CBSE
The mean of the data set comprising of 16 observations is 16. If one of the observation value 16 is deleted and three new observations valued3,4 and 5 are added to the data, then the mean of the resultant data is
16.8
16.0
15.8
14.0
D.
14.0
Given,
If m is the AMN of two distinct real numbers l and n (l,n>1) and G_{1}, G_{2}, and G3 are three geometric means between l and n, then equals
4l^{2} mn
4lm^{2}n
4 lmn^{2}
4l^{2}m^{2}n^{2}
B.
4lm^{2}n
Given,
m is the AM of l and n
l +n = 2m
and G_{1}, G_{2}, G_{3}, n are in GP
Let r be the common ratio of this GP
G1 = lr
G2 =lr^{2}
G3= lr^{3}
n = lr^{4}
The sum of coefficients of integral powers of x in the binomial expansion of is
A.
Let T_{r+1} be the general term in the expansion of
For the integral power of x, r should be even integer,
therefore, sum of coefficients=
Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A x B, each having at least three elements is:
219
256
275
510
A.
219
Given,
n(A) = 4 n (B) =2
⇒ n(A x B) = 8
Total number of subsets of set (A x B)= 2^{8}
Number of subsets of set A x B having no element (i.e, Φ) = 1
Number of subsets of set AxB having two elements = ^{8}C_{1}
Number of subsets of set A x B having two elements = ^{8}C_{2}
therefore, the number of subsets having atleast three elements,
= 2^{8} x (1+^{8}C_{1} + ^{8}C_{2})
= 2^{8} -1-8-28
= 2^{8} -37
= 256-37 = 219
If the angles of elevation of the top of a tower from three collinear points A, B and C on line leading to the foot of the tower are 30^{o}, 45^{o} and 60^{o} respectively, then the ratio AB: BC is
2:3
A.
6
-6
3
-3
C.
3
α and β are the roots of the equation
x^{2}-6x-2 =0
or
α^{2 }=6x+2
α^{2} = 6α +2
α^{10}= 6 α^{9}+2α^{8} ... (i)
β^{10}= 6 β^{9}+2β^{8} ... (ii)
On subtracting eq (ii) from eq(i), we get
α^{10}- β^{10}= 6 ( α^{9}-β^{9}) + 2 (α^{8} -β^{8})
a_{10} = 6a_{9} + 2a_{8} (∴ a_{n} = α^{n}- β^{n})
⇒ a_{10} -2a_{8} = 6a_{9}
⇒ a_{10}-2a_{8}/2a_{9} = 3
The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8 without repetition, is
216
192
120
72
B.
192
A complex number z is said to be unimodular, if |z|= 1. suppose z_{1} and z_{2} are complex numbers such that is unimodular and z_{2} is not unimodular. Then, the point z_{1} lies on a
straight line parallel to X -axis
straight line parallel to Y -axis
circle of radius 2
circle of radius
C.
circle of radius 2
If z unimodular, then |z| = 1, also, use property of modulus i.e.
Given, z2 is not unimodular i.e |z2|≠1 and is unimodular