Q 26 short solution
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St: some b are not a Con: 1. all a are b is a possibility. 2. No a are b is a possibility. Answer?
Tier 1ki.grammer mein kuch selected padhna hota hai kya.sirf tier1ka I am asking
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Q:- A person borrows some money for 5 yrs and the ratio of loan amount to total interest amount is 5:2 . The ratio of loan amount : interest rate is ??
Ques-If x^3 +y^3=72 and x*y=6(x>y),then x-y =?
SSC 2015 Question.
in an election only two candidates contested . 24 % per cent did not vote and 150 votes were declared invalid. the winner got 500 votes than his opponent and thus secured 40% of total votes on the voters list.the Percentage votes of the defeated out of the total vote caste.
45.11
48.7
50.67
52.63
62
Lo dosto 38 lakh bhare gye hai..SSC mein...Abh lelo ..Naukari..
Ye kiran 5800 leni.zaruri hai kya...kiran solved papers in maths le liye hain agar to? and paramount maths bhi ho to?
Type I: a sinɸ ± b cosɸ, a sinɸ ± b sinɸ, a cosɸ ± b cosɸ
Maximum value = √ (a2 + b2)
Minimum value = - √ (a2 + b2)
Example: Find the minimum and maximum value of 3 sinɸ + 4 sinɸ
Minimum value = - √ (32 + 42) = -5
Maximum value = √ (32 + 42) = 5
Type 2: (sinɸ cosɸ)^n
Minimum value = (1/2)^n
The maximum value can go up to infinity.
Example: Find the minimum value of sin^4ɸ cos^4ɸ
Minimum value = (1/2)^4 = 1/16
Type 3: a sin^2ɸ + b cos^2ɸ
If a > b, Maximum value = a and Minimum value = b
If a
Example: Find the minimum and maximum values of 3 sin^2ɸ + 5 cos^2ɸ
First check, here a So Maximum value = 5 and Minimum value = 3
*Note: You do not have to learn this formula, just observe here that if the equation is of type a sin^2ɸ + b cos^2ɸ, no matter what, the maximum value is the larger of values (a, b) and minimum value is smaller of values(a, b).
Type 4: a sin^2ɸ + b cosec^2ɸ, a cos^2ɸ + b sec^2ɸ, a tan^2ɸ + b cot^2ɸ
Minimum value = 2√(ab)
The maximum value can go up to infinity.
Example: Find the minimum value of 4 cos^2ɸ + 9 sec^2ɸ
Observe the case, so Minimum value = 2√(4*9) = 12
*Note: In these formulae, reciprocal of one another is there.
Now these above given formulae can be used to deduce minimum and maximum values of other trigonometric functions also.
We are providing some examples:
Example 1: Minimum value of a sec^2ɸ + b cosec^2ɸ ?
We do not have a formula for this, lets continue
The given function can be written as
a (1 + tan^2ɸ) + b(1 + cot^2ɸ)
= a + b + a tan^2ɸ + b cot^2ɸ
= (a+b) + (a tan^2ɸ + b cot^2ɸ)
Now observe that we have the formula for finding min value of a tan^2ɸ + b cot^2ɸ
So here minimum value is
(a+b) + 2√(ab)
Now find the minimum value of a question asked in SSC CGL 2012 Exam:
Example 2: sin^2ɸ + cos^2ɸ + sec^2ɸ + cosec^2ɸ + tan^2ɸ + cot^2ɸ
First try it yourself and then see the solution
sin^2ɸ + cos^2ɸ + sec^2ɸ + cosec^2ɸ + tan^2ɸ + cot^2ɸ
= 1 + sec^2ɸ + cosec^2ɸ + tan^2ɸ + cot^2ɸ.........................(i)
Now 1 + tan^2ɸ = sec^2ɸ
So (i) = 2sec^2ɸ + cosec^2ɸ + cot^2ɸ.......................................(ii)
Now cot^2ɸ = cosec^2ɸ - 1
So (ii) = 2sec^2ɸ + cosec^2ɸ + cosec^2ɸ - 1
= 2sec^2ɸ + 2cosec^2ɸ - 1
Now see we had find the min value of 2sec^2ɸ + 2cosec^2ɸ type above
So now min value = 2 + 2 + 2√(2*2) - 1 = 4 + 4 - 1 = 7
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hello friends i m new here pls tell me hws preparation going on for cgl ....and hw m i do......
I have given many mocks up till now and my average scoring section wise is 45,25,45,35 for reasoning, gk,math and eng respectively..I want to improve upon my gk...someone s suggest a suitable strategy for one month to improve my score in gk..thanks
is there any chance to increase cgl posts?
Q 104. Ans option 1. How to solve in less than 1 min??
Q 109. Ans option 4. How to solve this in less than 1 minute??
Driven by the desire to save trees (1) / residents of locality (2) / has started using solar appliances (3) / for their everyday needs. (4) / No error (5) Koi bataao iska bhai.. mujhe 'have' in plc of has lag raha in part 3. Bt kai bol rhe "being driven" in plc of driven! Wht shud be crrct???
Mahendra's online test series is good for ssc?