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class 12
| sbi examinations
Solutions for all the questions from class 12
of subject sbi examinations
CLASS
11
12
class 10
class 11
class 12
class 13
class 6
class 7
class 8
class 9
SUBJECT
sbi examinations
CHAPTER
algebra - previous year questions - for competition
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let
$S={1,,2,34}$
. The total number of unordered pairs of disjoint subsets of
$S$
is equal a.
$25$
b.
$34$
c.
$42$
d.
$41$
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let p be an odd prime number and
$T_{p}$
, be the following set of
$2×2$
matrices
$T_{p}={A=[ac ba ]:a,b,c∈{0,1,2,………p−1}}$
The number of A in
$T_{p}$
, such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let p be an odd prime number and
$T_{p}$
, be the following set of
$2×2$
matrices
$T_{p}={A=[ac ba ]:a,b,c∈{0,1,2,………p−1}}$
The number of A in
$T_{p}$
, such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let a1,a2,a3 ...... a11 be real numbers satisfying
$a_{1}=15,27−2a_{2}>0anda_{k}=2a_{k−1}−a_{k−2}$
for
$k=3,4,…..11$
If
$11a1_{2}+a2_{2}…….a11_{2} =90$
then find the value of
$11a_{1}+a_{2}….+a_{11} $
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
For
$r=0,1,…..,10$
, let
$A_{r},B_{r},andC_{r}$
denote, respectively, the coefficient of
$x_{r}$
in the expansions of
$(1+x)_{10},(+x)_{20}and(1+x)_{30}$
.Then
$r=1∑10 A_{r}(B_{10}B_{r}−C_{10}A_{r})$
is equal to
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let
$S_{k},k=1,2,,100,$
denotes thesum of the infinite geometric series whose first term s
$k!k−1 $
and the common ratio is
$k1 $
, then the value of
$100!100_{2} +k=1∑100 (k_{2}−3k+1)S_{k}$
is _______.
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let
$pandq$
be real numbers such that
$p=0,p_{3}=q,andp_{3}=−q˙$
If
$αandβ$
are nonzero complex numbers satisfying
$α+β=−pandα_{2}+β_{2}=q$
, then a quadratic equation having
$α/βandβ/α$
as its roots is
$(p_{3}+q)x_{2}−(p_{3}+2q)x+(p_{3}+q)=0$
$(p_{3}+q)x_{2}−(p_{3}−2q)x+(p_{3}+q)=0$
$(p_{3}+q)x_{2}−(5p_{3}−2q)x+(p_{3}−q)=0$
$(p_{3}+q)x_{2}−(5p_{3}+2q)x+(p_{3}+q)=0$
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let p be an odd prime number and
$T_{p}$
, be the following set of
$2×2$
matrices
$T_{p}={A=[ac ba ]:a,b,c∈{0,1,2,………p−1}}$
The number of A in
$T_{p}$
, such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let w be the complex number
$3cos(2π) +i3sin(2π) $
. Then the number of distinct complex numbers z satisfying
$∣∣∣∣∣∣∣ z+12w_{2} wz+w_{2}1 w_{2}1z+w ∣∣∣∣∣∣∣ =0$
is equal
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let
$pandq$
be real numbers such that
$p=0,p_{3}=q,andp_{3}=−q˙$
If
$αandβ$
are nonzero complex numbers satisfying
$α+β=−pandα_{2}+β_{2}=q$
, then a quadratic equation having
$α/βandβ/α$
as its roots is
$(p_{3}+q)x_{2}−(p_{3}+2q)x+(p_{3}+q)=0$
$(p_{3}+q)x_{2}−(p_{3}−2q)x+(p_{3}+q)=0$
$(p_{3}+q)x_{2}−(5p_{3}−2q)x+(p_{3}−q)=0$
$(p_{3}+q)x_{2}−(5p_{3}+2q)x+(p_{3}+q)=0$
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class 12
| sbi examinations
Solutions for all the questions from class 12
of subject sbi examinations
Filter Results
CLASS
11
12
class 10
class 11
class 12
class 13
class 6
class 7
class 8
class 9
SUBJECT
sbi examinations
CHAPTER
algebra - previous year questions - for competition
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let
$S={1,,2,34}$
. The total number of unordered pairs of disjoint subsets of
$S$
is equal a.
$25$
b.
$34$
c.
$42$
d.
$41$
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let p be an odd prime number and
$T_{p}$
, be the following set of
$2×2$
matrices
$T_{p}={A=[ac ba ]:a,b,c∈{0,1,2,………p−1}}$
The number of A in
$T_{p}$
, such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let p be an odd prime number and
$T_{p}$
, be the following set of
$2×2$
matrices
$T_{p}={A=[ac ba ]:a,b,c∈{0,1,2,………p−1}}$
The number of A in
$T_{p}$
, such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let a1,a2,a3 ...... a11 be real numbers satisfying
$a_{1}=15,27−2a_{2}>0anda_{k}=2a_{k−1}−a_{k−2}$
for
$k=3,4,…..11$
If
$11a1_{2}+a2_{2}…….a11_{2} =90$
then find the value of
$11a_{1}+a_{2}….+a_{11} $
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
For
$r=0,1,…..,10$
, let
$A_{r},B_{r},andC_{r}$
denote, respectively, the coefficient of
$x_{r}$
in the expansions of
$(1+x)_{10},(+x)_{20}and(1+x)_{30}$
.Then
$r=1∑10 A_{r}(B_{10}B_{r}−C_{10}A_{r})$
is equal to
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let
$S_{k},k=1,2,,100,$
denotes thesum of the infinite geometric series whose first term s
$k!k−1 $
and the common ratio is
$k1 $
, then the value of
$100!100_{2} +k=1∑100 (k_{2}−3k+1)S_{k}$
is _______.
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let
$pandq$
be real numbers such that
$p=0,p_{3}=q,andp_{3}=−q˙$
If
$αandβ$
are nonzero complex numbers satisfying
$α+β=−pandα_{2}+β_{2}=q$
, then a quadratic equation having
$α/βandβ/α$
as its roots is
$(p_{3}+q)x_{2}−(p_{3}+2q)x+(p_{3}+q)=0$
$(p_{3}+q)x_{2}−(p_{3}−2q)x+(p_{3}+q)=0$
$(p_{3}+q)x_{2}−(5p_{3}−2q)x+(p_{3}−q)=0$
$(p_{3}+q)x_{2}−(5p_{3}+2q)x+(p_{3}+q)=0$
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let p be an odd prime number and
$T_{p}$
, be the following set of
$2×2$
matrices
$T_{p}={A=[ac ba ]:a,b,c∈{0,1,2,………p−1}}$
The number of A in
$T_{p}$
, such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let w be the complex number
$3cos(2π) +i3sin(2π) $
. Then the number of distinct complex numbers z satisfying
$∣∣∣∣∣∣∣ z+12w_{2} wz+w_{2}1 w_{2}1z+w ∣∣∣∣∣∣∣ =0$
is equal
Class 12
SBI Examinations
Mathematics
Algebra - Previous Year Questions - For Competition
Let
$pandq$
be real numbers such that
$p=0,p_{3}=q,andp_{3}=−q˙$
If
$αandβ$
are nonzero complex numbers satisfying
$α+β=−pandα_{2}+β_{2}=q$
, then a quadratic equation having
$α/βandβ/α$
as its roots is
$(p_{3}+q)x_{2}−(p_{3}+2q)x+(p_{3}+q)=0$
$(p_{3}+q)x_{2}−(p_{3}−2q)x+(p_{3}+q)=0$
$(p_{3}+q)x_{2}−(5p_{3}−2q)x+(p_{3}−q)=0$
$(p_{3}+q)x_{2}−(5p_{3}+2q)x+(p_{3}+q)=0$
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