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Solve the equation

1÷2x-1÷y=-1

1x+1÷2y=8

Elasticity of demand, measured by comparing the ratio of percentage change in the quantity demanded to the percentage change in the price of a commodity, is known as

A Fruit Box costs Rs. 450 and the rate of sales tax is 10%. Find the Amount of Sales Tax.

Solve the inequation :

$3z-5\le z+3<5z-9;z\in R.$

Graph the solution set on the number line.

In the following diagram, and are tangents to the circle. Find the value of: a) $\angle$AOB b) $\angle$OBA given = 7 cm.

A histogram along side represents the marks obtained by some candidates in an examination. Using the data in the diagram, calculate the mean mark.

Rahul was asked to think of a natural number. He was asked to multiply its square by 5 then add 8 and then subtract half of the original number. He wrote 503.What was the number he thought of?

Shriya and Vidya solved a quadratic equation. While solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. Which of the following are correct about the correct roots of the equation?

In the given figure, DE || AC and DC || AP, such that BC = 4 cm and BP = 6 cm, then $\frac{BE}{EC}$ is equal to

Four defenders are standing in the coordinates A(-2,5), B(4,5), C(2,1) and D(-4,1). If B and D move two coordinates to the left and right respectively, to stop a striker. What is the shape of the final position?

If A and B are disjoint sets,then how can you find n(A union.B ).

Find the letter to be placed in place of ‘?’ in the figure given.

A triangle has sides 5 cm, 12 cm and 13 cm. Find the length to one decimal place on the perpendicular from the opposite vertex to the side whose length is 13 cm

Find the length of a diagonal of a rectangle whose adjacent sides are 30 cm and 16 cm.

If $\overrightarrow{a}$ is perpendicular to $\overrightarrow{b}$ and $\overrightarrow{r}$ is a non – zero vector such that $p\overrightarrow{r}+(\overrightarrow{r}.\overrightarrow{b})\overrightarrow{a}=\overrightarrow{c}$, then $\overrightarrow{r}$ is equal to

In the above figure k an l are parallel lines and m is the transversal, then

What is the Euclid's Division LemmLemma

The sum of the digits of a two digit number is 13.The number obtained by interchanging its digits exceeds the given number by 9.Find the number.

(Answer:67)

A sum of money is to be distributed among A, B, C, D in the proportion of 5: 2: 4: 3. If C gets Rs. 1000 more than D, what is B's share?

Solve the following systems of equations graphically:

2x - 3y + 13 = 0

3x - 2y + 12 = 0

Find the ratio of the areas of two triangles shown in the figure. If $\Delta ABC$ ~$\Delta PQR$ ​​​​​.

Mr. Ram Gopal invested ₹ 8000 in 7%. ₹ 100 shares at ₹ 80. After a year he sold there share at ₹ 75 each and invested the proceeds (including his dividend) in 18%. ₹ 25 shares at ₹ 41. Find this annual dividend in $1^{st}$ & $2^{nd}$ year are

Find the sum to 10 terms of the following sequence:1,3,5,7,… to 10 terms

The points A(5, 5), B(4, 4) and C(3, 3) form a triangle. What kind of a triangle would the three points form?

If $\frac{a}{x-2y+3z}=\frac{b}{y-2z+3x}=\frac{c}{z-2x+3y}$ and
$x+y+z\ne 0$, then each ratio is also equal to ______.

The mid-point of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a + 1). Find the values of a and b.

If A = {x: $x^2$ - 5x + 6 = 0}, B = {2,4} , C = {4,5}, then

A×(B $\cap$ C) is

The product of the two positive consecutive positive integers is 306.Find the integer.

1,$\alpha$,${\alpha }^2$,............................${\alpha }^6$ are the roots of the equation x = $(1{)}^{\frac{1}{7}}$.Find the quadratic equation whose roots are A = $\alpha$ + ${\alpha }^2$ + ${\alpha }^4$, B = ${\alpha }^3$ + ${\alpha }^5$ + ${\alpha }^6$.

A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.

Ram walks 5 km from his home to school on a straight road daily. In the same way, there is shop 2 km away from his house. What is the probability of Ram being in between home and shop?

Money at call, the very short period loans, are repayable on demand with in

Find the value(s) of k so that the quadratic equation $3x^2-2kx+12=0$ has equal roots.

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut ?

$\left(i\right)(1+cos\theta )(1-cos\theta )(1+co{t}^2\theta )=1\left(ii\right)cosec\theta (1+cos\theta )(cosec\theta -cot\theta )=1$

The radii of two circles are 19 cm and 9 cm respectively. Find the radius and area of the circle which has its circumference equal to the sum of the circumferences of the two circles.

Express each of the following in terms of T-ratios of angles lying between $0^{\circ }and{45}^{\circ }:$

(i) $sin{67}^{\circ }+cos{75}^{\circ }$ (ii) $cot{65}^{\circ }+tan{49}^{\circ }$

(iii) $sec{78}^{\circ }+cosec{56}^{\circ }$ (iv) $cosec{54}^{\circ }+sin{72}^{\circ }$

The difference of two numbers is 4. If the difference of their reciprocals is $\frac{4}{21}$, find the numbers.

IF the sum of first p terms of an AP is $(a{p}^2+bp),$ find its common difference.

The difference fo squares fo two numbers is 180. The square fo the smaller number is 8 times teh larger number. Find two numbers.

In the equation $ax+by+c=0$, where c is a constant, if $a=b=0$ then

Factors of $a^2-b+ab-a$ are

Express each of the following integers as a product of its prime factors:
(i) 420 (ii) 468 (iii) 945 (iv) 7325

In the given figure, QR is a common tangent to the given circles, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm then the length of QR is

(a) 1.9 cm (b) 3.8 cm (c) 5.7 cm (d) 7.6 cm

Question 29

If the sides of a parallelogram are increased to twice its original lengths, how much will the perimeter of the new parallelogram increase?

(a) 1.5 times
(b) 2 times
(c) 3 times
(d) 4 times

A two-digit number is such that the ten's digit exceeds twice the unit's digit by 2 and the number obtained by inter-changing the digits is 5 more than three times the sum of the digits. Find the two digit number.