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Solve the following equations

(1) (x + 4) (x − 4) = 6x

(2) 2(a² − 1) = a(1 − a)

(3) 3(b − 5) (b − 7) = 4 (b + 3)

(4) 8(s − 1) (s + 1) + 2(s + 3) = 1

(5) (n − 3)² + (n + 1)² = 16

(6) 11(m + 1) (m + 2) = 38(m + 1) + 9m

1. 18.75

Construct a triangle ABC, in which $ABC={75}^o$,AB=5 cm and BC=6.4 cm. Draw perpendicular bisector of side BC and also the bisector of Angle ACB.If these bisectors intersect each other at point P;prove that P is equidistant from B and C; and also from AC and BC.

1. 5

A letter is chosen at random from the letters of the word 'ASSOCIATION'. Find the probability that the chosen letter is a (i) vowel (ii) consonant (iii) an S.

A shopkeeper buys a certain number of books for Rs. 720. If the cost per book was Rs.5 less, the number of books that could be brought for Rs. 720 would be 2 more.

Taking the original cost of each book to be Rs. , write an equation in & solve it.

Question 1 (iii)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

$-3x^2+5x+12=0$

Suppose the daily revenue (R) from selling x boxes of candy is given by the equation R = ₹ 12x. The daily cost of operating the store and the production of candy (C) is given by the equation C = ₹(8x + 96) . For how many boxes of candy will the revenue exceed the cost of production

Find the G.P. if

(1) (a) T_n = 2 × 5⁽ⁿ⁻¹⁾

(b) T_n = 2 × 3⁽ⁿ⁻¹⁾

(c) T₇ = 243 and r = 3

(d)

(e)

Th sum of the first 30 terms of the arithmetic sequence 10, 18, 26... is ___.

Find the sum of the following geometric progressions :

(i) 2, 6, 18, ..... to 7 terms

(ii) 1, 3, 9, 27, .... to 8 terms

(iii) $1,-\frac{1}{2},\frac{1}{4},-\frac{1}{8},....$

(iv) $(a^2-b^2),(a-b),\left(\frac{a-b}{a+b}\right),.....$ to n terms

(v) 4, 2, 1, $\frac{1}{2}....$ to 10 terms.

If (2,2) lies on $4x+5y=k$, the value of $k$ is

if x+2 is a factor of $2x^2-kx$, whats the value of k

Thirty candies were distributed among some children. Relishing the sweet, the whiz-kid among them said, “If we were one short, we would all get one more.” How many kids were there?

Q. If two dice are tossed, what is the probability of getting the sum as 6?



Q. यदि दो पासे उछाले जाते हैं, तो योग के रूप में 6 प्राप्त करने की प्रायिकता क्या है?

In $\Delta ABC$ and A DEF, it is being given that: AB = 5 cm, BC = 4 cm and CA = 4.2 cm;
DE. 10cm, EF= 8cm and FD = 8.4cm. If $AL\perp BD$ and $DM\perp EF$, find AL : DM.

Match the following;
$\begin{array}{cc}Column-I& Column-II\\ \text{(A) In the given figure,}& \left(p\right){60}^{\circ }\\ \text{ABCD is a cyclic Quadrilateral.}& \\ \text{O is the centre of the circle.}& \\ \text{If}\angle BOD={160}^{\circ }\text{find the Measure of}\angle BPD.& \end{array}$


$\begin{array}{cc}\text{(B) In given figure, ABCD is a cyclic}& \left(q\right){65}^{\circ }\\ \text{quadrilateral whose side AB is a diameter}& \\ \text{of the circle through A, B, C, D.}& \\ \text{If}\angle ADC={130}^{\circ },\text{find}\angle BAC.& \end{array}$


$\begin{array}{cc}\text{(C) In the given figure BD = DC and}& \left(r\right){40}^{\circ }\\ \angle CBD={30}^{\circ }\text{Find m}\left(\angle BAC\right)& \end{array}$


$\begin{array}{cc}\text{(D) In the given figure, O is the centre of the}& \left(s\right){100}^{\circ }\\ \text{arc ABC subtends an angle of}{130}^{\circ }\text{at the centre.}& \\ \text{If AB is extended to Pm find}\angle PBC.& \end{array}$


Choose the correct option:

If α and β are the zeroes of the polynomial 5x² - 7x + 2, then sum of their reciprocals is:

]It two zeroes of the polynomial are, find other zeroes.

If √2 sin (60^o - α) = 1, then α is:

If you are asked to construct $△$APQ $\sim$ $△$ABC with the scale factor $\frac{3}{5}$, which of the following are correct? In $△ABC,AB=4cm$, $BC=3cm$ and $\angle ABC={90}^{\circ }$.​

If in two right triangles, hypotenuse and one side of one triangle are proportional to the hypotenuse and one side of the other triangle, then the two triangles are __________.

If $x=\frac{\sqrt{5}-2}{\sqrt{5}+2}$ then $x^2$ = ___

Simplify $\frac{x^2-7x+10}{x^2+5x-14}\times \frac{x^2+4x-21}{x^2-9x+18}.$