CBSE Multiple Choice Type Questions for 11th Class Applied Mathematics PDF formatted study resources are available for free download. These Grade 11 Applied Mathematics CBSE MCQ Mock Test helps you learn & practice the concepts in a fun learning way.

## Class 11 Applied Mathematics MCQs Multiple Choice Questions with Answers

Here are the chapterwise CBSE MCQ Quiz Test Questions for Class 11th Applied Mathematics in pdf format that helps you access & download so that you can practice online/offline easily.

### Basics Of Financial Mathematics Questions and Answers

Basics Of Financial Mathematics Quiz Question Answer
Anitha borrowed Rs.400 from her friend at the rate of 12% p.a for 2 and half year. Find the interest and amount paid by her? Rs.125, Rs.525
A car is valued at Rs. 500000 If sits value depreciates at 2 % p.a.  What will be its value after three years?  Rs. 470596
The population of a city increases by 30% every year. If the present population is 3,38,What will the population of the city two years ago? 2,00,000
If the amount repaid is Rs. $$450$$ and the principal is Rs. $$415$$, then interest is equal to Rs. $$35$$
_________ is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan.
compound interest
Identify in which type of interest rate is applied to the original principal and any accumulated interest?
compound interest
Annuity, where the payments start after specified no. of periods, is known as Deferred annuity
__________ is calculated on both the amount borrowed and any previous interest.
compound interest
If the account statement states that the interest is compounded annually, then $$n =$$ ?
$$1$$
The principal is Rs. $$1000$$, so if you pay off Rs. $$300$$, the remaining Rs. $$700$$ left to repay is also called the Principle

#### Circles Class 11 Commerce Applied Mathematics MCQ Quiz

The equation of the circle passing through the points of intersection of the lines $$2x+y=0,\ x+y+3=0$$ and $$x-2y=0$$ is $$x^{2}+y^{2}-x+7y=0$$
If $$x^{2}+y^{2}-2 x+2 a y+a+3=0$$ represents a real circle with non-zero radius, then most appropriate is
$$a \in(-\infty,-1) \cup(2 \infty)$$
Find the equation of a circle whose cemtre is $$\left( {2,1} \right)$$ and radius is 3 $${x^2} + {y^2} + 2x - 4y - 4 = 0$$
If the radius of the circle $${x}^{2}+{y}^{2}+2gx+2fy+c=0$$ be $$r$$, then it will touch both the axes, if  $$g=f=\sqrt{c}=r$$
If the radius of the circle $$x ^ { 2 } + y ^ { 2 }$$ - 18 x - 12 y + k = 0 be 11 then k =
-4
If the equation $$p{ x }^{ 2 }+(2-q)xy+3{ y }^{ 2 }-6qx+30y+6q=0$$ represents a circle, then the values of p and q are 3, 2
Equation of the circle whose radius is $$a+b$$ and centre $$(a, -b)$$ $${ x }^{ 2 }+{ y }^{ 2 }-2ax+2by=2ab$$
If  $$y ^ { 2 } - 2 x - 2 y + 5 = 0$$  is a circle with centre $$( 1,1 )$$
The equation of circle with centre (1, 2) and tangent $$x + y - 5 = 0$$ is $${x^2} + {y^2} - 2x - 4y + 3 = 0$$
The equation of circles passing through (3,-6) touching both the axes is  $$x^{2}+y^{2}-6x+6y+9=0$$

### Descriptive Statistics Questions and Answers

To prevent frauds in multiple mortgage cases, under SARFAESI Act, 2002, one special thing has been created and made operative from 01-04-Which one is that from the following?  Central Electronic Registry
If $$\sum _{ i=1 }^{ 18 }{ }$$ $$(X_{i}-8)=9$$ and $$\sum _{ i=1 }^{ 18 }{ }$$$$(x_{i}-8)^{2}=45$$ , then the standard deviation of $$x_{1},x_{2},.....,x_{18}$$ is  3/2
If $$b_{i} = 1 - a_{i}, na = \displaystyle \sum_{i = 1}^{n} a_{i}, nb = \displaystyle \sum_{i = 1}^{n}b$$, then $$\displaystyle \sum_{i = 1}^{n}a_{i}b_{i} + \displaystyle \sum_{i = 1}^{n} (a_{i} - a)^{2} =$$ $$nab$$
Tabulation of data makes the presentation of facts and figures ___________. Both a&b
Two distributions each of $$5$$ observations having veriance $$4$$ and $$5$$. If their arithmetic mean are $$2$$ and $$4$$ respectively., Find the variance of combined distribution  $$5/2$$
Two sets each of $$20$$ observations, have the same standard deviation $$'5'$$. The first set has a mean $$'17'$$ and the second set mean $$'22'$$ then standard deviation of the combining the given two sets is $$5.59$$
The standard deviation of a varibale x is$$\sigma$$. The standard devaition of the varibale $$\frac { ax+b }{ c }$$ where a, b, c are constant is _____________________. $$\left( \frac { a }{ b } \right) \sigma$$
Consider the first $$10$$ positive integers. If we multiply each number by $$-1$$ and then add $$1$$ to each number, the variance of the numbers so obtained is $$8.25$$
If 25% of the items are less than 10 and 25%  are more than 40, then the coefficient of quartile deviation is 30
The standard deviation of $$50$$ values of a variable x is $$15$$; if each value of the variable is divided by $$(-3)$$; then the standard division of the new set of $$50$$ values of x will be $$5$$

#### Differentiation Class 11 Commerce Applied Mathematics MCQ Quiz

Differentiation gives us the instantaneous rate of change of one variable with respect to another. True
If $$\displaystyle\mathrm{x}=\mathrm{e}^{\mathrm{y}+\mathrm{e}^{\mathrm{y}+\mathrm{e^y+...\infty}}},\ \mathrm{x}>0$$, then $$\displaystyle \frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}}$$ is
$$\displaystyle \frac{1-\mathrm{x}}{\mathrm{x}}$$
Let $$\mathrm{y}$$ be an implicit function of $$\mathrm{x}$$ defined by $$\mathrm{x}^{2\mathrm{x}}-2\mathrm{x}^{\mathrm{x}} \cot y - 1=0.$$ Then $$\mathrm{y}'(1)$$ equals
$$-1$$
If $$f(1)=1, f'(1)=3$$, then the value of derivative of $$f(f(fx)))+(f(x))^2$$ at $$x=1$$ is? $$33$$
For $$x\in R, f(x) = |\log2 - \sin x|$$ and $$g(x) = f(f(x))$$, then: $$g'(0) = \cos (\log 2)$$
Consider the functions defined implicitly by the equation $$\mathrm{y}^{3}-3\mathrm{y}+\mathrm{x}=0$$ on various intervals in the real line. If $$x \in(-\infty, -2)\cup (2, \infty)$$, the equation implicitly defines a unique real valued differentiable function $$\mathrm{y}=\mathrm{f}(\mathrm{x})$$. If $$x \in(-2,2)$$, the equation implicitly defines a unique real valued differentiable function $$\mathrm{y}=\mathrm{g}(\mathrm{x})$$ satisfying $$\mathrm{g}(\mathrm{0})=0$$.
If $$\mathrm{f}(-10\sqrt{2})=2\sqrt{2}$$, then $$\mathrm{f''}(-10\sqrt{2})=$$
$$-\displaystyle \frac{4\sqrt{2}}{7^{3}3^{2}}$$
Consider the functions defined implicitly by the equation $$\mathrm{y}^{3}-3\mathrm{y}+\mathrm{x}=0$$ on various intervals in the real line. If $$x \in(-\infty, -2)\cup (2, \infty)$$, the equation implicitly defines a unique real valued differentiable function $$\mathrm{y}=\mathrm{f}(\mathrm{x})$$. If $$x \in(-2,2)$$, the equation implicitly defines a unique real valued differentiable function $$\mathrm{y}=\mathrm{g}(\mathrm{x})$$ satisfying $$\mathrm{g}(\mathrm{0})=0$$.

$$\displaystyle \int_{-\mathrm{l}}^{1}\mathrm{g}'(\mathrm{x}) dx =$$
$$2\mathrm{g}(1)$$
The value of '$$a$$' in order $$f(x)=\sqrt{3}\sin x-\cos x -2ax+b$$ decrease for all real values of $$x$$, is given by $$a>1$$
$$\displaystyle \frac{d}{dx}(xe^{x})$$ $$xe^{x}+e^{x}$$
$$\displaystyle \frac{d}{dx}[f(x)\cdot g(x)] =f(x) \frac{d}{dx}g(x)+g(x) \frac{d}{dx}f(x)$$ is known as _____ rule. Product

#### Functions Class 11 Commerce Applied Mathematics MCQ Quiz

The domain of $$f(x)=\frac{1}{\sqrt{|x|-x}}$$ is $$(-\infty ,0)$$
A constant function $$f:A\rightarrow B$$ will be onto if $$n (B) = 1$$
The number of non-bijective mappings possible from $$A= \{1,2,3\}$$ to $$B=\{4, 5\}$$ is $$8$$
A constant function $$f:A\rightarrow B$$ will be one-one if $$n(A) = 1$$
If $$f:\mathbb{N} \rightarrow \mathbb{N}$$ and $$f(x) = x^{2}$$ then the function is
one to one function
$$f(x)=1$$, if $$x$$ is rational and $$f(x)=0$$, if $$x$$ is irrational
then  $$(fof) (\sqrt{5})=$$
$$1$$
The domain of the function,  f(x) = $$\sqrt {x-1}+\sqrt {5-x}$$  is [1, 5]
If $$f(x) = 3x + 2, g(x) = x^2 + 1$$, then the value of $$(fog) (x^2 +1)$$ is $$3x^4 + 6x^2 + 8$$
If $$f:A\rightarrow B$$ is surjective then every element of $$B$$ has at least one pre-image in $$A$$
$$f:R\rightarrow R , g:R\rightarrow R$$ and  $$f(x)= \sin x$$, $$g(x)=x^{2}$$ then $$fog(x)=$$
$$\sin x^{2}$$

### Limits And Continuity     Questions and Answers

Limits And Continuity     Quiz Question Answer
Evaluate $$\underset{x \rightarrow 3}\lim \sqrt[4] {x^3}$$ using the properties of limits. $$27^{1/4}$$
$$If {A_i} = \frac{{x - {a_i}}}{{\left| {x - {a_i}} \right|}}, \,i = 1,2,3,.....n$$ and $${a_1}< {a_2}< {a_3}....< {a_{n,}} \, then$$
$$\mathop {\lim }\limits_{x \to {a_m}} \left( {{A_1}{A_2}......{A_n}} \right), 1 \le m \le n$$
is equal to $${\left( { - 1} \right)^{n-m}}$$
$$\displaystyle \mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{\cot x - \cos x}}{{{{\left( {\frac{\pi }{2} - x} \right)}^3}}}$$ $$\dfrac{1}{2}$$
$$f(x)= x\sin\dfrac{1}{x} , \ for x\neq 0$$
$$= 0,\ for x=0$$
Then.
$$f'(0^+) \ and \ f'(0^-)$$ do not exit
$$\displaystyle\lim _{ x\rightarrow 0 }{ \dfrac { \sin ^{ -1 }{ x } -\tan ^{ -1 }{ x } }{ { x }^{ 3 } } }$$ is equal to  $$\dfrac{1}{2}$$
If $$\mathop {\lim }\limits_{x \to \infty } \left( {\frac{{{x^2} + x + 1}}{{x + 1}} - ax - b} \right)\, = 4$$,then $$a=1,b=-4$$
$$\displaystyle\lim_{n\rightarrow \infty}\left(\tan\theta +\dfrac{1}{2}\tan \dfrac{\theta}{2}+\dfrac{1}{2^2}\tan \dfrac{\theta}{2^2}+...+\dfrac{1}{2^n}\tan\dfrac{\theta}{2^n}\right)$$ equals? $$\dfrac{1}{\theta}-2\cot 2\theta$$
Let p= $$\lim_{x\rightarrow 0+}(1+tan^{2}\sqrt{x})^{\frac{1}{2x}}$$ then log p is equal to : $$\frac{1}{2}$$
$$\displaystyle \lim _{ x\rightarrow \frac { \pi }{ 4 } }{ { \left( \sin { 2x } \right) }^{ \sec ^{ 2 }{ 2x } } }$$ is equal to  $$e^{-\dfrac {1}{2}}$$
$$\displaystyle \lim _{ \theta \rightarrow \pi /2 }{ \dfrac { 1-\sin \theta }{ (\pi /2-\theta )\cos { \theta } } }$$ is equal to $$1$$

### Logarithm And Antilogarithm Questions and Answers

Logarithm And Antilogarithm Quiz Question Answer
Find the characteristic of $$\log 27.93$$ $$1$$
Find the characteristic of $$\log 7.93$$ $$0$$
Find the characteristic of $$\log 277.9301$$ $$2$$
The value of $$10^{\log_{10}{10}^{7}}$$ is: $$10^7$$
Solve the following using Product Law of Exponents.
$$a\times { a }^{ 2 }\times { a }^{ \tfrac { 1 }{ 2 } }$$
$${ a }^{ \tfrac { 7 }{ 2 } }$$
If $$\log_{10} x = a$$ and $$\log_{10} y = b$$, then $$10^{a-1}$$ in terms of $$x$$ will be
$$\displaystyle \frac{x}{10}$$
Simplify: $$\left((9)^{0} + (11)^{0} + (13)^{0}\right) \div (23)^{0}$$
$$3$$
The value of $$x$$ satisfying $$\log _{ 243 }{ x } =0.8$$ $$81$$
If $$7^{10}= 7 \times 7^n$$, what is the value of $$n$$? $$9$$
The value of $$x$$ satisfying the logarithm $$\log_{243} x = 0.8$$ is equal to
$$81$$

### Mathematical And Logical Reasoning Questions and Answers

Mathematical And Logical Reasoning Quiz Question Answer
Choose or find the odd number:
$$48,12,36,24,59$$
$$59$$
Choose or find the odd letter group
POCG, KLIZ, BUDX, FQMV, ARTG
FQMV
Choose or find the odd letter group
BCD, KMN, QRS, WXY
KMN
Choose or find the odd letter group
CFIL, PSVX, JMPS, ORUX, QTWZ
PSVX
Choose or find the odd letter group
CZHK, MLAG, XUBU, SENO, YDFP
XUBU
Choose or find the odd number:
$$8314,2709,1315,2518,3249$$
$$8314$$
64, 71, 80, 91, 104, 119, 135, 155 135
Choose or find odd letter group:
QUS, KOM, HLJ, NRP, BGD
BGD
Choose or find odd letter group:
BHE, DJG, SYV, JPM, PUS
PUS
Choose or find odd letter group:
CHM, HMR, RWB, DIN, LPU
LPU

### Number Theory Questions and Answers

If $$(\dfrac{3-z_{1}}{2-z_{1}})(\dfrac{2-z_{2}}{3-z_{2}})=k$$, then point $$A(z_{1}, z_{2}), C(3, 0)$$ and $$D(2, 0)$$ (taken in clockwise sense ) will lie on a circle only for $$k>0$$
If $$\tan^{-1}(\alpha+ i\beta) = x+iy,$$ then $$x$$ is equal to $$\frac{1}{2}\tan^{-1}\left ( \dfrac{2\alpha}{1-\alpha^2-\beta^2}\right)$$
The complex numbers $${ z }_{ 1 },{ z }_{ 2 },{ z }_{ 2 }$$ satisfying $$\dfrac { { z }_{ 1 }+{ z }_{ 3 } }{ { z }_{ 2 }-{ z }_{ 3 } } =\dfrac { 1-i\sqrt { 3 } }{ 2 }$$ If area zero
If $$z$$ is a complex number such that $$| z | = 1 , z \neq 1 ,$$ then the real part of $$\frac { z - 1 } { z + 1 }$$ is 0
Evaluate:
$$\dfrac {3+2 i\sin \theta}{1-2i \sin \theta},\theta \epsilon \left(-\dfrac {\pi}{2},\pi\right)$$ is
$$2\pi/3$$
Find the modules and amplitude for each of the following complex numbers 7-5i
Let $$\alpha,\ \beta$$ be real and $$\mathrm{z}$$ be a complex number. If $$\mathrm{z}^{2}+\alpha \mathrm{z}+\beta=0$$ has two distinct roots on the line $$Re(z) =1$$, then it is necessary that:

$$\beta\in(1, \infty)$$
Which of the following is/are not twin prime(s)? $$(2, 3)$$
Sum of first three prime numbers which end at 3 is:  39
Which of the following is the factor of all prime numbers? $$1$$

### Numerical Applications Questions and Answers

If x men working x hours a day for x days can produce x articles, then the number of articles produced by y men working for y hours a day for y days is _____________________. $$\displaystyle\frac{y^3}{x^2}$$
The greatest number that can be formed by the digits $$7,0,9,8,6,3$$ $$9,87,630$$
For a group of $$50$$ male workers , the mean and S.D. of their daily wages are Rs. $$630$$ and Rs. $$90$$ respectively. For a group of $$40$$ female workers, these are Rs.$$540$$ and Rs.$$60$$ respectively.The S.D. of these $$90$$ workers is _____________. $$90$$
If 20 pumps of equal capacity can fill a tank in 7 days, then how many more such pumps will be required to fill the tank in 5 days?  28
If $$\displaystyle\sum^m_{k=1}(k^2+1)k!=1999(2000!)$$, then m is? $$1999$$
Ramu scored $$2$$ times more than the rahim scored. In an examination and shashi scored $$30$$ marks more than ram in total they scored $$240$$ marks. What was rahim score? $$42$$
At $$8:00\ a.m$$., Uday started from city $$A$$ and travelled towards city $$B$$ at $$50\ kmph$$ and at $$9:30\ a.m$$ Vikram started from city $$A$$ and travelled to city $$B$$ at $$60\ kmph$$. At what would Vikram overtake Uday? $$4:00\ p.m.$$
The number of 5 letter words formed  using letters of word "CALCULUS" is   $$1110$$
A person is standing on the top of a tower of height $$15(\sqrt{3} +1)$$ and observing a car coming towards the tower . He observed that angle of depression changes from $$30^0$$ to $$45^0$$ in $$3$$ second. What is the speed of the car in km/hr?  $$36$$ km/hr.
If $$n\ \in\ N$$ & $$n$$ is even, then $$\dfrac {1}{1\ .\ (n-1)\ !}+\dfrac {1}{3\ !(n-3)\ !}+\dfrac {1}{5\ !\ (n-5)\ !}+....+\dfrac {1}{(n-1)\ !\ 1\ !}=$$  $$\dfrac {2^{n-1}}{n\ !}$$

### Permutations And Combinations Questions and Answers

Permutations And Combinations Quiz Question Answer
$$\dfrac { { C }_{ 1 } }{ { C }_{ 0 } } +\dfrac { 2{ C }_{ 2 } }{ { C }_{ 1 } } +...\dfrac { 3{ C }_{ 3 } }{ { C }_{ n-1 } } =$$ $$\dfrac { n\left( n+1 \right) }{ 2 }$$
If $$^nC_{10}={^{n}C_{14}}$$, then $$n=?$$ $$24$$
When simplified, the expression
$$^{ 47 }{ C }_{ 4 }+\sum _{ j=1 }^{ 5 }$$   $$^{ 52-j }{ C }_{ 3 }$$ equals to
$$^{ 52 }{ C }_{ 4 }$$
The total number of 5- digit telephone numbers that can be composed with distinct digits, is None of these
If $$^{ n }{ C }_{ r-1 }=10,$$ $$^{ n }{ C }_{ r }=45,$$ and $$^{ n }{ C }_{ r+1 }=120,$$ then r equals $$2$$
If $$\sum\limits_{r = 0}^n {\left( {\frac{{r + 2}}{{r + 1}}} \right)} \,{\,^n}{C_r} = \frac{{{2^8} - 1}}{6},$$ then 'n' is

5
The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is $$150 \times 21 ^ { 2 }$$
$$\dfrac { { C }_{ 1 } }{ { C }_{ 0 } } +\dfrac { 2{ C }_{ 2 } }{ { C }_{ 1 } } +\dfrac { { 3C }_{ 3 } }{ { C }_{ 2 } } +.....+\dfrac { { nC }_{ n } }{ { C }_{ n-1 } } =$$ $$\dfrac { n(n+1) }{ 2 }$$
The number of odd numbers lying between 40000 and 70000 that can be made from the digits 0, 1, 2, 4, 5, 7 if digits can be repeated any number of times is  1296
In a shop there are five types of ice-creams available. A child buys six ice-creams.
Statement-l: The number of different ways the child can buy the six ice-creams is $$^{10}{C_{5}}$$.
Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 $$\mathrm{A}$$'s and 4 $$\mathrm{B}$$'s in a row.

Statement-1 is false, Statement-2 is true.

#### Probability Class 11 Commerce Applied Mathematics MCQ Quiz

If $$\phi$$ represents an impossible event, then $$P(\phi) =$$ ?
$$0$$
A glass jar contains $$10$$ red, $$12$$ green, $$14$$ blue and $$16$$ yellow marbles. If a single marble is chosen at random from the jar, find the sample space.
{red, green, blue, yellow}
Toss a fair coin $$3$$ times in a row, how many elements are in the sample space?
$$8$$
All possible outcomes of a random experiment forms the -
Sample space
The sum of the probabilities of all the elementary events of an experiment is ____? $$1$$
A ball is drawn at random from box $$I$$ and transferred to box $$II$$. If the probability of drawing a red ball from box $$I$$, after this transfer, is $$\dfrac{1}{3}$$, then the correct option(s) with the possible values of $$n_1$$ and $$n_2$$ is (are)
$$n_1=3$$ and $$n_2=6$$
A computer producing factory has only two plants $${ T }_{ 1 }$$ and $${ T }_{ 2 }$$. Plant $${ T }_{ 1 }$$ produces $$20\%$$ and plant $${ T }_{ 2 }$$ produces $$80\%$$ of total computers produced. $$7\%$$ of computers produced in the factory turn out to be defective. It is known that $$P$$ (computer turns out to be defective given that it is produced in plant $${ T }_{ 1 }$$) $$=10P$$ (computer turns out to be defective given that it is produced in plant $$\displaystyle { T }_{ 2 }$$).
where $$P(E)$$ denotes the probability of an event $$E$$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $${ T }_{ 2 }$$ is
$$\displaystyle \frac { 78 }{ 93 }$$
Write the sample space when a coin is tossed. S = [H, T]
A bag contains 12 balls out of which x are white.If one ball is drawn at random, what is the probability it will be a white ball? $$\displaystyle \frac{x}{12}$$
A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is $$\displaystyle \frac{11}{20}$$ and that of blue ball is $$\displaystyle \frac{1}{5}$$, then the number of black ball is? $$10$$

#### Relations Class 11 Commerce Applied Mathematics MCQ Quiz

What is general representation of ordered pair for two variables $$a$$ and $$b$$? $$(a, b)$$
Ordered pairs $$(x, y)$$ and $$(-1, -1)$$ are equal if $$y = -1$$ and $$x =$$ _____
$$-1$$
Is the following statement is true for $$(a, a)\in R$$  $$\forall a\in N?$$
False
If R={$$(x,y)/3x+2y=15$$ and x,y $$\displaystyle \epsilon$$ N}, the range of the relation R is________ $$\{3,6\}$$
If $$x$$ co-ordinate of a point is $$2$$ and $$y$$ co-ordinate is $$0$$, then ordered pair for its coordinate on $$XY$$ plane is $$(2, 0)$$
Let $$R$$ be the relation in the set $$N$$ given by $$R=\left\{(a, b): a=b-2, b>6\right\}$$. Choose the correct answer.
$$(6, 8)\in R$$
If ordered pair $$(a, b)$$ is given as $$(-2, 0)$$, then $$a =$$ $$-2$$
If $$x$$ and $$y$$ coordinate of a point is $$(3, 10)$$, then the $$x$$ co-ordinate is $$3$$
What are the ways of representing a relation? All of these
If $$x$$ and $$y$$ co-ordinate of a point is $$(3, 10)$$, then $$y$$ co-ordinate is $$10$$

### Sequences And Series Questions and Answers

Sequences And Series Quiz Question Answer
33, 43, 65, 99, 145 ? 203
If D=4 and COVER = 63, then BASIC is equal to 34
Calculate the geometric mean of $$3$$ and $$27$$.
$$9$$
Directions for questions 1 to 3: Find the related word/ letters/numbers from given alternatives.
12:72::8:?
32
If $$12\times 16 = 188$$ and $$14\times 18 = 248$$, then find the value of $$16\times 20 = ?$$ $$316$$
Find the sum of Arithmetic means of $$3 , 9$$ and $$12 , 8$$.

$$16$$
State true/false:
$$3,4,5,6,7,......$$ forms a progression. As they are formed by the rule $$n+1$$
True
The arithmetic mean of $$4$$ and $$14$$ is  $$9$$
If AM of two numbers a and 17 isThen a is ___ 13
Insert an arithmetic mean between $$7$$ and $$21$$ $$14$$

### Set Theory Questions and Answers

Examine the following statements:
$$\left \{ a, b \right \} \subset$$ { b, a,  c]
True
If $$X$$ and $$Y$$ are any two non empty sets then what is $$\displaystyle \left ( X-Y \right )'$$ equal to? $$\displaystyle {X}'\cup Y$$
If $$A$$ and $$B$$ are non empty sets and A' and B' represents their compliments respectively then $$A - B = B' - A'$$
If $$\displaystyle \xi =\left \{ 2,3,4,5,6,7,8,9,10,11 \right \}$$
$$\displaystyle A =\left \{ 3,5,7,9,11 \right \}$$
$$\displaystyle B =\left \{ 7,8,9,10,11 \right \}$$, then find $$(A - B)'$$
$$(A - B)' = \{2,4,6,7,8,9,10,11\}$$
State True or False
$$\displaystyle A\cup A'=\phi$$
False
The set of all those elements of A and B which are common to both is called intersection of two sets
Given $$K=\left \{B, A, N, T, I\right \}$$. Then the number of subsets of K, that contain both A, N is 8
In an examination $$70\%$$ students passed both in Mathematics and Physics $$85\%$$ passed in Mathematics and $$80\%$$ passed in Physics If $$30$$ students have failed in both the subjects then the total number of students who appeared in the examination is equal to :  $$600$$
If $$n(A) = 65, n(B) = 32$$ and $$\displaystyle n\left ( A\cap B \right )=14$$, then $$\displaystyle n\left ( A\Delta B \right )$$ equals $$69$$
If $$n(A) = 115$$, $$n(B) = 326$$, $$n(A - B) = 47$$ then $$\displaystyle n\left ( A\cup B \right )$$ is equal to $$373$$

### Straight Lines Questions and Answers

If the point (x,y) is equidistant from (a,0) and (2a,a) then x+y=2a
If the distance between the origin and (x,3)is 5 then x= $$\displaystyle \pm 4$$
The vertices P, Q, R, and S of a parallelogram are at (3,-5), (-5,-4), (7,10) and (15,9) respectively The length of the diagonal PR is $$\displaystyle \sqrt{241}$$
If P(1,4), Q(9,-2), and R(5,1) are collinear then R lies between P and Q
A triangle has two of its vertices at (0, 1) and (2, 2) in the cartesioan plane. Its third vertex lies on the x-axis. If the area of the triangle is 2 square units then the sum of the possible abscissae of the third vertex, is - -4
Let P and Q be points $$(4, 4)$$ and $$(9, 6)$$ of parabola $${y^2} = 4a\left( {x - b} \right)$$ If R be a point on the arc of the parabola between P and Q, such that the area of  $$\Delta PRQ$$ is largest, then R is $$\left( {4,4} \right)$$
The perpendicular distance between the lines represented by  $${ x }^{ 2 }-4xy+{ 4y }^{ 2 }+x-2y-6=0\quad is-$$ $$\sqrt { 5 }$$
The distance between the points $$(3,5)$$ and $$(x,8)$$ is $$5$$ units. Then the value of $$x$$  $$7$$
The middle point of the line segment joining $$(3 , 1)$$ and $$(1 , 1)$$ is shifted by two units ( in the sense increasing y) perpendicular to the line segment. Then the coordinates of the point in the new position is $$(2,3)$$
Area of the triangle formed by $${ (x }_{ 1 },{ y }_{ 1 })$$,$${ (x }_{ 2 },{ y }_{ 2 })$$,
$${ (3x }_{ 2 }-{ 2x }_{ 1 },{ 3y }_{ 2 }-{ 2y }_{ 1 })$$ is
0 sq.units

### Tangents And Its Equations Questions and Answers

Tangents And Its Equations Quiz Question Answer
The equation of normal to the curve $$3x^2-y^2 =8$$ which is parallel to the line $$x+ 3y=8$$ is $$x+3y \pm 8 = 0$$
Let N be the set of positive integers. For all $$n \in N$$, let
$$f_n = (n + 1)^{1/3} - n^{1/3}$$ and $$A = \left\{n \in N : f_{n +1} < \dfrac{1}{3(n + 1)^{2/3}} < f_n \right\}$$
Then
A = N
for $$f(x)=\displaystyle \int _{ 0 }^{ x }2 \left| t \right| dt$$, the tangent lines which are parallel to the bisector of the first co-ordinate angle is  $$y=x+\frac{1}{4}$$
At any point on the curve $$2x^{2}y^{2}-x^{4}=c$$, the mean proportional between the abscissa and the difference between the abscissa and the sub-normal drawn to the curve at the same point is equal to  ordinate
Given $$g(x)= \dfrac{x+2}{x-1}$$ and the line 3x + y -10 =0, then the line is  tangent to g(x)
The angle formed bt the positive y-axis and the tangent to $$y = x^{2}+4x-17$$ at $$(5/2, -3/4)$$ is $$\tan ^{-1}(9)$$
The abscissa of a point on the curve $$xy = (a+y)^{2}$$, the normal which cuts off numerically equal intercept from the coordinate axes, is  $$-\dfrac{a}{\sqrt{2}}$$
The co-ordinates of the point (s) on the graph of the function $$f(x)= \dfrac{x^{3}}{3} - \dfrac{5x^{2}}{2} + 7x - 4$$, where the tangent drawn cuts off intercept from the co-ordinate axes which (2, 8/3)
The equation of the curve $$y = be^{-x/a}$$ at the point where it crosses the y-axis is $$\dfrac{x}{a}+\dfrac{y}{b}=1$$
A curve is represented by the equations $$x=sec^{2}t$$ and $$y=\cot t,$$ where t is a parameter. If the tangent at the point P on the curve, where $$t=\pi /4$$, meets the curve again at the point Q, then $$\left | PQ \right |$$ is equal to $$\dfrac{3\sqrt{5}}{2}$$

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