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Binomial Theorem Quiz Question  Answer 

The sum of coefficient of integral powers of $$x$$ in the binomial expansion of $$(12\sqrt x)^{50}$$ is :  $$\dfrac {1}{2}(3^{50}+1)$$ 
If $$(2+\dfrac {x}{3})^{55}$$ is expanded in the ascending powers of $$x$$ and the coefficients of powers of $$x$$ in two consecutive terms of the expansion are equal, then these terms are :  $$8^{th}$$ and $$9^{th}$$ 
If the sum of odd numbered terms and the sum of even numbered terms in the expansion of $$(x + a)^{n}$$ are $$A$$ and $$B$$ respectively, then the value of $$(x^{2}  a^{2})^{n}$$ is  $$A^{2}  B^{2}$$ 
$${ _{ }^{ 15 }{ C } }_{ 3 }+{ _{ }^{ 15 }{ C } }_{ 5 }+....+{ _{ }^{ 15 }{ C } }_{ 15 }$$ will be equal to  $${2}^{14}15$$ 
Find the sum of coefficient of middle terms of the expansion $$\left(3x\dfrac{x^3}{6}\right)^7$$:  $$\dfrac {595}{48}$$ 
The total number of terms in the expansion of $$(x+y)^{50}+(xy)^{50}$$ is  $$26$$ 
In the expansion of $$(\sqrt 2+\sqrt [3]{5})^{20}$$ the number of rational terms will be:  $$4$$ 
What is $$\displaystyle\sum _{ r=0 }^{ n }{ C\left( n,r \right) } $$ equal to?  $${2}^{n}$$ 
The number of rational terms in the expansion of $$(9^{1/4} + 8^{1/6})^{1000}$$ is: 
$$501$$ 
The $$3rd$$ term of $${\left( {3x  \dfrac{{{y^3}}}{6}} \right)^4}$$ is  $$^4{C_2}{\left( {3x} \right)^2}{\left( {  \dfrac{{{y^3}}}{6}} \right)^2}$$ 
Complex Numbers And Quadratic Equations Quiz Question  Answer 

Express $$\dfrac{1}{(1  cos \theta + 2 i sin \theta)}$$ in the form $$x + iy$$  $$\left(\displaystyle \frac{1}{5 + 3 cos \theta}\right) + \left(\displaystyle \frac{2 cot \theta/2}{5 + 3 cos \theta}\right)i$$ 
If $$z = x + iy$$ and $$\omega = \dfrac{(1 iz)}{(zi)}$$, then $$\left\omega\right = 1$$ implies that in the complex plane  z lies on the real axis 
If $$a, b$$ and $$c$$ are real numbers then the roots of the equation $$(x  a)(x  b) + (x  b)(x  c) + (x  c)(x  a) = 0$$ are always  Real 
If $$(x+iy)(23i)=4+i$$ then (x, y) =  $$\left ( \dfrac{5}{13},\dfrac{14}{13} \right )$$ 
If $$z =3+5i$$, then $$z^3+z+198=$$  $$3 + 15i$$ 
If $$z=23i$$ then $$z^24z+13=$$  $$0$$ 
The complex number $$\displaystyle \frac{1+2i}{1i}$$ lies in the quadrant : 
II 
$$\sqrt{3}\sqrt{75}=$$  $$15$$ 
The sum of two complex numbers $$a + ib$$ and $$c +id$$ is a real number if  $$b + d = 0$$ 
The locus of complex number z such that z is purely real and real part is equal to  2 is  The point (2, 0) 
Conic Sections Quiz Question  Answer 

If the lines $$2\mathrm{x}+3\mathrm{y}+1=0$$ and $$\mathrm{3x} \mathrm{y}4=0$$ lie along diameters of a circle of circumference $$ 10\pi$$, then the equation of the circle is: 
$$\mathrm{x}^{2}+\mathrm{y}^{2}2\mathrm{x}+2\mathrm{y}23=0$$ 
The circle $$x^{2}+y^{2}8x=0$$ and hyperbola $$\dfrac{x^{2}}{9}\dfrac{y^{2}}{4}=1$$ intersect at the points $$A$$ and $$B$$. then the equation of the circle with $$AB$$ as its diameter is 
$$x^{2}+y^{2}12x+24=0$$ 
The length of the latus rectum of the parabola $$169 \left[(x1)^2+(y3)^2\right]=(5x12y+17)^2$$ is:  $$\displaystyle \frac { 28 }{ 13 } $$ 
Equation of the ellipse in its standard form is $$\displaystyle \frac{x^2}{a^2}\frac{y^2}{b^2}=1$$  False 
The equation of the circle touching $$x = 0, y = 0$$ and $$x = 4$$ is  $$x^2 + y^2  4x  4y + 16 = 0$$ 
The radius of the circle with center (0,0) and which passes through (6,8) is  10 
Assertion is incorrect but Reason is correct  
The equation of circle with its centre at the origin is $$x^2+y^2=r^2$$  True 
Which of the following equations of a circle has center at (1, 3) and radius of 5?  $$\displaystyle \left ( x1 \right )^{2}+\left ( y+3 \right )^{2}=25$$ 
Determine the area enclosed by the curve $$\displaystyle x^{2}10x+4y+y^{2}=196$$  $$225\pi$$ 
Introduction To Three Dimensional Geometry Quiz Question  Answer 

Distance between $$A(4,5,6)$$ from origin $$O$$ is  $$\sqrt {77}$$ 
In the given figure, coordinates of the midpoint of $$AB$$ are 
$$(3,1)$$ 
Name three undefined terms. 
All of the above 
State the following statement is True or False If two distinct lines are intersecting each other in a plane then they cannot have more than one point in common. 
True 
Distance between the points $$(12,4,7)$$ and $$(10,5,3)$$ is  $$\sqrt{21}$$ 
The three planes divides the space into  eight parts 
A point on XOZplane divides the join of $$(5, 3, 2)$$ and $$(1, 2, 2)$$ at  $$\left(\displaystyle\frac{13}{5}, 0, 2\right)$$ 
In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are  three mutually perpendicular lines 
If G is centroid of $$\triangle ABC$$, then  $$3\overrightarrow {G}=\overrightarrow {a}+ \overrightarrow {b}+\overrightarrow {c}$$ 
Find the distance between $$(12,3,4)$$ and $$(4,5,2)$$  $$\sqrt {72}$$ 
Limits And Derivatives Quiz Question  Answer 

Differentiation gives us the instantaneous rate of change of one variable with respect to another.  True 
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  $$a>1$$ 
$$\displaystyle \frac{d(\tan x.)}{dx}$$  $$\sec^2 x$$ 
$$\displaystyle \frac{d(\sin x)}{dx}.$$  $$\cos x$$ 
Differentiate $$\displaystyle \cos x$$ 
$$\displaystyle \sin x$$ 
$$\displaystyle \dfrac{d}{dx} \sec x=$$  $$\sec x \tan x$$ 
State if the given statement is True or False Derivative of $$y= \cos x$$ with respect to $$x$$ is $$\sin x$$. 
False 
For instantaneous speed, the distance traveled by the object and the time taken are both equal to zero.  False 
Derivative of $$2\tan x  7\sec x$$ with respect to $$x$$ is: 
$$\sec x (2 \sec x  7 \tan x)$$ 
$$\displaystyle \frac{d}{dx}(\sin^{2}x)$$  $$sin2x$$ 
Linear Inequalities Quiz Question  Answer 

Which equation has the solution shown on the number line? 
$$1\leq x < 4$$. 
Ordered pair that satisfy the equation $$x + y + 1 < 0$$ is:  Both (B) and (C) 
Which of the following number line represents the solution of the inequality $$15 < 4x + 3 \le 31$$ ? 

Which equation has the solution shown on the number line? 
$$x \geq 6$$ 
If you multiply an inequality by a negative number, when should you reverse the inequality symbol?  Always 
Which equation has the solution shown on the number line? 
$$3\leq x < 0 $$. 
Find solution of following inequality also show it graphically. $$x<5,x\in W$$. 

Solve the following inequality and show it graphically: $$2<x+3<5,x\in Z$$ 

Which of the following number line represents the solution of the inequality $$2x+1 \ge 9$$?  
Find the solution of following inequality, also show it graphically: $$x<4,x\in R$$ 
Mathematical Reasoning Quiz Question  Answer 

The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times"' is:  If the area of a square does not increase four times, then its side is not doubled 
Consider the following two statements: P: If $$7$$ is an odd number, then $$7$$ is divisible by $$2$$. Q: If $$7$$ is a prime number, then $$7$$ is an odd number. If $$V_{1}$$ is the truth value of the contrapositive of P and $$V_{2}$$ is the truth value of contrapositive of Q, then the ordered pair $$(V_{1}, V_{2})$$ equals: 
$$(F, T)$$ 
The Boolean expression $$( ( p \wedge q ) \vee ( p \vee \sim q ) ) \wedge ( \sim p \wedge \sim q )$$ is equivalent to :  $$(\sim { p })\wedge (\sim { q })$$ 
The negation of $$\sim s \vee (\sim r\wedge s)$$ is equivalent to  $$S\wedge\ r$$ 
The contrapositive of the statement 'If I am not feeling well, then I will go to the doctor' is:  If I will not go to the doctor, then I am feeling well 
The contrapositive of the statement 'I go to school if it does not rain' is:  If I do not go to school, it rains. 
The contrapositive of the statement "If it is raining, then I will not come", is :  If I will come, then it is not raining. 
The contrapositive of "If $$x\in A\cup B$$, then $$x\in A$$ or $$x\in B$$", is 
If $$x\not\in A$$ and $$x\not\in B$$, then $$x\not\in A\cup B$$. 
Earth is a planet. Choose the option that is a negation of this statement. 
Earth is not a planet 
The converse of "if $$x\in A\cap B$$ then $$x\in A$$ and $$x\in B$$", is 
If $$x\in A$$ and $$x\in B$$, then $$x\in A\cap B$$. 
Permutations And Combinations Quiz Question  Answer 

If $$\displaystyle { S }_{ { n } }=\sum _{ { r }=0 }^{ { n } } \frac { 1 }{ ^{ n }{ { C }_{ r } } } $$ and $$\displaystyle { t }_{ { n } }=\sum _{ { r }=0 }^{ { n } } \frac { { r } }{ ^{ n }{ { C }_{ r } } } $$, then $$\displaystyle \frac { { t }_{ { n } } }{ { s }_{ { n } } } =$$  $$\displaystyle \frac{1}{2}{n}$$ 
The value of $$^{50}C_{4}+ \sum _{r=1}^{6}\ ^{56r}C_{3}$$ is  $$^{56}C_{4}$$ 
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is.  $$46^{th}$$ 
Statementl: $$\displaystyle \sum_{r=0}^{n}(r+1)^{n}C_{r}=(n+2)2^{n1}$$ Statement2: $$\displaystyle \sum_{r=0}^{n}(r+1)^{n}C_{r}x^{r}=(1+x)^{n}+nx(1+x)^{n1}$$ 
Statement1 is true, Statement2 is true; Statement2 is a correct explanation for Statement1. 
The total number of 4digit numbers in which the digits are descending order is  $${ _{ }^{ 10 }{ C } }_{ 4 }$$ 
An automobile dealer provides motorcycles and scooters in three body patterns and $$4$$ different colors each. The number of choices open to a customer is  $$4\times 3\times 2$$ 
There are $$'m'$$ copies each of $$'n'$$ different books in a university library. The number of ways in which one or more than one book can be selected is  $$(m+1)^n  1$$ 
In a crossword puzzle, $$20$$ words are to be guessed of which $$8$$ words have each an alternative solution also. The number of possible solutions will be  $$ 256 $$ 
$$ ^xC_7  ^xC_5 = 0 $$, then $$x = $$  12 
$$15$$ buses operate between Hyderabad and Tirupathi.The number of ways can a man go to Tirupathi from Hyderabad by a bus and return by a different bus is  $$210$$ 
Principle Of Mathematical Induction Quiz Question  Answer 

Statementl: For every natural number $$n\geq 2,\ \displaystyle \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\ldots\ldots+\frac{1}{\sqrt{n}}>\sqrt{n}$$. Statement2: For every natural number $$n\geq 2,\ \sqrt{n(n+1)}<n+1$$. 
Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for Statement1. 
Let $$S(k) = 1 + 3 + 5 + .... + (2k  1) = 3 + k^2$$. Then which of the following is true?  $$S (k)$$ $$\Rightarrow$$ $$S (k + 1)$$ 
Mathematical Induction is the principle containing the set 
N 
Let $$P(n)$$ be a statement and $$P(n)=P(n+1) \forall n\in N$$, then $$P(n)$$ is true for what values of $$n$$? 
For all $$n$$ 
State whether the following statement is true or false. cos x + cos 2x + .... + cos nx = $$\dfrac{cos\left (\dfrac{n \, + \, 1 }{2} \right )x sin \dfrac{nx}{2}}{sin\dfrac{x}{2}}$$ 
True 
$$1+3+5+....+(2n1)=n^2$$.  True 
A bag contains $$3$$ red and $$2$$ black balls. One ball is drawn from it at random. Find the probability of drawing red ball is $$\dfrac 35$$ 
True 
Let $$P(n)$$ be the statement $$"3^n>n"$$. If $$P(n)$$ is true, $$P(n+1)$$ is true.  True 
Let $$P(n)= 5^{n}2^{n}$$. $$P(n)$$ is divisible by $$ 3\lambda$$ where $$\lambda$$ and $${n}$$ both are odd positive integers, then the least value of $$n$$ and $$\lambda$$ will be 
$$1$$ 
For every integer $$n\geq 1, (3^{2^{n}}1)$$ is always divisible by 
$$2^{n+2}$$ 
Probability Quiz Question  Answer 

A set $$A$$ is containing $$n$$ elements. A subset $$P$$ of $$A$$ is chosen at random. The set is reconstructed by replacing the elements of $$P$$. A subset $$Q$$ of $$A$$ is again chosen at random. The probability that $$P$$ and $$Q$$ have no common elements is:  $$\left (\dfrac {3}{4}\right )^n$$ 
If events $$A$$ and $$B$$ are independent and $$P(A)=0.4, P(A\cup B)=0.6$$, then $$P(B)=$$ 
$$\dfrac{1}{3}$$ 
Let $$S$$ and $$T$$ are two events defined on a sample space with probabilities $$P(S)=0.5,P(T)=0.69,P(S/T)=0.5$$ Event $$S$$ and $$T$$ are  independent 
If $$P(A)=\dfrac {1}{8}$$ and $$P(B)=\dfrac {5}{8}.$$ Which of the following statements is not correct?  $$P(\overline A\cap B)\leq \dfrac {5}{8}$$ 
If events $$A$$ and $$B$$ are independent and $$P(A)=0.15, P(A\cup B)=0.45,$$ then $$P(B)$$ is:  $$\dfrac {6}{17}$$ 
If events $$A$$ and $$B$$ are independent and $$P(A)=0.15, P(A\cup B)=0.45$$, then $$P(B)=$$  $$\dfrac {6}{17}$$ 
A bag contains four tickets marked with $$112, 121, 211, 222$$, one ticket is drawn at random from the bag. Let $$E_i(i=1, 2, 3)$$ denote the event that $$i^{th}$$ digit on the ticket is $$2$$ then :  $$E_3$$ and $$E_1$$ are independent 
A coin is tossed 15 times and the outcomes are recorded as follows: $$H\, T\, T\, H\, T\, H\, H\, H\, T\, T\, H\, T\, H\, T\, T$$ The chance of occurrence of a head is $$50$$ per cent. 
False 
One or more outcomes of an experiment make an event.  True 
E and F are two independent events,The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2.Then,  $$P(E)=1/3,P(F)=1/4$$ 
Relations And Functions Quiz Question  Answer 

For nonnegative integers s and r, let $$\begin{pmatrix} s \\ r \end{pmatrix}$$ $$ \left\{\begin{matrix} \dfrac{s!}{r!(s  r)!} & if \ r \le s\\ 0 & if \ r > s \end{matrix}\right.$$ For positive integers m and n, let $$g(m, n) = \sum_{p = 0}^{m+n} \dfrac{f(m, n, p)}{\begin{pmatrix} n + p \\ p \end{pmatrix}}$$ where for any nonnegative integer p, $$f(m, n, p) = \sum_{i = 0}^p \begin{pmatrix} m \\ i \end{pmatrix} \begin{pmatrix} n + i \\ p \end{pmatrix} \begin{pmatrix} p + n \\ p  i\end{pmatrix}$$. Then which of the following statements is/are TRUE? 
$$g(2m, 2n) = (g(m, n))^2$$ for all positive integers $$m, n$$ 
$$A$$ and $$B$$ are two sets having $$3$$ and $$4$$ elements respectively and having $$2$$ elements in common. The number of relations which can be defined from $$A$$ to $$B$$ is:  $$2^{12}$$ 
Let $$R$$ be a relation from a set $$A$$ to a set $$B$$, then:  $$R\subseteq A\times B$$ 
If $$\displaystyle a  \frac{1}{a} = 8$$ and $$\displaystyle a \neq 0$$; find :$$\displaystyle a + \frac{1}{a}$$.  $$\displaystyle \pm 2 \sqrt{17}$$ 
If $$f(x)=3x+1, g(x)= x^{3}+2,$$ then $$(f+g)(0)f(0)g(0)=$$ 
$$1$$ 
Let $$x$$ be a real number $$\left [ x \right ]$$ denotes the greatest integer function, and $$\left \{ x \right \}$$ denotes the fractional part and $$(x)$$ denotes the least integer function,then solve the following. $$\left [ 2x \right ]2x=\left [ x+1 \right ]$$ 
$$\left \{ 1,\displaystyle\frac{1}{2} \right \}$$ 
If $$A=\left \{x:x^23x+2=0\right \}$$ and $$B=\left \{x:x^2+4x5=0\right \}$$ then the value of AB is  $$\left \{2\right \}$$ 
If R={$$(x,y)/3x+2y=15$$ and x,y $$\displaystyle \epsilon $$ N}, the range of the relation R is________  $$\{3,6\}$$ 
If $$x$$ coordinate of a point is $$2$$ and $$y$$ coordinate is $$0$$, then ordered pair for its coordinate on $$XY$$ plane is  $$(2, 0)$$ 
If $$(x+3, 4y)=(1,7)$$, then $$(x3, 4+y)$$ is equal to  $$(5, 1)$$ 
Sequences And Series Quiz Question  Answer 

The value of $$\displaystyle \sum_{r = 16}^{30}{ (r + 2)(r  3) } $$ is equal to :  $$7780$$ 
Let $$\mathrm{a}_{1},\ \mathrm{a}_{2},\ \mathrm{a}_{3},\ \ldots,\ \mathrm{a}_{11}$$ be real numbers satisfying $$\mathrm{a}_{1}=15,272\mathrm{a}_{2}>0$$ and $$\mathrm{a}_{\mathrm{k}}=2\mathrm{a}_{\mathrm{k}1}\mathrm{a}_{\mathrm{k}2}$$ for $$\mathrm{k}=3,4,\ \ldots, 11.$$ If $$\displaystyle \frac{a_{1}^{2}+a_{2}^{2}+\ldots+a_{11}^{2}}{11}=90$$, then the value of $$\displaystyle \frac{a_{1}+a_{2}+\ldots+a_{11}}{11}$$ is equal to 
$$0$$ 
$$x\left (x + \dfrac {1}{x}\right )^{2} + \left (x^{2} + \dfrac {1}{x^{2}}\right )^{2} + \left (x^{3} + \dfrac {1}{x^{3}}\right )^{2}$$ .... upto $$n$$ terms is  $$\dfrac {x^{2n}  1}{x^{2}  1}\times \dfrac {x^{2n + 2} + n}{x^{2n}} + 2n$$ 
Which letter will be the fifth from the right if the first and second, the third and fourth and so on are interchanged among each other in the word "COMPANIONATE"?  I 
If the sum of the first n natural numbers is 1/5 times the sum of the their squares, then the value of n is  7 
Mean of the first $$n$$ terms of the A.P. $$a, (a + d), (a + 2d), ........$$ is  $$\displaystyle a + \frac{(n  1)d}{2}$$ 
The sum of $$n$$ terms of the series whose $$n^{th}$$ term is $$n(n + 1)$$ is equal to.  $$\dfrac {n(n + 1)(n + 2)}{3}$$ 
The sum of nn is equal to  $$\dfrac {1}{4}n(n+1)(n+2)(n+3)$$ 
In numbers from $$1 \ to\ 100$$ the digit "$$0$$" appears ____________times.  $$11$$ 
The spread sheet on the right contains 20 cells. A cell In a spread sheet can be identified fIrst by the column letter and then by the row number. For example,. the number 10 is found in cell CIf the number in cell A3 =B43(E2 +D4) then which of the following must be the number in cell E2? 
12 
Sets Quiz Question  Answer 

If P is true and Q is false, then Biimplication of p and q is  False 
For any two sets $$ A$$ and $$B, A = B$$ is equivalent to 
$$A \cup C = B \cup C$$ and $$A \cap C = B \cap C $$ for any set $$C$$ 
If A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {1, 3, 5, 7}, then find $$A  B$$ and $$A \cap B$$ 
{2, 4, 6, 8} and {1, 3, 5, 7} 
Suppose $${ A }_{ 1 },{ A }_{ 2 },...,{ A }_{ 30 }$$ are thirty sets, each with five elements and $${ B }_{ 1 },{ B }_{ 2 },...,{ B }_{ 30 }$$ are $$n$$ sets ecah with three elements. Let $$\displaystyle \bigcup _{ i=1 }^{ 30 }{ { A }_{ i }= } \bigcup _{ j=1 }^{ n }{ { B }_{ j } } =S$$ If each element of $$S$$ belongs to exactly ten of the $${ A }_{ i }'s$$ and exactly none of the $${ B }_{ j }'s$$ then $$n=$$ 
45 
A $$\bigcup \phi = $$ 
A 
If $$A=\left \{ 1,2,3 \right \};B=\left \{ 2,3,4 \right \},$$ then $$AB=$$  $$\left \{ 1 \right \}$$ 
Let $$n$$ be a fixed positive integer. Let a relation $$R$$ defined on $$I$$ (the set of all integers) as follows: $$aRb$$ iff $$n/(ab)$$, that is, iff $$ab$$ is divisible by $$n$$, then, the relation $$R$$ is 
An equivalence relation 
Let $$A=\left\{ 1,2,3,4 \right\} $$ and $$B=\left\{ 2,3,4,5,6 \right\} $$ then $$A \triangle\ B$$ is equal to  $$\left\{ 1,5,6 \right\} $$ 
If X $$=$$ (multiples of 2), Y $$=$$ (multiples of 5), Z $$=$$ (multiples of 10), then $$X \cap ( Y \cap Z )$$ is equal to 
multiples of 10 
In a locality twothirds of the people have cable TV onefifth have Dish TV and onetenth have both What is the fraction of people having either cable TV or Dish TV? 
$$\displaystyle \frac{2}{3}$$ 
Statistics Quiz Question  Answer 

The mean of $$x, y, z$$ is $$y$$, then $$x+z =$$  $$2y$$ 
Value of the middlemost observation(s) is called:  Median 
The ________ is the difference between the greatest and the least value of the variate.  Range 
Median divides the total frequency into _____ equal parts.  $$2$$ 
The modal value is the value of the variate which divides the total frequency into two equal parts.  False 
The difference between the maximum and the minimum obervations in data is called the ____________.  range of the data 
The variance is the _______ of the standard deviation.  Square 
State true or false: The mode is the most frequently occurring observation. 
True 
A child says that the median of $$3, 14, 18, 20, 5$$ is $$18$$. What concept does the child missed about finding the median? 
The order of numbers. 
Median of $$15, 28, 72, 56, 44, 32, 31, 43\ and\ 51\ is\ 43.$$  True 
Straight Lines Quiz Question  Answer  

Area of a triangle formed by the points A(5, 2), B(4, 7) and C(7, 4) is _____.  2 sq. units  
$$A(0, 0), B(7, 2), C(7, 7)$$ and $$D(2, 7)$$ are the vertices of a quadrilateral. The respective slopes of diagonals $$AC$$ and $$BD$$ are 
$$1, 1$$  
Let $$\mathrm{P}(\mathrm{x}_{1},\mathrm{y}_{1})\mathrm{b}\mathrm{e}$$ any point on the cartesian plane then match the following lists:

$$A  2, B  4, C  3$$  
If A and B are the points $$(6,7)$$ and $$(1,5)$$ respectively, then the distance 2AB is equal to 
$$26$$  
The vertices of a triangle are $$(2,0) ,(2,3)$$ and $$(1, 3)$$ , then the type of the triangle is  scalene  
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  $$\displaystyle \sqrt{241}$$  
The distance between (a,b) and (a, b) is given by  2a  
The area of a triangle whose vertices are $$(a, c+a), (a, c) $$ and $$(a, ca) $$ are  $$\displaystyle a^{2}$$  
Equation of the line y = 0 represents  xaxis  
The points $$(2, 1), (1, 0),(4, 3),$$ and $$(1, 2)$$ are the vertices  Parallelogram 
Trigonometric Functions Quiz Question  Answer 

The number of $$x\epsilon [0, 2\pi]$$ for which $$\sqrt {2\sin^{4} x + 18\cos^{2}x}  \sqrt {2\cos^{4} x + 18\sin^{2} x} = 1$$ is:  $$8$$ 
For $$x \in (0, \pi)$$, the equation $$\sin x + 2 \sin 2 x  \sin 3x =3$$, has  no solution 
If $$0^{\circ}\leq \theta\leq 90^{\circ}$$ and $$\sqrt{3} tan\theta  sec\theta=1$$, then $$\theta$$ has the value 
$$60^{\circ}$$ 
The of value of $$\quad \sin60^{\small\circ}\cos30^{\small\circ} + \cos60^{\small\circ}\sin30^{\small\circ}$$ is equal to 
$$\sin 90^0$$ 
Which one of the following relations is true ? 
$$\sec^2 \theta  \tan^2 \theta=1$$ 
Which is true for all values of $$\theta$$? 
$$\text{cosec}^2\theta \cot^2 \theta=1$$ 
If $$0^{\circ} \leq \theta \leq 90^{\circ}$$ and $$\sqrt{2} tan \theta  sec \theta =0$$, then the value of $$(\sqrt{2} sin \theta + 2 tan \theta)$$ is  
3 
The value of $$ 1+ \cot^2 A$$ is 
$$\text{cosec}^2 A$$ 
$$sin^2x+cos^2x=$$ 
1 
The solution of equation $$\cos^2 \theta +\sin \theta+1=0$$ lies in the interval  $$\displaystyle \left ( \frac{5\pi}{4}, \frac{7\pi}{4} \right )$$ 
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