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8^th term of the series $2\sqrt{2}+\sqrt{2}+0+....$ will be

If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ for the system of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$

Find the median from the following data: $\begin{array}{cccccccccc}\text{Class}& 1-5& 6-10& 11-15& 16-20& 21-25& 26-30& 31-35& 36-40& 41-45\\ \text{Frequency}& 7& 10& 16& 32& 24& 16& 11& 5& 2\end{array}$

A wire when bent in the form of an equilateral triangle encloses an area of $121\sqrt{3}c{m}^2$. The same wire is bent to form a circle. Find the area enclosed by the circle.

The angle of elevation of an aeroplane from a point on the ground is ${45}^{\circ }$. After flying for 15 seconds, the elevation changes to ${30}^{\circ }$. If the aeroplane is flying at a height of 2500 metres, find the speed of the aeroplane.

Using prime factorisation, find the HCF and LCM of :

(i) 8, 9, 25 (ii) 12, 15, 21 (iii) 17, 23, 29

(iv) 24, 36, 40 (v) 30, 72, 432 (vi) 21, 28, 36, 45

In triangle ABC, right angled at B, find the expressions of cos A and sin C.

Show that the equation $2(a^2+b^2)x^2+2(a+b)x+1=0$ has no real roots, when $a\ne b.$

Find the term of the arithmetic progression 9,12,15,18,... which is 39 more than is 36th term.

A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 $m^3$. Find the maximum volume available to place machinery in the factory. (Take $\pi =\frac{22}{7}$)

In a cricket tournament following was the number of runs scored by the cricketers. Plot a frequency plot of the data.

$\begin{array}{cc}Runs& NumberOfCricketers\\ 0-10& 10\\ 10-20& 3\\ 20-30& 14\\ 30-40& 25\\ 40-50& 11\end{array}$
[2 MARKS]

You pick a card from a standard deck. What is the probability that the card will be a number card less than 5? [2 MARKS]

Calculate the Mean of the given distribution, using Assumed mean Method.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 10-20& 2\\ 20-30& 6\\ 30-40& 10\\ 40-50& 12\\ 50-60& 9\\ 60-70& 8\\ 70-80& 4\\ 80-90& 3\end{array}$

1. 48.89

Question 5
Find the mean salary of 60 workers of a factory from the following table:
$\begin{array}{cc}\text{Salary (in Rs)}& \text{Number of workers}\\ 3000& 16\\ 4000& 12\\ 5000& 10\\ 6000& 8\\ 7000& 6\\ 8000& 4\\ 9000& 3\\ 10000& 1\\ \text{Total}& 60\end{array}$

If x : y = 4 : 7, Find the value of (3x+ 2y) : (5x + y).

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

Question 108

Priyanka took a wire and bent it to form a circle of radius 14 cm. She bent it into a rectangle with one side 24 cm long. What is the length of the wire? Which figure encloses more area, the circle or the rectangle?

If ax+by +c = 0 , doesn’t touch the y axis , then which of the coefficients are 0?

A ball falls vertically after being dropped. The ball falls a distance d metres in a time of t seconds. d is directly proportional to the square of t.
The ball falls 20 metres in a time of 2 seconds.
The time (in seconds) that the ball takes to fall 605 m is

Question 52

Solve the following:

$\frac{8}{x}=\frac{5}{x-1}$

Find a value of $\theta$ being given that sin$\theta$ = cos 4$\theta$

Sevwn times a two digit no. Is equal to four times the no. Obtained by reversing the digits .if the difference of the digit is 3 ,determine the no.

An observer 1.5 m tall, is 28.5 m away from a tower 30 m high. Determine the angle of elevation of the top of the tower from his eye.

In which of the following expressions, prime factorization has been done:

(i) $24=2\times 3\times 4$
(ii) $56=7\times 2\times 2\times 2$
(iii) $70=2\times 5\times 7$
(iv) $54=2\times 3\times 9$

Two circles of radii 25cm and 9cm touch each other externally. Find the length of the direct common tangent. [4 MARKS]

Find the value of 'a' for which the following points A(a, 3), B(2, 1) and C(5, a) are collinear.

If A:B=5:9,B:C=2:7,C:D=14:2 then A:D=

Find the smallest number which when increased by 17 is exactly divisible both 520 and 468.

Fill in the blank with a modal auxiliary showing possibility.

She _____ be in the library, but I am not sure if she has your book.

Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the ratio of S and S'.

Solutions of the inequalities comprising a system in variable x are represented on number lines as given below, (black color is taken in consideration)

Use the sign of >, < or = in the blank to make the statement true.

(-4 $\times$ 2) + 10 __ (6 - 7) $\times$ -2

If the cumulative frequency for the class interval (30-40) is 70 and for class interval (50-60) is 150 , then the value of y =

$\begin{array}{ccccccc}\text{Class Interval}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Frequency}& 12& 20& x& 18& 10& y\end{array}$

The sum of r terms of an AP is 2 r^2+3r. What is the nthterm??

Explain closure, associative, multiplicative and distributive properties of multiplication of matrices.

In the given figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.

If two vertices of a triangle are (6,4), (2,6) and its centroid is (4, 6), then the third vertex is

A cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid(in $c{m}^2$ ).

What is the value of cos8x=?

The 20th term of AP exceeds its 15th term by 10. Find the common difference.

A circle having radius 4cm contains a chord of length 4cm and subtends an angle of 60 degrees. Find the area (in $c{m}^2$)of the minor segment of the chord.

From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. Points O and P are joined. The ratio of angles OPR and OPQ is