Some Algebraic Implications of Inequalities
Trending Questions
Q.
If then find the value of .
Q.
If then
Q. A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less th an 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?
Q. Let a=log3 log3 2. An integer k satisfying 1<2(−k+3−a)<2, is
Q. A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by
Q. IQ of a person is given by the formula Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.
Q. 17. How to solve log5 +log6
Q. 23.Find all pairs of consecutive odd positive integers both of which are smaller than10 such that their sum is more than 11
Q. 23. Let S={1, 2.100}. The prob of choosing an integer k, 1
Q. If , then is equal to
(a) {f(x)}2
(b) {f(x)}3
(c) 2f(x)
(d) 3f(x)
(a) {f(x)}2
(b) {f(x)}3
(c) 2f(x)
(d) 3f(x)
Q. 33. Solve: log1/2 (x-1/7-x)>1
Q. If , then is equal to
(a) [f(x)]2
(b) [f(x)]3
(c) 2f(x)
(d) 3f(x)
(a) [f(x)]2
(b) [f(x)]3
(c) 2f(x)
(d) 3f(x)
Q. 26.A man wants to cut three lengths from a single piece of board of length 91cm.The second length is to be 3cm longer than the shortest and the third length is tobe twice as long as the shortest. What are the possible lengths of the shortestboard if the third piece is to be at least 5cm longer than the second?rtest board, then xlengths of the second and third piece, respectively. Thus, x+(x +3)+2xs 91 and2x 2 (x 3) 5],
Q. If mC1 = nC2 , then
(a) 2 m = n
(b) 2 m = n (n + 1)
(c) 2 m = n (n − 1)
(d) 2 n = m (m − 1)
(a) 2 m = n
(b) 2 m = n (n + 1)
(c) 2 m = n (n − 1)
(d) 2 n = m (m − 1)
Q. 25.The longest side of a triangle is 3 times the shortest side and the third side is 2 cmshorter than the longest side. If the perimeter of the triangle is at least 61 cm, findthe minimum length of the shortest side.
Q. How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
Q. For all positive integers n, show that 2nCn + 2nCn − 1 = (2n + 2Cn + 1).
Q. The values of x satisfying log3 are
(a) 2, −4
(b) 1, −3
(c) −1, 3
(d) −1, −3
(a) 2, −4
(b) 1, −3
(c) −1, 3
(d) −1, −3
Q. If P equal to whole root 16 +8√3 - whole root 21- 12√3 then what is the value of p?
Q. Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
(a)
(b) n · n − 1Cr − 1 = (n − r + 1) nCr − 1
(c)
(iv) nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.
(a)
(b) n · n − 1Cr − 1 = (n − r + 1) nCr − 1
(c)
(iv) nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.