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A flaw is detected in an underground cable of length 2000m. The flaw is equally likely to be located anywhere. What is the probability that the flaw is located within 100m from the centre? [3 MARKS]

Solve the following equation using completing the square method.

$2x^2-x+\frac{1}{8}=0$

A positive integer a is written as a=3q+r and a=4k+r, where q,k and r are whole numbers. Find the possibilities of q and k?

The sum of $4$ consecutive numbers in an AP is $32$ and the ratio of the product of the first and the last term to the product of two middle terms is $7:15.$ find the number.

If the speed of an aeroplane is reduced by 40 km per hr, it takes 20 minutes more to cover 1200 km. Find the speed of the aeroplane.

Find the median for the distribution given below.

$$\begin{array}{cccccc}\text{Wages}& 200-300& 300-400& 400-500& 500-600& 600-700\\ \text{Number of labourers}& 3& 5& 20& 10& 6\end{array}$$

1. 470

The graphical representation of Linear equation is

Question 1
If a hexagon ABCDEF circumscribe a circle. Prove that AB + CD + EF = BC + DE + FA

If D, E, F are the midpoints of sides BC, CA and AB of $△$ ABC, then the ratio of the area of $△$ DEF to $△$ ABC is:

If ${\log }_{a}x>y$ and $0<a<1$ . Then

In a box containing 18 balls of 3 different colours red, green and blue, if 10 are red and 4 are green, then what is the probability of getting a blue ball in the first attempt?

Two dice are thrown together. The probability of getting the same number on both dice is
(a) $\frac{1}{2}$ (b) $\frac{1}{3}$ (c) $\frac{1}{6}$ (d) $\frac{1}{12}$

The linear inequality representing the solution set given in fig.

The square of a positive integer cannot be a form/(, K is an integer) :

(a) 3 k + 1

(b) 4 k + 2

(c) 5 k + 1

(d) 5 k + 4

Expand ${(2+\sqrt{2})}^2$.Is it rational? [3 MARKS]

If the height of a vertical pole is equal to the length of its shadow on the ground, the angle of elevation of the sun is

(a) $0^{\circ }$

(b) ${30}^{\circ }$

(c) ${45}^{\circ }$

(d) ${60}^{\circ }$

Find the value of x in the figure below.

Which of the following is a solution to 3x+4y = 38 ?

Four pipes each of 5 cm in diameter are to be replaced by a single pipe discharging the same quantity of water. If the speed of water remains same in both the cases, then the diameter (in cm) of the single pipe is:

$\frac{cosecA}{cosecA-1}+\frac{cosecA}{cosecA+1}=2se{c}^{2}A$

The coach of a cricket team bought 7 bats and 6 balls for Rs. 3800. Later, she bought 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.

Solve: $(x^2-x{)}^2+5(x^2-x)+4=0$

Prove that the squares of any terms of the sequence are not terms of the sequence.

In the following figure, if the chords AB and CD are equal to 6cm, then find the distance of the chords AB and CD from the centre of the circle of radius 5 cm.

Degree of zero polynomial is​​_________

Two circles intersect in A and B. Quadrilaterals PCBA and ABDE are inscribed in these two circles such that PAE and CBD are line segments.

$\angle P={95}^0$ and$\angle C={40}^0$

Find the value of Z.

If one of the zeroes of a quadratic polynomial of the form x
2+ax + b is the negative
of the other, then it
(A) has no linear term and the constant term is negative.
(B) has no linear term and the constant term is positive.
(C) can have a linear term but the constant term is negative.
(D) can have a linear term but the constant term is positive.

If the mth term of an A.P. be 1/n and its nth term be 1/m , then show that it's mn term is 1.

In triangle ABC, $\angle B={30}^{\circ }$ and $\angle C={45}^{\circ }$. If AB =4 cm, then find the length of CD.

Find q and r for the following pairs of positive integers a and b ,satisfying a= bq+ r. (1) a=13,b=3 (2) a=80,b=8 . From the above questions , what is the nature of q and r.?

Solve for $x:x^2-(2b-1)x+(b^2-b-20)=0$

A test paper contains 100 true/false questions. The number of questions with answer "true" was 59. Find the probability that a question’s answer is "false".

In an A.P., the sum of first n terms is $\frac{3n^2}{2}+\frac{5n}{2}$. Find its ${25}^{th}$ term

In Fig. 7.145, PA, QB and RC are each perpendicular to AC. Prove that $\frac{1}{x}+\frac{1}{z}=\frac{1}{y}$

Ritu can row downstream 20 km in 2 hours, and uptream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Find the coordinates of the midpoint of the line segment joining

(i) A(3,0) and B(-5, 4) (ii) P(-11, -8) and Q(8, -2).

Find the sum of first 51 terms of an A.P. whose second and third terms are 14 and 18 respectively.

Number of polynomials having 3 and 7 as zeroes are?

How much should a man invest in ₹ 50 shares selling at premium of ₹ 60 to obtain an income of ₹ 1500, if the dividend % is 20

Is the pair of following equations , consistent and dependent, or consistent or inconsistent. Give reasons for your answer.

x = 5

y = 3

A cricket ball of radius r is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface area of the cricket ball to the surface area of the tin is

In the above triangle ABC, point P is the centroid of the triangle. The length of AE is 15 cm. Find the length of AP and PE.

Find the ${20}^{th}$ term of the series 3 + $\frac{1}{2}$(3 + 5) + $\frac{1}{3}$(3 + 5 + 7) + $\frac{1}{4}$(3 + 5 + 7 + 9) + .........

Which of the following should be the LAST sentence after rearrangement?