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The $6^{th}$ term of an arithmetic progression is -10 and the ${10}^{th}$ term is -26. Determine the ${15}^{th}$ term of the AP.

Find the area of the quadrilateral ABCD whose vertices are respectively A (1, 1), B (7, –3) C (12, 2) and D (7,21).

Find the value of the middle term of the following AP $-6,-2,2,.....,58$

In $△$ABC, right angled at B, BC = 5 cm, $\angle$ BAC = ${30}^{\circ }$ , find the length of the sides AB and AC.

Question 11(b)

Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of:

The number of students who opted cricket to the number of students opting basketball.

Solve the inequalities in exercieses 17 to 20 and show the graph of the solution in each case on number line.

$\frac{x}{2}\ge \frac{(5x-2)}{3}-\frac{(7x-3)}{5}$

Find the number of three digit natural numbers which are divisible by 11

Choose the correct options.

The Point A(2,-3) is reflected in the x axis onto the point A'.Then the point A' is reflected in the line x=4 onto the point A''.

1)Write the coordinates of A' and A''

2)Find the ratio in which the line segment AA'' is divided by the x-axis.Also Find the coordinates of the point of division.

The students of a class are made to stand in rows. If 4 students are extra in a row there would be 2 rows less. If 4 students less in a row there would be 4 rows more. Find the number of students in the class

If $P\left(E\right)$ and $P\left(\overline{E}\right)$ are the probabilities of two complementary events, then which of the following is always true?

The ratio of the sum and the product of the roots of $5x^2–14x+8=0$ is___:___.

[Ratio in its reduced form]

How many prime factors are there in prime factorisation of 5005?

1. Rohit invested Rs.9600 on rs.100 shares at rs.20 premium paying 8% dividend. Rohit sold these shares when the price rose to rs.160. he invested the proceeds (excluding dividend) in 10% Rs..50 shares at Rs.40. find

the :

1. Original number of shares.

2. Sale proceeds.

The sum$(\alpha +\beta )$ and product$\left(\alpha \beta \right)$ of zeros of polynomial $2x^2-x+5$ is _______

Find the value of k if (x-3) is a factor of k square × x square - k × x-2

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

Find the square root of $\left[\right(x^2+5x+6\left)\right(x^2+7x+10\left)\right(x^2+8x+15\left)\right]$

$Let{x}_1,x_2,x_3,......x_{n}beinanA.P.If{x}_1+x_4+x_9+x_{11}+x_{20}+x_{22}+x_{27}{x}_{30}=272,then{x}_1+x_2+x_3+......x_{29}+x_{30}isequalto$

If $\frac{3+5+7+......nterms}{5+8+11+.........+10terms}$ = 7, the value of n is:

The median of first ten natural numbers is

In the given figure AD = 5 cm, AB = 15 cm, AE = 6 cm, AC = 24 cm. Then which of the following is correct ?

If $\Delta ABC$ is similar to $\Delta DEF$, then

$\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

Write the converse of the above statement.

The perimeter of a certain sector of a circle is equal to the length of the arc of the semi-circle having the same radius,express the angle of the sector in degrees, minutes and seconds.

Find the domain and the range of the real function, $f\left(x\right)=\frac{3-x}{x-3}$

If there are 15 people in the height range 150-160 cm in a class of 120 people, the percentage of people in the height range 150-160 cm is__________.

1. 300

The two similar triangles are equal in area. Prove that the triangles are congruent.

In a two digit number the sum of the digits is 7. If the number with the order of the digits reversed is 28 greater than twice the units digit of the original number, find the number.

Salman buys 50 shares of face value Rs 100 available at Rs 132. Then which of the following is/are correct if dividend is 7.5%.

If sin theta= 21/29 then evaluate sec thetha/ tan theta - sin theta

The ${17}^{th}$ term of an AP exceeds its ${10}^{th}$ term by $7.$ Find the common difference.

A shopkeeper buys a camera at a discount of 20% from the wholesaler, the printed price of the camera being ₹ 1600 and rate of sales tax is 6 %. The shopkeeper sells it to the buyer at the printed price and charges sales tax at the same rate. Find

i) the price at which the camera can be bought

ii) the VAT ( Value Added Tax) paid by the shopkeeper

$\sqrt{\frac{1+cosA}{1-cosA}}$ = ?

Select all that apply.

The roots of the quadratic equation $(x+\beta )(x-\alpha )=0$ are:

If A=$\left[\begin{array}{cc}3& 1\\ -1& 2\end{array}\right]$ and I $=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, find 5A-3I

Represent the following situations in the form of quadratic equations.
The area of a rectangular plot is $528m^2$. The length of the plot (in metres) is one more than twice its breadth. Find the length and breadth of the plot.

Nikhil expressed the quadratic equation $x^2+10x+16=0$ in the form $x^2+px+qx+16=0$ such that the product of p and q is 16. Choose the correct values of p and q.

A tree casts a shadow 4 m long on the ground, when the angle of elevation of the sun is 45^o. The height of the tree is:

Chords AB and CD of a circle with centre O intersect at a point E. If OE bisects angle AED, then prove that AB = CD.

If cot A = ¹²/₅, then the value of (sin A + cos A) x cosec A is :

Find the area of a circle whose centre is (5 , -3) & which passes through the point (-7 , 2).

The centre of a circle of radius 13 units is the point (3, 6). P(7, 9) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB.

The percentage increase in the area of a rectangle, if each of its side is increased by 20% is