﻿ 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: from Mathematics Class 12 JEE Year 2015 Free Solved Previous Year Papers

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# JEE Mathematics 2015 Exam Questions

#### Multiple Choice Questions

1.

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,

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2.

If m is the AMN of two distinct real numbers l and n (l,n>1) and G1, G2, and G3 are three geometric means between l and n, then  equals

• 4l2 mn

• 4lm2n

• 4 lmn2

• 4l2m2n2

B.

4lm2n

Given,
m is the AM of and n

l +n = 2m

and G1, G2, G3, n are in GP
Let r be the common ratio of this GP
G1 = lr
G2 =lr2
G3= lr3
n = lr4

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3.

The sum of coefficients of integral powers of x in the binomial expansion of  is

A.

Let Tr+1 be the general term in the expansion of

For the integral power of x, r should be even integer,
therefore, sum of coefficients=

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4.

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)= 28
Number of subsets of set A x B having no element (i.e, Φ) = 1
Number of subsets of set AxB having two elements = 8C1
Number of subsets of set A x B having two elements = 8C2
therefore, the number of subsets having atleast three elements,
= 28 x (1+8C18C2)
= 28 -1-8-28
= 28 -37
= 256-37 = 219

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5.

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 30o, 45o and 60o respectively, then the ratio AB: BC is

• 2:3

A.

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6.

The sum of first 9 terms of the series  is

• 71

• 96

• 142

• 192

B.

96

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7.
Let α and  β be the roots of equations x2-6x-2 = 0. If ann- βn, for n≥1, the value of a10-2a8/2a9 is equal to
• 6

• -6

• 3

• -3

C.

3

α and β are the roots of the equation
x2-6x-2 =0
or
α=6x+2
α2 = 6α +2
α10= 6 α9+2α8 ... (i)
β10= 6 β9+2β8 ... (ii)
On subtracting eq (ii) from eq(i), we get
α10- β10= 6 ( α99) + 2 (α88)
a10 = 6a9 + 2a8 (∴ an = αn- βn)
⇒ a10 -2a8 = 6a9
⇒ a10-2a8/2a9  = 3

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8.

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

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9.

A complex number z is said to be unimodular, if |z|= 1. suppose z1 and z2 are complex numbers such that  is unimodular and z2 is not unimodular. Then, the point z1 lies on a

• straight line parallel to X -axis

• straight line parallel to Y -axis

C.

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

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10.

The negation of  is equivalent to

D.

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