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A cylindrical water tank of diameter 1.4 m & height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m/sec. Calculate in minutes the time it takes to fill the tank.

All the vertices of a rhombus lie on a circle. Find the area of rhombus,if area of circle is 2826cm².

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see the given figure), each piece measuring 20cm, 50cm and 50cm.How much cloth of each colour is required for the umbrella?

[4 MARKS]

AB is a line segment which is inclined to line XY, such that they intersect at point O. A line PQ is drawn which intersects the line XY at point P at the same angle of inclination as AB. Line PQ is _________ to line segment AB.

In $\Delta ABC,AB=10cm,AC=6cm,\angle A={70}^{\circ }$. Find the length of the side BC. $[cos{70}^{\circ }=0.34,sin{70}^{\circ }=0.94]$

For what value of $n,$ the $n^{th}$ term of A.P. $63,65,67,........$ and $n^{th}$ term of A.P. $3,10,17,..........$ are equal to each other?

The speeds of three cars are in the ratio 2: 3: 4. The ratio between the times taken by these cars to travel the same distance is ___________

which of the following polynomials has the factors (x+3) (x-4) ?

If the diameter of a circle is equal to the diagonal of a square, then the ratio of their areas is
(a) $7:1$ (b) $1:1$ (c) $11:7$ (d) $22:7$

Question 126 (i)

If $\Delta$ is an operation, such that for integers a and b. We have $a\Delta b=a\times b-2\times a\times b+b\times b(-a)\times b+b\times b,$ then find
$4\Delta (-3)$
Also, show that $4\Delta (-3)\ne (-3)\Delta 4$

If two positive integers P and Q are written as P=A² B³and Q=A³b, A, B are prime numbers, then Verify LCM (p,q)× HCF (p, q) =pq ?

In the adjoining figure, AB = AC and AP $\perp$ BC.

Which of the following option is correct?

Consider the arithmetic sequence with first termand common difference. Is 1 a term of this sequence? What about 2?

Write the algebraic form of this sequence. Prove that all natural numbers occur in this sequence.

Arjun and Karna had an archery competition where they had to shoot a target board with 7 concurrent circles dividing the board into 8 concurrent circular strips. Score for each outcome decreases by unity with centermost circle having score of 8. Dronacharya had difficulty in deciding who the winner was after the scores were recorded. Calculate the mean deviation about the score of innermost circle so as to decide who the winner is assuming the winner is less deviated from the bulls eye.

$$\begin{array}{ccccccccc}Points& 8& 7& 6& 5& 4& 3& 2& 1\\ Arjun\left(f_i\right)& 5& 7& 14& 23& 11& 10& 4& 3\\ karana\left(f_i\right)& 5& 8& 11& 24& 14& 8& 5& 3\end{array}$$

I have a total of rupees 300 in coins of denominations rupee 1, rupee 2, and rupee 5. The number of rupee 2 coins is 3 times the number of rupee 5 coins. The total number of coins is 160. How many coins of each denomination are with me?

The circumferences of two circles are in the ratio 3 : 4. The ratio of their area is

(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

Which of the following refers to administrative revenue fees?

Which of the following is a random experiment?

1) Tossing a coin

2) Throwing a die

3) Drawing a card out from a deck of 52 cards

Evaluate each of the following

$ta{n}^2{30}^o+ta{n}^2{60}^o+ta{n}^2{45}^o$

If a,b and c are three nonzero numbers and the polynomial p(x) = x³ + ax² + bx - c factors as (x - a) (x - b ) (x - c ), then the value of p(3) is

Determine the value of k so that the following system of equation have no solution

(3k+1)x+3y-2=0

(K^2+1)x+(k-2)y-5=0

Question 68(ii)

Find the SP, if
MP = Rs. 1300 and discount = 1.5%

Given $A=\left[\begin{array}{cc}2& -6\\ 2& 0\end{array}\right],B=\left[\begin{array}{cc}-3& 2\\ 4& 0\end{array}\right]andC=\left[\begin{array}{cc}4& 0\\ 0& 2\end{array}\right]$ Find the matrix X such that
A + 2X = 2B + C.

Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
$2x^2-7x+3=0$

An observer 2.25 m tall is 42.75 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45${}^{\circ }$. What is the height of the chimney?

Let p be a prime number. If p divides $a^2$ then p divides a, where a is a positive integer. Which theorem is this statement previously based on?

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients :

$x^2-2x-8$

The median of the following data is:

Write each of the polynomial listed below as a product of two first degree polynomials:

(i) 2x² + 5x + 3

(ii) x² + 2x − 1

(iii) x² + 3x + 2

(iv) x² − 2

(v) 4x² + 20x + 25

(vi) x² − x − 1

Solve each of the following systems of eqautions by the method of cross-multiplication:

$\frac{x}{a}=\frac{y}{b}$

$ax+by=a^2+b^2$

Find the ${12}^{th}$ term from the end of the A.P $-2,-4,-6,...-100.$

A contractor plans to install two slides for the children to play in a park for elder children. She wants to have a steep slide at a height of 6 m, and inclined at an angle of ${60}^{\circ }$ to the ground. What should be the length of the slide (in m)?