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Question 11
A mason constructs a wall of dimensions 270 cm×300 cm× with the bricks each of size $22.5cm\times 11.25cm\times 8.75cm$ and it is assumed that $\frac{1}{8}$ space is covered by the mortar. Then, the number of bricks used to construct the wall is Thinking process If we divide the volume of the wall except the volume of mortar are used on wall by the volume of one brick, then we get the required number of bricks used to construct the wall.
(A) 11100
(B) 11200
(C) 11000
(D) 11300

Adjoining figure shows the snapshot of two waves A and B at any time t. The equation for A is $y=Asin(kx-\omega t-\varphi )$, and for B it is y = A sin $(kx-\omega t)$. It is clearly shown in the figure that wave A is ahead of B by a distance $\frac{\varphi }{k}$.

The motion of a single point in time, i.e., y versus t for two waves is best represented by

Which of the following is the mixture of two tax systems?

A locus of points which is equidistant from three non-collinear points is the ___ centre of the circle through the given points.

Which of the following are the factors of $x^2+7x+12$ ?

Question 9 (ii)
In triangle ABC, right-angled at B, if tan A = $\frac{1}{\sqrt{3}}$, find the value of:
(ii) cos Acos C - sinAsin C

Given that N = {1, 2, 3, 4,…… 50} . Then write

a) the subset of N consisting of all the prime numbers.

b) the subset of N consisting of all the perfect cubes.

(i) Complete the following table:

$\begin{array}{cc}\text{Event:'Sum of 2 dice'}& \text{Probability}\\ 2& \frac{1}{36}\\ 3& \\ 4& \\ 5& \\ 6& \\ 7& \\ 8& \frac{5}{36}\\ 9& \\ 10& \\ 11& \\ 12& \frac{1}{36}\end{array}$

(ii) A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}$. Do you agree with this argument? Justify your answer.

A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been I hour 40 minutes less. Find the original speed of the car.

Find a point on 6x - 5y = 4 whose ordinate is twice the abscissa. [2 MARKS]

Find the equation of the line which is perpendicular to the line $\frac{x}{a}-\frac{y}{b}=1$ at the point where this line meets y-axis.

In the given figure, ABCD is a cyclic quadrilateral. What is the value of $\frac{x^{\circ }}{{50}^{\circ }}$?

Find AB in the given figure

The 10th term of an arithmetic sequence is 65 and its 15th term is 20. Then 20th term is

A boy is trying to catch fish sitting at a height of 12 m from the surface of the water.A big fish is at a horizontal distance of 5 m from him. What should be the length of his string to get the fish?

Question 2 (vi)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

4, 1

Question 3 (i)
Prove that $\frac{1}{\sqrt{2}}$ is irrational.

A boat travels at 8 km/hr in still water and water flows at 4 km/hr. The speed of the boat if it goes against the water stream is?

Which of the following options is/are equal to $ta{n}^{2}A+co{t}^{2}A+2$ ?

Two persons are standing on the opposite sides of a tower. They observe the angles of elevation of the top of the tower to be ${30}^{\circ }$ and ${38}^{\circ }$ respectively. Find the distance between them, if the height of the tower is 50 m. [$\tan {38}^{\circ }=0.7813$] [2 MARKS]

The total surface area of a cube of side a is ______.

In $\Delta ABC,AB=10cm,\angle A={40}^{\circ },\angle B={110}^{\circ }.$ The area of the triangle will be equal to ______. $[Tan{40}^{\circ }=0.84,Tan{70}^{\circ }=2.75]$

The median for grouped data is given by:

The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by x-axis is _____.

The expression we get after factorising $2x^2+x-3$ is ___

Identify the number of triangles similar to $△$ABC if B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC.

If $\alpha ,\beta$ and $\gamma$ are the zeroes of the cubic polynomial $a{x}^3+b{x}^2+cx+d$,
then $\alpha +\beta +\gamma$ is equal to

The probability of an impossible event is___

Solution of the pair of equations x + 2y = 5 and 7x + 3y = 13 is

$\Delta ABD$ is a right triangle right-angled at A and AC \perp BD. Show that
(i) $A{B}^2=BC.BD$
(ii) $A{C}^2=BC.DC$
(iii) $A{D}^2=BD.CD$
(iv) $\frac{A{B}^2}{A{C}^2}=\frac{BD}{DC}$

From an external point P, two tangents are drawn that touches the circle at points Q and R. The triangle PQR is necessarily a/an ___triangle.

In an isosceles $\Delta ABC$, the base AB has produced both ways in P and Q such that $AP\times BQ=A{C}^2$.

Prove that $\Delta ACP\sim \Delta BCQ$.

In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If $\angle BAC={30}^{\circ }$, then $\angle ACD=$ ______.

$$\begin{array}{cccccc}Weeklywages(inRs.)& 0-100& 100-200& 200-300& 300-400& 400-500\\ Numberofworkers& 40& 39& 34& 30& 45\end{array}$$

What is the number of people whose wage is less than Rs.400?

Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company which manufactures airplane toys and incurred huge losses amounting to $k(>0)$ times the wealth he inherited from his father. His total assets now stand at debt of Rs. 4 crore. For what value of $k$ is this scenario possible?

If $a_1,a_2,a_3,a_4$ are in AP, then .

If the ratio between 8 and 11 is the same as the ratio (2x-y) to (x + 2y).
The value of $\frac{28x}{27y}=$

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

In a rectangle ABCD, AB = 20 cm, $\angle$ BAC = ${60}^{\circ }$. Then, side BC =

If a circle is drawn with centre c(4,0) and radius 5 cm as shown in the below figure then find the coordinates of 'R' and 'S'.