AM,GM,HM Inequality
Trending Questions
Q. If a, b, c, d be in H.P., then
- ac+bd>b2+c2
- a2+c2>b2+d2
- a2+d2>b2+c2
- ac+bd>b2+d2
Q. The minimum value of the sum of real numbers a−5, a−4, 3a−3, 1, a8 and a10 with a > 0 is___
Q. If a, b, c, d are in H.P., then [RPET 1991]
- a + d > b + c
- ad > bc
- None of these
Both (a) and (b)
Q. A straight line through the vertex P of a traingle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then
- 1PS+1ST<1√QS×SR
- 1PS+1ST>2√QS×SR
- 1PS+1ST<4QR
- 1PS+1ST>4QR
Q. Let bi>1 for i=1, 2, ..., 101. Suppose logeb1.logeb2, ......, logeb101 are in Arithmetic Progression (A.P) with the common diffrence loge2. Suppose a1, a2, ....., a101 are in A.P. such that a1=b1 and a51=b51. If t=b1+b2+...+b51 and s=a1+a2+......+a53. then
- s<t and a101>b101
- s<t and a101<b101
- s>t and a101<b101
- s>t and a101>b101
Q. If x + y + z = 1 and x, y, z are positive numbers such that (1−x)(1−y)(1−z)≥kxyz, then exact value of k is equal to
- 4
- 8
- 16
- 2
Q.
If A is the area and 2s the sum of 3 sides of triangle then
A≤s23(√3)
A≤s22
A>s2(√3)
None of these
Q.
If x, y, z∈R+ then xyx+y+yzy+z+xzx+z is always
≤2(x+y+z)
≤12(x+y+z)
≤4(x+y+z)
None of the above
Q. Let bi>1 for i = 1, 2, .... , 101. Suppose loge b1, loge b2, ……loge b101 are in AP with the common difference loge2. Suppose a1, a2, ……a101 are in AP, such that a1=b1 and a51=b51. If t=b1+b2+……+b51 and s=a1+a2+……+a51, then
- s>t and a101>b101
- s>t and a101<b101
- s<t and a101<b101
- s<t and a101>b101
Q.
If p and q are positive real numbers such that p2+q2=1, then the maximum value of (p+q) is
2.
12
1√2
√2