CBSE
A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are
12 kg and 13 kg
5 kg and 5 kg
5 kg and 12 kg
5 kg and 13 kg
C.
5 kg and 12 kg
In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals
D.
A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60º at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30º. The height of the tower is
C.
The sum of the series ^{20}C_{0} – ^{20}C_{1} + ^{20}C_{2} – ^{20}C_{3} + …… - ….. + ^{20}C_{10} is-
– ^{20}C_{10}
0
B.
(1 + x)^{20} = ^{20}C_{0} + ^{20}C_{1}x + … + ^{20}C_{10}x_{10} + …+ ^{20}C_{20}x^{20}
put x = − 1,
0 = ^{20}C_{0} − 2^{0}C_{1} + … − ^{20}C_{9} + ^{20}C1_{0} − ^{20}C_{11} + … + ^{20}C_{20}
0 = 2 (^{20}C_{0} − ^{20}C_{1} + … − ^{20}C_{9}) +^{ 20}C_{10}
⇒ ^{20}C_{0} − ^{20}C_{1} + … + ^{20}C_{10 }=
Consider a family of circles which are passing through the point (-1, 1) and are tangent to x-axis. If (h, K) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interva
0 < k < 1/2
k ≥ 1/2
– 1/2 ≤ k ≤ 1/2
k ≤ ½
B.
k ≥ 1/2
Equation of circle (x − h)^{2}+ (y − k)^{2} = k^{2}
It is passing through (− 1, 1) then
(− 1 − h)^{2}+ (1 − k)^{2}= k^{2}
h^{2}+ 2h − 2k + 2 = 0
D ≥ 0
2k − 1 ≥ 0 ⇒ k ≥ 1/2.
The differential equation of all circles passing through the origin and having their centres on the x-axis is
C.
General equation of all such circles is
x^{2}+ y^{2} + 2gx = 0.
Differentiating, we get
If p and q are positive real numbers such that p^{2} + q^{2} = 1, then the maximum value of (p + q) is
2
1/2
D.
The set S: {1, 2, 3, …, 12} is to be partitioned into three sets A, B, C of equal size. Thus, A ∪ B ∪ C = S, A ∩ B = B ∩ C = A ∩ C = φ. The number of ways to partition S is-
12!/3!(4!)^{3}
12!/3!(3!)^{4}
12!/(4!)^{3}
12!/(3!)^{4}
C.
12!/(4!)^{3}
Number of ways
In the binomial expansion of (a - b)n, n ≥ 5, the sum of 5th and 6th terms is zero, then
a/b equals
5/n −4
6 /n −5
n -5 /6
n -4 /5
D.
n -4 /5