# Relation between Variables and Equations

## Trending Questions

**Q.**

$3{(\mathrm{sin}\left(x\right)\u2013\mathrm{cos}\left(x\right))}^{4}+6{(\mathrm{sin}\left(x\right)+\mathrm{cos}\left(x\right))}^{2}+4\left({\mathrm{sin}}^{6}\left(x\right)+{\mathrm{cos}}^{6}\left(x\right)\right)=?$

$11$

$12$

$13$

$14$

**Q.**

$\int \frac{sin\left(2x\right)}{si{n}^{2}\left(x\right)+2co{s}^{2}\left(x\right)}dx=?$

$\u2013\mathrm{log}(1+{\mathrm{sin}}^{2}x)+c$

$\mathrm{log}|1+{\mathrm{cos}}^{2}x|+c$

$\u2013\mathrm{log}|1+{\mathrm{cos}}^{2}x|+c$

$\mathrm{log}(1+{\mathrm{tan}}^{2}x)+c$

**Q.**You have been asked to plot graphs of the following equations:

Equation 1: 3x+2y=1

Equation 2: y−2x=2

Fill the following tables (find p, q, r, s) which you will use to plot the graphs:

Equation 1:

x05ypq

Equation 2:

xrsy05

- p=12, q=−7, r=−1, s=32
- p=2, q=7, r=2, s=3
- p=3, q=12, r=23, s=0
- p=3, q=5, r=2, s=8

**Q.**

The point of intersection of axes is

**Q.**

Find the coordinates of the point where the line 2x-y=3 meets both the Axes

**Q.**

The total height of the Statue of Liberty and its pedestal is $153$ feet more than the height of the statue. What is the height of the statue? Justify your answer.

**Q.**

Let $0<x<\frac{\pi}{4}$ then $\mathrm{sec}\left(2x\right)-\mathrm{tan}\left(2x\right)$ equals

$\mathrm{tan}\left(x-\frac{\pi}{4}\right)$

$\mathrm{tan}\left(\frac{\pi}{4}-x\right)$

$\mathrm{tan}\left(x+\frac{\pi}{4}\right)$

${\mathrm{tan}}^{2}\left(x+\frac{\pi}{4}\right)$

**Q.**If abscissa of a point is zero, on which axis do the point lies

**Q.**

The point of intersection of the lines x = 4 and y = -3 is

(4, -3)

(4, 3)

(-4, 3)

(-4, -3)

**Q.**If 3x+b1y+5=0 and 4x+b2y+10=0 cut the x-axis and y-axis in four concyclic points , then the value of b1b2 i

**Q.**

**Question 4**

The taxi fare in a city is as follows: For the first kilometre, the fare is Rs. 8 and for the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total fare as Rs. y, write a linear equation for this information, and draw its graph.

**Q.**

The parameter, on which the value of the determinant $\left|\begin{array}{ccc}1& a& {a}^{2}\\ \mathrm{cos}\left(\left(p-d\right)x\right)& \mathrm{cos}\left(px\right)& \mathrm{cos}\left(\left(p+d\right)x\right)\\ \mathrm{sin}\left(\left(p-d\right)x\right)& \mathrm{sin}\left(px\right)& \mathrm{sin}\left(\left(p+d\right)x\right)\end{array}\right|$ does not depend upon is

$a$

$p$

$d$

$x$

**Q.**

${}^{15}C_{3}+{}^{15}C_{5}+...+{}^{15}C_{15}$ is equal to

${2}^{14}$

${2}^{14}-15$

${2}^{14}+15$

${2}^{14}-1$

**Q.**

**Represent the following situations mathematically:**

(i) John and Jivanti together have $45$marbles. Both of them lost $5$marbles each, and the product of the number of marbles they now have is$124$. We would like to find out how many marbles they had to start with.

(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be$55$ minus the number of toys produced in a day. On a particular day, the total cost of production was `$750$. We would like to find out the number of toys produced on that day.

**Q.**

If point P lies on the line y = 2, then what is its y-coordinate?

2

-2

0

Cannot be determined

**Q.**

Question 47

In the following question, state whether the given statement is true (T) or false (F).

The number LIV is greater than LVI.

**Q.**

You have a total of $18$ math and science exercises for homework.

You have six more math exercises than science exercises.

How many exercises do you have in each subject?

**Q.**

**Question 1**

Draw the graph of each of the following linear equations in two variables:

(i) x+y=4 (ii) x−y=2 (iii) y=3x (iv) 3=2x+y

**Q.**

**Question 5**

From the choices given below, choose the equation whose graphs are given in Fig. 4.6 and Fig. 4.7.

For Fig.4.6 For Fig.4.7

(i)y=x (i)y=x+2

(ii)x+y=0 (ii)y=x−2

(iii)y=2x (iii)y=−x+2

(iv)2+3y=7x (iv)x+2y=6

**Q.**A line passes through A(1. 1) and B(100, 1000). The number of points with integral co-ordinates on the linestrictly between A and B is

**Q.**

A man is $7$ times as old as his son. If he is $56$ years, find the age of his son.

**Q.**

The function $\frac{a\mathrm{sin}\left(x\right)+b\mathrm{cos}\left(x\right)}{c\mathrm{sin}\left(x\right)+d\mathrm{cos}\left(x\right)}$ is decreasing, if

$ad-bc>0$

$ad-bc<0$

$ab-ad>0$

$ab-cd<0$

**Q.**

Gina has $15$ dollars more than twice as much money as her sister Maria. If Gina gives Maria $30$ dollars, then Gina will have half as much money as her sister. How many dollars does Gina have?

**Q.**Question 7

2x3=18

**Q.**

To plot the graphs of the following equations:

Equation 1: 3x+2y=1

Equation 2: y−2x=2

Fill in the values of p, q, r, and s in the given tables.

Equation 1:

x05ypq

Equation 2:

xrsy05

- p=12, q=−7, r=−1, s=32
- p=2, q=7, r=2, s=3
- p=3, q=12, r=23, s=0
- p=3, q=5, r=2, s=8

**Q.**

Suppose you start at the origin, move along the $x$-axis a distance of $4$ units in the positive direction, and then move downward along the $z$-axis a distance of $5$ units.

What are the coordinates of your position? $(x,y,z)$

**Q.**What is co-ordinate geometry?

**Q.**

Apples are to be transferred from larger baskets to smaller baskets. When a larger box is emptied, the apples from it fill three smaller baskets and still, $16apples$ remain outside. If the number of apples in a small basket is taken to be $x$, what is the number of apples in the larger basket?

**Q.**Prove that composition of two continuous function is continuous.

**Q.**

If ${x}^{2}\ne n\pi +1$, $n\in N$, then $\int x\sqrt{\frac{2\mathrm{sin}\left({x}^{2}-1\right)-\mathrm{sin}2\left({x}^{2}-1\right)}{2\mathrm{sin}\left({x}^{2}-1\right)+\mathrm{sin}2\left({x}^{2}-1\right)}}dx$ is equal to:

$\mathrm{ln}\mathrm{cos}\left(\frac{{x}^{2}-1}{2}\right)+c$

$\frac{1}{2}\mathrm{ln}\mathrm{cos}\left(\frac{{x}^{2}-1}{2}\right)+c$

$\mathrm{ln}\mathrm{sec}\left(\frac{{x}^{2}-1}{2}\right)+c$

$\frac{1}{2}\mathrm{ln}\mathrm{sec}\left(\frac{{x}^{2}-1}{2}\right)+c$