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The length of the diagonal of a square is $10\sqrt{2}$ cm. Its area is

(a) 200 $c{m}^2$ (b) 100 $c{m}^2$ (c) 150 $c{m}^2$ (d) $100\sqrt{2}c{m}^2$

Which of the following is a compulsory payment imposed on persons or companies by the government to meet the expenditure incurred on providing benefits to the people?

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of articles produced in a day. On a particular day, the total cost of production was Rs. 750. If x denotes the number of toys produced that day, form the quadratic equation of find x.

If the lines mx - ny + 5 = 0 and 2x + 3y + 6 = 0 are perpendicular to each other, then find the relation between m and n

The curved surface area of a cone of radius 'r', height 'h' and slant height 'l' is ___.

In two similar triangles ABC and PQR, if their corresponding altitudes AD and PS are in the ratio 4 : 9, find the ratio of the areas of $△$ABC and $△$PQR.

Question 4 (v)

Find the values of p and q for the following pair of equations 2x + 3y = 7 and 2px + py = 28 – qy, if the pair of equations has infinitely many solutions.

By selling a chair for Rs. 75, Mohan gained as much percent as its cost. Calculate the cost of the chair.

The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its

The houses of 4 friends are located at the points (6, 6), (0, 6), (3, 3) and (6, 0) as shown in the figure. A, C and B are the vertices of a right triangle. Find the coordinates of the midpoint of the line segment joining the points B(0, 6) and C(6, 6).

Find the sum of n terms of the following series:
$(4-\frac{1}{n})+(4-\frac{2}{n})+(4-\frac{3}{n})+\cdots$

If ⁿP₄ = 12 ⁿP₂ the find n.

Write the roots of the quadratic equation $x^2+8=0$.

How many cylinder glasses of 3cm base radius and height 8cm can be refilled from a cylindrical vessel of base radius 15cm which is filled up to a height of 32 cm

Find the discriminant of the following quadratic equation
$x^2+5x–3=0$ [1 MARK]

The reflection of point A(-6, 10) about Y = 2 is (c, d). The value of c+d is ___.

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

Which one of the following has 2 solutions ?

The lengths of two sides of a triangle are 6 centimetres and 4 centimetres; and the angle between them is 130°. What is its area?

SAT is a triangle. P and Q are points on SA and ST respectively such that PQ || AT. If M is a point on SA such that MQ || PT, then which of the following is always true?

Let $ABC$ be an isosceles triangle with base $BC$ . If $r$ is the radius of the circle inscribed in the $△ABC$ and $\rho$ be the radius of the circle escribed opposite to the angle $A$, then the product $\rho r$ can be equal to

$($ Note: $R$ is the circum radius of the triangle $ABC)$

The integer ${}^{\prime }{k}^{\prime }$, for which the inequality $x^2-2(3k-1)x+8k^2-7>0$ is valid for every $x$ in $R$ is :

The base edges of two square pyramid are in the ratio 1 : 2 and their heights are in the ratio 1 : 3. The volume of the first pyramid is 180 cubic centimetres. What is the volume of the second?

The sum of the digits of a two digit number is 13 the number obtained by interchanging its digits exceeds the given number by 9 find the original number

A tangent is drawn at a point P on a circle. A line through the centre O of the circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

Arrange the polynomials in the increasing order of their degree (bottom to top).

Question 2 (i)
Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows.
(i) a = 10, d = 10