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Solution:
N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = (1 + 1 + 2 + 0) = 4

Aren't we supposed to find the HCF (1305, 4665, 6905) rather than that of the HCF(4665 - 1305), (6905 - 4665) and (6905 - 1305)?

If the roots of the equation $(a^2+b^2)x^2+2(ac+bd)x+(c^2+d^2)=0$ are real, a,b,c,d $ϵ$ R, then roots are :

Find the curved surface area of a hemisphere whose radius is $7cm$.

The marks obtained by the sudents of a class, in an exam which was out of 50 marks,is given below.

$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 5& 1\\ 7& 2\\ 11& 2\\ 16& 3\\ 21& 5\\ 24& 6\\ 28& 3\\ 32& 5\\ 34& 8\\ 39& 6\\ 43& 4\\ 45& 2\\ 49& 3\end{array}$ [4 MARKS]

(i)Find mode for the ungrouped data.

(ii) Represent the same as grouped data, with class intervals of width = 10 and find the mode for the grouped data.

In the diagram given AC is the diameter of the circle, with centre O. CD||BE, ∠AOB = 80⁰ and ∠ACE = 10⁰. Calculate ∠BCD, ∠CED.

What is the ratio of volume of a sphere to volume of cylinder with an equivalent radius and height equal to the diameter?

Question 7
Draw a $\Delta ABC$ in which $AB$= $4$ cm, $BC$ =$6$ cm and $AC$ = $9$ cm, construct a triangle similar to $\Delta ABC$ with scale factor $\frac{3}{2}$. Justify the construction. Are the two triangles congruent? Note that, all the three angles and two sides of the two triangles are equal.

Solution

Thinking process

Triangles are congruent when all corresponding sides and interior angles are congruent The triangles will have the same shape and size, but one may be a mirror image of the other.

So, first, we construct a triangle similar to $\Delta ABC$ with scale factor $\frac{3}{2}$ and use the above concept to check the triangles are congruent or not.

In the next six questions there is no negative marking. The best answer carries one mark while other answer choices carry less than one mark

Q77. . In a meeting with officers from field, on how to start implementation of a new programme, Deshmukh, a senior officer from the Ministry gives out a series of instructions. He brusquely brushes aside the problems which some officers raise. For example, when a field officer pointed out logistic problems in monsoon season, Deshmukh quipped 'How much rains have you seen? I've served long in a district with highest rainfall in India. Deshmukh's style is

1. -4

A man invested Rs 45,000 in 15% Rs 100 shares quoted at Rs 125. When the M.V. of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8,400 .Calculate :

(i) the number of shares he still holds;

(ii) the dividend due to him on these remaining shares.

: A rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles

A man invests Rs 20020 in buying shares of nominal value Rs 26 at $10\%$ premium. The dividend on the shares is $15\%$ per annum. Calculate the number of shares he buys.

A cottage industry produces a certain number of articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced.

The line $2x+3y-5=0$ cuts the line joining $A(8,-9)$ and $B(2,1)$ at point $P$. The coordinates of $P$ are:

In fig, side QR of $\Delta PQR$ has been produced to S. If $\angle P:\angle Q:\angle R=3:2:1$ and RT is perpendicular to PR. Find $\angle TRS$. [3 MARKS]

Two poles of equal heights are standing opposite each other on either side of the road, which is 100 m wide. From a point between them on the road, the distance from one of the poles to the point with an elevation of ${30}^{\circ }$ is 70m. Then, find the distance from the point to the $2^{nd}$ pole with an elevation of ${60}^{\circ }$ from the point

Solve the quadratic equation $4x^2+12x+9=81$ by completion of squares method. What is the magnitude of sum of both the roots ?

Find the nth term of the series

2.5 + 5.8 + 8.11 + ------------

Integrate the following:

sec²x/cosec²x

In the given figure $\angle ABC={38}^{\circ },$ then $\angle BAC$ is equal to

The perimeter of a rectangle is 24 cm and its area is 32 sq. cm. Find the length of the longer side.

8meb and 12boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days .find the time taken by one men alone and that by one alone to finish the work.

Question 6 (i)
A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out an orange flavoured candy?

If one root of the equation $2x^2+ax+6=0$ is $3$, then find the value of $a$

In the given triangle ABC, $\angle A={45}^{\circ }$, BC = 9 cm as shown in the figure. The diameter of the circumcircle is equal to

In the given figure, AB is the diameter of the circle, with centre O, and AT is the tangent calculate the numerical value of x.

Tangents AP and AQ are drawn to a circle, with centre O, from an exterior point A. Then, which of the following statements are true?

What is the effect of an increase in the bank rate on the volume of credit?

Find the remainder when $x^3+{3x}^2+3x+1$ is divided by:
$\left(i\right)x+1$
$\left(ii\right)5+2x$ [4 MARKS]

In $△$ABC, the medians BE and CF intersect at G. AGD is a line meeting BC in D. If GD is 1.5 cm, then AD is equal to -

In triangle ABC, right angled at B, if $\angle$A is made larger and larger till it becomes ${90}^{\circ }$, what can you say about AC and AB if BC = 1 unit?

You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.

The income tax paid by workers of a certain organisation is given in the table.

$\begin{array}{cc}\text{Income tax (Rs)}& \text{No. of workers}\\ 1000-2000& 8\\ 2000-3000& 10\\ 3000-4000& 15\\ 4000-5000& 18\\ 5000-6000& 8\end{array}$

Find the Median Tax paid by them.

If 4 is a root of the equation x² + 3x + k = 0 , then k is

Find the values of y if $y=x^2-1$ and x = 2y - 1.

If sin θ = cos θ, then the value of θ is:

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then the height of the cone is

Find the value of 'a' for which the following points A(a, 3), B(2, 1) and C(5, a) are collinear.