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Read the given passage and then choose the best answer to each question(Q.N: 36 to 40) that follows.
Very closely associated with the beauty of the mountains are some special emotions that the highest and wildest peaks provoke. The companionship provided by climbing together is almost universally valued by mountaineers.Lonely though the mountain peaks are, the teams of mountaineers who climb them find a unique kind of bond developing between them. The friendship established in the mountains is lasting and irreplaceable when you have walked the feather edge of danger with someone. When you have held his life at the end of a rope in your hand, and he has later held yours, you have an almost impregnable foundation for friendship, for the deepest friendships spring from sharing failure as well as success, danger as well as safety.
We are excited to offer video solutions for BCA-2022 Entrance Questions of Mathematics. These videos are designed to help you understand the concepts clearly and provide detailed explanations for each question. By watching these videos, you can enhance your learning experience and ensure a thorough understanding of the material.
The Bachelor in Computer Application (BCA) program, initially introduced in Nepal by Purbanchal University and Pokhara University, was later adopted by Tribhuvan University (TU) after four years of careful research to develop a curriculum aligned with current market needs. Like B.Sc. CSIT, BIT, and BIM, BCA is a core domain within the field of Information Technology.
TUβs BCA program, now preparing to welcome its 7th batch of students, operates on a four-year, semester-based structure. What sets the BCA apart from other IT programs, such as B.Sc. CSIT, BIT, or BIM, is its inclusion of three comprehensive projects throughout the course and four elective subjects, offering unique practical exposure and flexibility in learning.
BCA-2017 Entrance Questions: Dive into our extensive collection of BCA-2017 Entrance Questions designed to help you excel in your entrance exams. Our platform offers a comprehensive range of multiple-choice questions (MCQs) across various subjects, tailored specifically for the 2017 BCA entrance exams.
Subject-Specific MCQs: Explore a wide array of BCA-2017 Entrance Questions to enhance your practice and preparation. These carefully selected questions ensure a thorough understanding of each topic, equipping you with the knowledge needed to tackle your exams with confidence.
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We are excited to offer video solutions for BCA-2017 Entrance Questions in Mathematics. These videos are designed to help you understand the concepts clearly and provide detailed explanations for each question. By watching these videos, you can enhance your learning experience and ensure a thorough understanding of the material.
Logarithmic Function videos are designed to provide you with a thorough understanding of the topic in a clear and accessible manner. Whether you’re new to Logarithmic Function or looking to reinforce your knowledge, these videos cover everything you need. You’ll find explanations of key concepts, step-by-step solutions to important questions, and insights into how to approach problems effectively.
In addition to covering the fundamentals, these videos also include past exam questions and frequently repeated questions to help you prepare thoroughly. By engaging with this content, you’ll gain a deeper understanding of Logarithmic Function and be well-prepared for any related assessments or exams.
Examples: 1. If the graph of π¦ = πx contains the points (3,64) then the base a is (2077 Questions)
a. 4 b. 3 c. 64 d. 2
Solution: Given, π¦ = πx ———(i) and point is (3,64) Putting the given point in equation(i) we get, 64 = a3 Or, 43=a3 Hence, the base is same so a=4 Hence, the correct answer is option a. 4
Example: 2. If log2(π₯ β 7) = 1 then x is (2074 Questions)
a. Not Known b. 8 c. 6 d. 9
Solution: Given, log2(π₯ β 7) = 1———–(i) Put the value of x from the given option. We know that,
BCA stands for Bachelor in Computer Application which was first introduced by Purbanchal University and Pokhara University in Nepal. TU launched the BCA program after 4 years of researching in a course which meets the current market demand. BCA is also the Domain of IT like B.Sc.CSIT, BIT and BIM. As of now, there has been only the 6th batch of BCA in TU and this year, the 7th batch would be there. It is a four-year course with a semester system along with 3 total projects which no other IT course provides; neither B.Sc.CSIT, BIT nor BIM, plus four elective subjects.
What is BCA?
The main focus of BCA course is towards application development, i.e. most of the BCA graduates work as software engineerβs. Most of the programming courses are introduced as core subjects of BCA along with database, network, computer architecture, data structures and algorithms, digital logic and so on.
Why Study BCA?
BCA is the domain of IT. IT is taken as the most successful course in the world in the recent date and is expected to be the same because we all are directly or indirectly connected with Information Technology. There is no sector, where computers aren’t being used in the modern time, and undoubtedly, there is at least one IT officer in each sector where technology is being used. Demand of IT is everywhere; whether it be in a hospital or a construction company as well as software and telecommunication companies and banks. It is also a great thing that IT course graduates can work in multinational companies like Google, Facebook, Viber, PayPal, etc. as well as establish their own company. In the present world, people hardly know the name of doctors and engineers, but everyone knows the CEOs of top IT companies as they have got their name, fame and wealth. Who doesn’t know about Mark Zuckerberg, Steve Jobs or Bill Gates? Most of the successful business people are either from the IT domain or they are making use of IT in their works. Rejecting an IT course would be the worst decision ever taken as the world is living in the age of Information and Technology.Β
What are the scopes of BCA?
BCA graduates have good scope in jobs as a Web Developer, Web Designer, Network Administrator, System Manager, Computer Programmer, Software Developer, Software Tester, Project manager etc.Β
What after BCA?
1) Education wise :
After completing BCA students can apply for MCA, MBA and MIT which is taken as the most reputed Master degree all around the world.
2) Work wise
After completing BCA students can work in any field as mentioned previously
a) Medicinal industry & Hospital
b) Banks
c) Internet company
d) IT company
e) Software house
f) Airport
g) Cybercrime bureau
h) Army / National agency
i) Telecom
j) NGOs, INGOs
k) Government officer
Almost every sector is touched and linked with IT.
Why choose BCA over other IT domains like B.Sc.CSIT, BIT and BIM?
BCA is a newly introduced course, rather than other courses with infrequently updated syllabus. If you want to meet current market demand, you can chose BCA and plus point is no study load to the student with almost 40 marks practical knowledge and 60 marks written, where it’s divided into 2 parts, first part 10 marks MCQ and 50 marks pure written with 3 hours of exam duration and BCA provides 3 project starting from 2nd year, 3rd year and 4th year. Due to this, students can focus on other IT topics like python, CCNA, Ethical Hacking etc. easily without taking semester pressure.
Disadvantages:-
1) You’ll not be able to write an engineer in your name tag after graduation.
2) As you know, this is like a sub branch of IT which focus on application specially coding so, there are not enough field like csit where you can join after graduation.
Β 3) BCA affiliated by TU falls in Humanities faculty so, be clear about this things.
TU Affiliated BCA Colleges in Nepal include a total of 118 Campus/Colleges offering the Bachelor of Computer Applications (BCA) program. Among these, 14 are Constituent Campuses (government campuses or colleges), located both inside and outside the Kathmandu Valley. These Constituent Campuses are part of the government’s effort to provide quality education across various regions of the country. Additionally, 27 colleges are Affiliated Campuses situated outside the Valley, while 77 are Affiliated Campuses located within the Valley.
Relations, Functions and Graphs videos are designed to provide you with a thorough understanding of the topic in a clear and accessible manner. Whether you’re new to Relations, Functions and Graphs or looking to reinforce your knowledge, these videos cover everything you need. You’ll find explanations of key concepts, step-by-step solutions to important questions, and insights into how to approach problems effectively.
In addition to covering the fundamentals, these videos also include past exam questions and frequently repeated questions to help you prepare thoroughly. By engaging with this content, you’ll gain a deeper understanding of Relations, Functions and Graphs and be well-prepared for any related assessments or exams.
1. Ordered Pair: A pair having one element as the first and the other as the second is called an ordered pair. An ordered pair having a as the first element and b as the second element. It is denoted by (a,b).
An ordered pair (a,b) is generally not the same as the ordered pair (b,a). But this will happen so when the two elements are identical. Thus, (5,6) different from (6,5); but (2,2) is the same as (2,2).
Two ordered pairs (a,b) and (c,d) are said to be equal if and only if a=c and b=d.
Example: If (2x-1, -3) = (3, y+3), then (2072 Questions) a. x = 1, y = 0 b. x= – 1, y = – 3 c. x = 2, y = – 6 d. x = 0, y = – 1
solution: Given, (2x-1, -3) = (3, y+3)
from the definition of ordered pair
2x-1 = 3 & -3 = y+3
2x=3+1 -3-3=y
x=2 y=-6
(x,y)=(2,-6)
Hence, the correct answer is option c. x=2, y= -6
2. Cartesian Product: Given two sets A and B, the set of all ordered pairs(a,b) such that aβA and bβB is called the cartesian product of A and B. It is denoted by AxB. It is read as A cross B.
In the set-builder notation, we have
AxB={(a,b):aβA,bβB}
Example: The cartesian product of A={1,2} and B={2,3,4}
AxB={(1,2),(1,3),(1,4),(2,2),(2,3),(2,4)}
It is different from the cartesian product of B={2,3,4} and A={1,2}
i.e. BxA={(2,1),(2,2),(3,1),(3,2),(4,1),(4,2)}
Note:
i). In general, AxB β BxA
ii). If m is the number of elements in A and n is the number of elements in B, then the number of elements in AxB or BxA is mn
iii). If β is the set of real numbers, then the cartesian product of β on β.
i.e βxβ or RΒ² is the set {(x,y):xββ, yββ}.
This cartesian product is represented by the entire cartesian coordinates plane.
Relation: Any subset of a cartesian product AxB of two sets A and B is called a relation. A relation from a set A to a set B is denoted by xβy if xβA and yβB or simply by β if (x,y) β β.
A relation from a set A to itself is called a relation on A. Relations may be expressed in various ways. Here are the some examples.
A={1,2} and B={2,3,4}
AxB={(1,2),(1,3),(1,4),(2,2),(2,3),(2,4)}
β={(2,2),(2,4)} β AxB, is a relation from A to B
Note:
If β is a relation from A to B then
i). It is not necessary that every element of A has β relation with some element of B.
ii). It is also not necessary that if aβb and b is unique
iii). If B = A then ββAxA and in such a case we read it as ‘β is a relation on A’
iv). If β = AxA, then β is called universal relation on A.
v). β= ΙΈ is called void relation on a set A.
Domain :The domain of a relation β is the set of all first members of the pairs (x,y) of β. It is denoted by Dom(β).
Symbolically, Dom(β) ={x:(x,y) β β for some y β B}
Inverse Relation: An inverse relation is the inverse of a given relation obtained by Interchanging or swapping the elements of each ordered pair. In other words, if (x, y) is a point in a relation β, then (y, x) is an element in the inverse relation Rβ1.
A relation β from set A to B is a subset of the Cartesian product of A and B. β is a subset of AΒ ΓΒ B. The elements of β of the form of an ordered pair (a, b) where aΒ βΒ A and bΒ βΒ B.
The inverse relation of β is denoted by Rβ1. Rβ1 is a subset of B Γ A. The elements of Rβ1 of the form of an ordered pair (b, a) where b β B and aβ A.
Given a Relation: β={(x,y): x βA,yβB} β AxB
then its inverse is given by; Rβ1 = {(y,x): yβB,x βA}
Example: β={(1,2),(1,3),(1,4),(2,2),(2,3),(2,4)}, then Rβ1 ={(2,1),(3,1),(4,1),(2,2),(3,2),(4,2)}
Note: For Inverse Relation Simply interchanging the value of x & y
Types of Relation: The different types of Relation are describe below;
a. Reflexive Relation: A relation β on a set A is reflexive if every element is related to itself.
Mathematically:
βaβA,Β (a,a)ββ
Example: On the set A={1,2,3}, the relation β={(1,1),(2,2),(3,3),(1,2),(2,1)} is reflexive.
b. Symmetric Relation: A relation β on a set A is symmetric if whenever (a,b)ββ, then (b,a)ββ as well.
Example: For A={1,2,3}, the relation β={(1,2),(2,3),(1,3)} is transitive.
e. Equivalence Relation: A relation β on a set A is an equivalence relation if it is reflexive, symmetric, and transitive.
Example: Equality == is an equivalence relation on any set because it is reflexive, symmetric, and transitive.
Function: Let A and B be two non-empty sets. A function f from A to B is a set of ordered pairs with the property that for each element x in A there is an unique element y in B. The Set A is called the domain of the function and the set B is called co-domain. If(x,y) β f, it is customary to write y=f(x), y is called image of x and x is a pre-image of y.The set consisting all the images of the elements of a under the function f is called range of f. It is denoted by f(A)
1. Domain of the Function: The domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of all values that can be plugged into the function without causing any undefined behavior.
If f is a function defined by f:AβB, where A is a set of possible inputs and B is a set of possible outputs, then, The domain of f is the set A, which consists of all elements for which f(x) is defined.
Shortcut Method:
i). The domain of β(a^2 – x^2) is [-a,a]
ii). The domain of 1/ β(a^2 – x^2) is (-a,a)
iii). The domain of β(x^2 – a^2) is (-β,a] U [a,β)
iv). The domain of 1/β(x^2 – a^2) is (-β,a) U (a,β)
v). The domain of β{(x – a) (b-x)} when a<b is [a,b]
vi). The domain of 1/ β{(x – a) (b-x)} when a<b is (a,b)
Example: Find the domain of f(x)= β(2-x) is
solution: Clearly,2-xβ₯ 0
= 2β₯x
= xβ€2
Hence, the domain of f(x)=β(2-x) is (-β,2]
2. Co-domain of the function: The set B is known as the co-domain of the function.
3. Range of the Function: The set of values of y=f(x)βB for every xβA is known as rage of the function f.It is denoted by R(f).
R(f)={y:yβB,y=f(x) for all xβA}
How to find range: First put y=f(x) by suitable substitution, find x in term of y. Then find all such y for which x is defined in the domain set of these values of y is called the range of f(x).
Example: Find the domain and range of y=f(x)=x^2 – 6x + 6
solution: given,
y=f(x)=x^2 – 6x + 6
The given function is a polynomial of degree two in x,y is defined for all x ββ,so domain of
f=dom(f)=β = (-β,β)
Again,
y=x^2 – 6x + 6
y+3=(x-3)^2
y= -3 +(x-3)^2
since, (x-3)^2β₯ 0 so for all x ββ,yβ₯-3
Hence, range of y=f(x)=x^2 – 6x + 6 is [-3,β)
4. Image: The element yβB with which the element xβA associates, is known as the image of x under f. It is also known as the value of f at x.
5. Pre-image: The element xβA which associates with yβB, is known as the pre-image of y under f.
6. Equal function: Two functions f and g are said to be equal i.e f=g if domain of f=domain of g and f(x)=g(x) for all x belonging to the domain of f(or domain of g).
Types of Functions: The types of function are give below
a. One-to one or Injective Function: A function f from a set A to another set B i.e. f: A β B is said to be one-one (1-1) or injective if distinct elements (or pre-images) in A have distinct images in B. In symbols, for any x, y Π A,
In symbols, for any x, y Π A,
x β yβ f(x) β f(y); f(x) = f(y) βx= y.
or, equivalently,
In other words, a function f is said to be one-one or injective if (x, f(x)), (y, f(y)) Π Ζβx= y. Thus, under one-one function all elements of A are related to different elements of B.
b. Onto or Surjective Function: A function Ζ from a set A to another set B i.e., f: A β B is said to be onto or surjective, if every element of B is an image of at least one element of A, i.e., every element of B has a pre-image or, if Ζ (A) = B. Sometimes such a function becomes a many-one onto function.
c. One to one correspondence or Bijective Function: A function that is both one-one and onto (i.e., injective and surjective) is called a bijective function. It is also known as a one-to-one correspondence. In particular, a bijective function from a set A to itself is known as a permutation or operator on A.
d. Composition of Functions: If f: A β B and g: B β C be any two functions, then the composite function of f and g(also known as the product function or function of a function) is the function,
gof: A β C
defined by the equation (gof)(x)=g(f(x)).
The composition of two functions g and f is the new function we get by performing f first, and then performing g. For example, if we let f be the function given by f(x) = x^2 and let g be the function given by g(x) = x + 3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)).
So we write down what f(x) is first, and then we apply g to the whole of f(x). In this case, if we apply g to something we add 3 to it. So if we apply g to x^2, we add three to x^2. So we obtain
gf(x) = g(f(x)) = g(x^2) = x^2 + 3.
e.Odd Function: A function is an odd function if f(-x)= -f(x) for all x
f.Even Function: A function is an even function if f(-x)= f(x) for all x
g. Inverse/Invertible function: Let f: A β B be a one-one and onto function, then there exists a unique function g: B β A
Such that f(x)=y β g(y)=x, {g(y)=f-1 (y) } β xΠ A and yΠ B
Then, g is said to be inverse of f.
If any function f takes x to y then, the inverse of f will take y to x. If the function is denoted by f or F, then the inverse function is denoted by f-1Β or F-1. One should not confuse (-1) with exponent or reciprocal here.Β
Periodic Function: A function f(x) is said to be a periodic function of x, if there exist a positive real number T such that f(x+T)=f(x) for all x.
S.N
Periodic Function
Period
1
sinx, cosx, secx, cosecx
2Ο
2
tanx, cotx
Ο
3
|sinx|, |cosx|, |tanx|, |secx|, |cosecx|,|cotx|
Ο
4
sinn(x), cosn(x), secn(x), cosecn(x)
2Ο(if n is odd)
Ο(if n is even)
5
tann(x), cotn(x),
Ο
If period of f(x) is T then function 1/f(x), βf(x) are also function of same period.
If Period of f(x) is T then period of f(ax+b) is T/|a|
Example: Find the period function of sin(2x)
Given, sin(2x)= sin(2x+0)
we know, f(ax+b) then a=2 and b=0
Period of sin(2x) is T/|a|= 2Ο/2 = Ο
Hence, the Period of sin(2x) is Ο
From the Relations Functions and Graphs Chapter Video.
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In addition to covering the fundamentals, these videos also include past exam questions and frequently repeated questions to help you prepare thoroughly. By engaging with this content, you’ll gain a deeper understanding of Set Theory and be well-prepared for any related assessments or exams.
