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Following Trial Balance has been extracted from the books of Prasad on 31st March, 2019:

Additional Information:

(i) Outstanding salaries were ₹ 45,000.

(ii) Depreciate Machinery at 10%.

(iii) Wages outstanding were ₹ 5,000.

(iv) Rent prepaid ₹ 10,000.

(v) Provide for interest on capital 5% per annum.

(vi) Stock on 31st March, 2019 ₹ 8,00,000.

Prepare Trading and Profit and Loss Account for the year ended 31st March, 2019 and Balance Sheet as at that date.

A para-glider from a chopper in mid-night is going to land in the terrain shown in the figure below. The shaded region is land surface whereas blank region shows water bodies. If the para-glider does not know how to swim, find the chances of his survival. (Radius of circular region = 50 m)

If f(x) = $\sqrt{x}$ and $g\left(x\right)=x$ , then $\left(\frac{f}{g}\right)\left(x\right)$ equals to $(x\ne 0)$

If $sin3\theta =cos(\theta -{26}^{\circ }$), where $3\theta$ and $(\theta$-${26}^{\circ })$ are acute angles, then find the value of $\theta$.

Two triangles are similar by SAS similarity if:

The first term of an AP is 12 and the common difference is -2. Which term of the AP will be 0?

Solve the following system of equations
8v-3u=58v
6v-5u=-2uv

The sum of the first three terms of a GP is 39/10 and their product is 1.Find the common ratio and the terms.

The domain of the function $f\left(x\right)=\frac{\ln (3x-x^2)}{x}$ is



[2 marks]

For which angle $\theta$, the value of $sin\theta$ and $cos\theta$ remains the same?

Question 7 (i)

The value of $\pi$ up to 50 decimal places is given below:

3.14159265358979323846264338327950288419716939937510

(i) Make a frequency distribution of the digits from 0 to9 after the decimal point.

Let $S_n$ denote the sum of first $n$-terms of an arithmetic progression. If $S_{10}=530,S_5=140,$ then $S_{20}-S_6$ is equal to:

Gladolia, the narrator's cook, is an African. The language she speaks is different from that of the others. This is known as a dialect. A dialect consists of words or phrases that reflect the regional variety of a language. An author often uses a regional dialect to make the dialogue more authentic. Initially a dialogue may seem a little difficult to understand. However, as you continue reading, the language will become more comprehensible.

Working in groups, write what Gladolia's words mean as shown.

Which is a solution of the linear equation 3x + 4y = 2?

A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

1. 20

Identify the common difference of the given AP: a, a+d, a+2d, a+3d, ...

The sum of the first n terms of an arithmetic sequence is 2n² + 3n. find the algebraic form of this sequence.

If d is the hcf of 45 and 27 , find the value of x and y satisfying d = 27x +45y give solutions step by step

The midpoint of line segment joining (2a, 4) & (–2, 2b) is (2, 2a + 1). Find the values of a & b.

Question 6
The marks obtained (out of 100) by a class of 80 students are given below:

$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 10-20& 6\\ 20-30& 17\\ 30-50& 15\\ 50-70& 16\\ 70-100& 26\end{array}$

Construct a histogram to represent the data above.

Factorize $\sqrt{3}$ $x^2$ + 5x + 2$\sqrt{3}$ = 0 into (ax+b)(cx+d)=0. What is the value of a + b + c - d ?

In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is $10cm,BC=38cm,$ $PB=27cm$ and $AD\perp CD$ then the length of $CD$ is

(a) $11cm$ (b) $15cm$ (c) $20cm$ (d) $21cm$

If cot θ =, evaluate

(i) (ii) cot² θ

$△ABC$ is such that $AB=3cm,BC=2cm$ and $CA=2.5cm.△DEF$ is similar to $△ABC.$ If $EF=4cm,$ then the perimeter of $△DEF$ is

Question 5

Show that the square of any odd integer is of the form 4m + 1, for some integer m.

If 3 cot A = 4, check whether $\frac{1-ta{n}^{2}A}{1+ta{n}^{2}A}=co{s}^{2}A-si{n}^{2}A$ or not.

If the sum of zeros of the quadratic polynomial p(x)=kx²+2x+3k is equal to their product find the value of k

How many small cubes are there in the above shown figure. [2 MARKS]

The angle of elevation of the top of a tree from a point A on the ground is ${60}^{\circ }$ . On walking 20 m away from point A, to a point B, the angle of elevation changes to ${30}^{\circ }$. Find the height of the tree.

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

$\begin{array}{cccccccc}\text{Number of days}& 0-6& 6-10& 10-14& 14-20& 20-28& 28-38& 38-40\\ \text{Number of students}& 11& 10& 7& 4& 4& 3& 1\end{array}$