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A die is tossed 200 times and the outcomes are recorded as below:

Question 3 (iv)
Explain how a square is:

(iv) A rectangle

Question 88

Study the pie chart given below depicting the marks scored by a student in an examination out of 54. Find the marks obtained by him in each subject. ?

If $(4^{\sqrt{x}{)}^{\sqrt{x}}}=256$, the value of x is

The Line segment AB has 2 points P and Q lying on it as shown in the figure.

The Ratio between BQ , QP and AP is 5 : 2 : 3. If the length of AP is 6 cm, what is the length of AB?

The angle between the altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is ${60}^{\circ }$.
Find the angles of the parallelogram.

Question 5(i)

Give expression for the following case.

11 added to 2m.

The ordinate of all points on the x-axis is ____.

Question 1(iv)

Find the common factors of the terms

$2x,3x^2,4$

Sum of three consecutive even numbers is 24. Represent it as an equation.

The difference between the measure of an internal angle to that of an external angle of a regular polygon is ${90}^{\circ }$. The value of `n' is

On selling an article for Rs. 48, a shopkeeper loses 20 %. In order to gain 20 %, what would be the selling price ?

(a) Rs. 52

(b) Rs. 56

(c) Rs. 68

(d) Rs. 72

If a + b + c = 2s, then prove the following identities

(a) s² + (s − a)² + (s − b)² + (s − c)² = a² + b² + c²

(b) a² + b² − c² + 2ab = 4s (s − c)

(c) c² + a² − b² + 2ca = 4s (s − b)

(d) a² − b² − c² + 2ab = 4(s − b) (s − c)

(e) (2bc + a² − b² − c²) (2bc − a² + b² + c²) = 16s (s − a) (s − b) (s − c)

(f)

If x and y are inversely proportional then find the value of b.

Find the smallest number by which 9408 must be divided, so that quotient is a perfect square. Find the square root of the quotient?

The cost of 3 duck eggs is same as 4 hen eggs and the cost of 4 swan eggs is same as 7 duck eggs. Given that the cost of 2 hen eggs is ₹ 8, then find the cost of swan’s egg.

If the sum of five consecutive multiple of 8 is 240, Find these multiples. [4 MARKS]

In a triangle ABC, ∠B = 50° and ∠A = 60°. Suppose BC is extended to D. Find ∠ACD.

Expand:
$(x+1)(x+2)(x+3)$

What will be the compound interest on a sum of ₹7500 at 4% per annum for a period of 2 years, compounded annually?

Asha sold goods worth Rs. 19,000 to Nisha on 2nd March, 2016. Rs. 4,000 were paid by Nisha immediately and for the balance, she accepted the bills of exchange drawn upon her by Asha payable after 3 months. Asha discounted the bill immediately with her bank. On the due date, Nisha dishonoured the bill and the bank paid Rs. 30 as noting charges.

Record the necessary journal entries in the books of Asha and Nisha.

The C.I. to be paid when a sum of ₹ 1,600 is taken for 24 months at 8% per annum compounded semi annually is

(Calculator may be used for calculations)

Factorize:

$y^3-3y^2+2y-6-xy+3x$

Four-digit smallest perfect square is.

Each exterior angle of a regular decagon is

Is it possible to construct a square if only one of its diagonal is given?

The sides of a parallelogram are 25 centimetres and 15 centimetres. The height to the 25 centimetres side is 15 centimetres. What is the speciality of this parallelogram?

Turtles are found along the stretch of $2$ and $\frac{2}{4}km$, and $3$ and $\frac{1}{4}km$.

Calculate the combined distance.

Simplify the following expression such that the result has positive exponents: $\left(25M^2{N}^{-4}{)}^{1/2}\right(M^3{N}^{1/2}{)}^2$.

A rectangular water tank is 80 m $\times$ 40 m. Water flows into it through a pipe 40 sq.cm at the opening at a speed of 10 km/hr. By how much, the water level will rise in the tank in half an hour?

Match the following figures with the fractions represented by the shaded portion.

Question 84 (i)

Simplify

$(3x+2y{)}^2+(3x-2y{)}^2$