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The sum of the numerator and the denominator of a fraction is equal to 7. Four times the numerator is 8 less than 5 times the denominator. Find the fraction.

Given that, x² + 2x - 3 is a factor of x⁴ + 6x³ + 2ax² + bx - 3a. Find the values of a and b.

Identify the countable noun in the sentence.

Two hundred invitations were sent out but only one-fifty invitations were confirmed.

In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km², show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

Figure shows a sector of a circle, centre O, containing an angle $\theta {}^{\circ }$. Prove that:

(i) Perimeter of the shaded region is $r(tan\theta +sec\theta +\frac{\pi \theta }{180}-1)$

(ii) Area of the shaded region is $\frac{r^2}{2}(tan\theta -\frac{\pi \theta }{180})$

LCM of $v^2-v$, $v^2-1^2$, and $v^3-1$

From an external point P, two tangents are drawn that touches the circle at points Q and R. The triangle PQR is necessarily a/an ___triangle.

The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm². The area of the curved surface of cone is ___

If $sec\theta$ + $tan\theta$ = x, then $tan\theta$ is:

Which of the following does not have a diagonal?

The first term and common difference of some arithmetic sequence are given below. Write each of them in the form x_n = a_n + b; also write down the first three terms of each:

(i) first term −2, common difference 5

(ii) first term 2, common difference −5

(iii) first term 1, common difference

If one of zeros of a polynomial 3x^2-8x+(2k+1) is 7 times of the Other find the value of k

In a given $\Delta ABC,DE\parallel BC$ and $\frac{AB}{DB}=\frac{3}{5}$. If AC = 5.6, find AE. [3 MARKS]

1. 10

The ratio of surface areas of $1$ cube of volume $64c{m}^3$ and 64 cubes of volume $1c{m}^3$ is:

A shopkeeper purchases a certain number of books for Rs.960. If the cost per book was Rs.8 less, the number of books that could be purchased for Rs.960 would be 4 more. Write an equation with cost of each book as Rs. & solve it to find the original cost of the books.

A(-3, -4) , B(3, 0) , C(-5, 0) are the vertices of $△$ABC. Find the co-ordinates of the circumcentre of $△$ABC.

A triangle similar to given $\Delta ABC$with sides equal to $\frac{3}{4}$ of the sides of $\Delta ABC$ is constructed.



$\frac{B{C}^{\prime }}{BC}$ is equal to____.

Prove that is irrational.

A number X is selected at random from 1, 2, 3and 4. Another number Y is selected at random from the numbers 1,4,9 and 16. Find the probability that product of X and Y is less than 16.

If the mean of a, b, c, d and e is 28, mean of a, c and e is 24 and mean of b and d is $n^2-2$, then the value of n is $\pm k$, where k is

A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 $m^2$. Find the width of the path.

If $\alpha and\beta$ are the roots of the quadratic equation $x^2–5x+2=0,$ then a quadratic equation whose roots are can be $\frac{\alpha }{\beta }and\frac{\beta }{\alpha }$ can be

Find the quadratic polynomial whose sum of its zeroes (roots) is $-\frac{8}{5}$ and the product of the zeroes (roots) is $\frac{7}{5}$.

(1) If alpha and beta are the zeroes of the polynomaial 2X(square)-5X+7 , Find a polynomial whose zeroes are 2 alpha + 3 beta and 3 alpha + 2 beta.

(2) If alpha and beta are the zeroes of the polynimial 3X(square)-4X+1 , Find a polynomial whose zeroes are alpha(square) by (divided by ) beta and beta (square) by alpha.

please help me....

Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations:

$(2a-1)x+3y=5,3x+(b-1)y=2$

The number of common solution(s) of $y=3^x$ and $y=\ln (4+x)$ is