10 11 12 13"),("defective parts",),("Days","50 32 22 18 12 12 10 10 10 8 6 6 2 2"):}| Determine the probability that tomorrow's output will have : (i) no defective part. (ii) at least one defective part, (iii) not more than 5 defective parts, (iv) more than 13 defective parts.

Pipes A, B and C can fill an empty tank in 12 minutes, 24 minutes and 36 minutes respectively. Pipes D and E can empty the full tank in 18 minutes and 72 minutes respectively. If all of them are opened simultaneously, then find the time taken to fill the empty tank. The following are the steps involved in solving the above problem. Arrange them in sequential order. (11)/(72)-(5)/(72)=(6)/(72)=(1)/(12) The work done by 5 pipes in1 minute. =((1)/(12)+(1)/(24)+(1)/(36))-((1)/(18)+(1)/(72)) ((6+3+2)/(72))-((4+1)/(72)) The part of tank filled by A,B and C in 1 minute is 1/12,1/24 and 1/36 respectively. The part of the tank emptied by D and E in 1 minute is 1/18 and 1/72 respectively.

Pipes A, B and C can fill an empty tank in 12 minutes, 24 minutes and 36 minutes respectively. Pipes D and E can empty the full tank in 18 minutes and 72 minutes respectively. If all of them are opened simultaneously, then find the time taken to fill the empty tank. The following are the steps involved in solving the above problem. Arrange them in sequential order. (11)/(72)-(5)/(72)=(6)/(72)=(1)/(12) The work done by 5 pipes in1 minute. =((1)/(12)+(1)/(24)+(1)/(36))-((1)/(18)+(1)/(72)) ((6+3+2)/(72))-((4+1)/(72)) The part of tank filled by A,B and C in 1 minute is 1/12,1/24 and 1/36 respectively. The part of the tank emptied by D and E in 1 minute is 1/18 and 1/72 respectively.

Stearic acid [CH_(3)(CH_(2))_(16)CO_(2)H] is a fatty acid the part of fat that stores most of the energy .1.0 g of Stearic acid was burnt in a bomb calorimeter . The bomb had capacity of 652 J//^(@)C . If the temperature of 500 g water rose from 25.0 to 39.3^(@)C how much heat is released when the stearic acid was burned? ["Given "C_(p)(H_(2)O)=4.18J//g^(@)c]