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12 defective pens are accidently mixed with 132 good ones. It is not possible to just look at pen and tell whetehr or not it is defective. One of them is taken out at random from this lot. Find the probability that the pen taken out taken out is good one.

A jar contains $54$ marbles, each of which some are blue, some are green and some are white, the probability of selecting a blue marble at random is $\frac{1}{3}$ and the probability of selecting a green marble at random is $\frac{4}{9}$. How many white marbles does the jar contain?

Show that the points (-4 ,-1), (-2, -4), (4, 0) and (2, 3) are the verticies points of a rectangle.

A ladder of length 6 metres makes an angle of ${45}^{\circ }$ with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of ${60}^{\circ }$ with the floor. Find the distance between two walls of the room.

Solve for x and y:

$\frac{3}{x+y}+\frac{2}{x-y}=2,\frac{9}{x+y}-\frac{4}{x-y}=1.$

The length of an arc which subtends an angle $\theta$ at the centre of a circle of radius r is

A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7m and height of the cone is 1m, what is the area of cloth required? ($\sqrt{2}=1.414$)

In a circus, a motorcyclist performs his stunts in a hollow sphere. Assume the thickness of the sphere to be negligible. If the diameter of the hollow sphere is 14 m, then find the area available for the motorcyclist to perform his stunts.(Take $\pi =\frac{22}{7}$)

A 60cm tall girl spots a balloon moving with the wind in a horizontal line at a height of 87.6 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is ${60}^{\circ }$. After some time, the angle of elevation reduces to ${30}^{\circ }$. Find the distance travelled by the balloon during the interval.

Question 4

If marked price of an article is Rs 1200 and the discount is 12%, then the selling price of the article is
(a) Rs 1056
(b) Rs 1344
(c) Rs 1212
(d) Rs 1188

Answer the following: [3 MARKS]

a) Make two equations where the solution is 6.

b) Make two equations where the solution is -8.

If $A=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$ and $A^2$ = I then x = ___

Write down the decimal expansions of : $\frac{17}{8}$

A person buys 120 shares at a nominal value of Rs 40 each, which he sells at Rs 42.50 each. Find his profit and profit percent.

Two natural numbers differ by 3 and their product is 504. Find the numbers.

The sum and the product of the zeros of a quadratic polynomial are 3 and -10 respectively. The quadratic polynomial is

(a) $x^2-3x+10$ (b) $x^2+3x-10$ (c) $x^2-3x-10$ (d) $x^2+3x+10$

The sum of two natural numbers is 28 and their product is 192. Find the numbers.

Find the sum of first n even natural numbers.

The length, breadth and height of a rectangular solid are in the ratio 6 : 5 : 4. If the total surface area is 5328 $c{m}^2$ , find the length, breadth and height of the solid.

Find the remainder when $27x^3-9x^2+5x-1$ is divided by $3x+1$

If HCF of two numbers is 6 and lcm of two same two numbers is 72.Find the numbere

A trader brought a number of articles for Rs. 900,five articles were found damaged. He sold each of the remaining articles at Rs.2 more than what he paid for it. He got a profit of Rs.80 on the whole transactions. Find the number of articles he bought.

A triangle ABC is right-angled at B. AB = 6 cm and BC = 8 cm. What is the length of AC?

Mixed ratio or compound ratio of 6:5,5:3,4:9 will be

Fourth proportional of 2,3 and 4 is

The value of k for which the points $A(2,3),B(4,k),$ and $C(6,-3)$ are collinear.

The HCF of $3(x^2-9)(x+4)and12(x-3{)}^2$ is:

Sum of first 20 terms of an AP is and its first term is 7. Find its ${24}^{th}$ term.

In given figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, $\angle$B = ${90}^{\circ }$ and DS = 5 cm, then the radius of the circle is ___ cm.

4

7 10

13 16 19

22 25 28 31

............................

..................................

Write the next two lines of the pattern and calculate the first and last terms of the 20th line

A man invests Rs 3.072 in a company paying 5 % per annum, when its Rs 10 share can be bought for Rs 16 each. Find :

(i) his annual income;

(ii) his percentage income on his investment.

Base of a triangle is 9 cm and the height is 5 cm. Base of another triangle is 10 cm and height is 6 cm. Find the ratio of areas of these triangles.

If cos 3$\theta$= $\sqrt{3}$/2; 0 < $\theta$ < 200, then value of $\theta$ is:

Given $A=\{x:-1<x\le 5,x\in R\}andB=\{x:-4\le x<3,x\in R\}$

Represent on different number lines :

(i) $A\cap B$ (ii) $A^{\prime }\cap B$ (iii) $A-B$

State De Morgan’s laws for set difference and De Morgan’s laws for complementation.

If both of the roots of an upward facing parabola are real and different, then which of the following is correct?

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

$5x-3\ge 3x-5$

The mid - points of class intervals $x_i$ along with respective frequencies $f_i$ for recorded observations are given. Calculate the mean deviations about mean $x$

Prove that if x and y are both odd positive integers then X square + Y square is even but not divisible by 4

Question 2 (iii)
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

If $A=\left[\begin{array}{cc}1& -1\\ 1& 1\end{array}\right]$ then $A^{16}$ =

In the figure given above, AX = 5. AB is a tangent at B, AB = 20 cm. Find XC.