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units of 7 754 =7 377 *7 2 therefore 7 2 =49 and the units digit of it is 9
Two events are independent if the occurence of one event does not effect the probability of other. Lets say 1 st event to be A and 2 nd to be B. Let C to be intersection of A and B. A and B are...
You will get infinite number of ordered pairs for this equation. 10y + 10 x = xy –1 y = – (1 + 10x)/(10 – x) & x = – (1 + 10y)/(10 – y) This is not defined for x = 10 & y = 10
Engineering mathematics Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of...
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HI Student, The cofficient of middle term is greatest for an expansion in the form of (1+x)n . If n is odd there are even terms there will be 2 middle terms and if n is even there will be odd terms...
HI Student The cofficient of middle term is greatest for an expansion in the form of (1+x) n . If n is odd there are even terms there will be 2 middle terms and if n is even there will be odd terms...
Approach: we’ll first satisfy the condition given in the question. Answer: For filling each row with four letters taken at random, choices are 4. So in 4! ways. Now, we are free to fill the...
Hello, girija its simple. 93 is not a prime number because 93 is divisible by 3. To prove, any number as a prime number or vice-versa, just try to divide it from prime numbers like 2, 3, 5, 7, 11, 13,...
91 is not a prime number it has 4 factors 1,7,13,19
We have 1 + w + w 2 = 0 & w 3 = 1 (1 – w)(1 – w 2 )(1 – w 4 )(1 – w 5 ) = (1 – w)(1 – w 2 )(1 – w 3 .w)(1 – w 3 .w 2 ) = (1 – w)(1 – w 2 )(1 – w)(1 – w 2 ) (Since w 3 = 1) = (1 – w) 2 (1 – w 2 ) 2 =(1...
For AP a=1 2nd term(AP) = a+d =1st term of (GP)= b1 10th term(AP) = a+9d =2nd term of (GP)=b2 34th term(AP) = a+33d =3rd term of (GP)=b3 For a GP (b2)^2 = b1*b3 Put the values, form a quadratic...
xyz+xy+xz+yz can be expressed as (x + 1)(y + 1)(z + 1) - (x + y + z + 1) Since x+y+z=10 xyz+xy+xz+yz = (x + 1)(y + 1)(z + 1) - 11 So now we have to maximize (x + 1)(y + 1)(z + 1) - 11 Hello Student,...
Hello Student, Please find the solution Given a+b+c =3 Write this as Now we will use AM >= GM So Therefore, So greatest value of is
please provide the limits of sigma...
Hello Student, Please find the trick to solve the question define a polynomial in 'a' like this f(a)= (a+b)^3- (a-b)^3-8ab^2 Now check the value of f(b)= (b+b)^3- (b-b)^3-8b*b^2 = 0 since...
Q – √x / X its same as you divide √2 / 2 = 1/ √2 => √x / x = 1/√x but if you want full derivation here it is since we know that √x = x ½ ------------------------------------- 1 and x = x 1...
its not coming take it as 10 > d so d should be less than 10
Sorry sir.. i am extremely sorry.. Actually i typed in the wrong question.. it was (7-5x)^11, where x=2/3.. I am extremely sorry once again. Sir please give me the correct answer for this.
xy + x + y = 23 xy+x+y+1=24 (x+1)(y+1)=24..........................1 xz + x + z = 41 xz + x + z + 1 = 42 (x+1)(z+1) = 42..............2 yz + y + z +1 = 28 (y+1)(z+1) = 28...................3 from 1, 2...
look sakshi, please solve this problem by drawing a neat diagram. it is given that triangle ABC is a right angled triangle right angled at C and D is the mid point of bc . by applying pythagoras...
Let the roots of the equation are . Given that . From the equation Also …...........(1) ….............(2) Also ….......(3) Use (1) and (3) to find . Use the values in (2) to find...
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