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Salil wants to put a picture in a frame. The picture is $7\frac{3}{5}$ cm wide. To fit in the frame the picture cannot be more than $7\frac{3}{10}$ cm wide. How much should the width be trimmed?

What is the value of x if 4x -7 = 3x +5 ?

Observe the following graph and answer the questions. [4 MARKS]

(i) In which year is the population highest?

(ii) What is the population in the year 2010?

(iii) Compare the ratio of the population of the years 2008 and 2013.

(iv) In which year is the population lowest?

A piece of thread tied at two ends without any slack will be ___

Which of the following numbers is the multiplicative inverse of $\frac{7}{29}$?

Find the supplementary angles corresponding to all the angles of a right angle isosceles triangle? [2 MARKS]

If $m=2$ and $n=-2$, find the value of $6m^3+4n^{-2}$

Two coins are tossed 1000 times and the outcomes are recorded as below
$\begin{array}{cccc}\text{Number of heads}& 2& 1& 0\\ \text{Frequency}& 200& 550& 250\end{array}$

Based on this information, the probability for atmost one head is:

A) $\frac{1}{5}$
B) $\frac{1}{4}$
C) $\frac{4}{5}$
D) $\frac{3}{4}$

1. 58.125

Factorise: $4x^2+4xy+y^2$

Question 27
Take a square piece of paper as shown in figure (1). Fold it along its diagonals as shown in figure (2). Again fold it as shown in figure (3). Imagine that you have cut off 3 pieces of the form of the congruent isosceles right-angled triangle out of it as shown in figure (4).

On opening the piece of paper which of the following shapes will you get?

a)

b)

c)

d)

Question 81(iii)

Two angles have a common vertex and their arms form opposite rays (figure). Then
Write all the pairs of vertically opposite angles

Question 17

Rajni and Mohini deposited Rs. 3000 and Rs. 4000 in a company at the rate of 10 % per annum for 3 yr and $2\frac{1}{2}yr$, respectively. The difference of the amounts received by them will be
(a) Rs. 100
(b) Rs. 1000
(c) Rs. 900
(d) Rs. 1100

In the 1st figure, the left hand side (LHS) and the right hand side (RHS) of the weighing machine are equal to each other. If we add 2 on the RHS, the balance looks like figure 2. What should we do to equalize LHS and RHS again?

Insert one of the following {>, <, =} in the given expression.

(-3)-(-4) ____ (-4)+(-3)

Two numbers are in the ratio 5 : 10 . If the larger number is 150 , find the smaller number

Which of the following is the correct formula for arithmetic mean?

$△$ABC is a right angled triangle, right angled at B. BD is a perpendicular as shown. Which of the following is true?

How to find total surface area of a cuboid

Statement 1: Regular polygons have finite lines of symmetry.

Statement 2: Circle has infinite lines of symmetry.

Statement 3: Circle is a polygon with infinite sides.

Statement 4: Circle is a regular polygon with infinite sides.

Which of the above statements is/are incorrect?

Consider the following figure:

$\stackrel{⟷}{AP}and\stackrel{⟷}{BC}$ are parallel. Find the value of (x + y).

Continuing with the previous question, what angle do we have at the end of four arcs?

With B as the centre and any radius more than half of AB, draw another arc as shown. This is the third arc. With A as the centre and the same radius as above, cut the previously drawn arc in Y. This would be the fourth arc. Join PY.

What is the angle ∠ YPA?

Answer the following:
i. Which number will we reach if we move 4 numbers to the right of -2?
ii. Which number will we reach if we move 1 number to the left of 5?
iii. If we are at -8 on the number line, in which direction should we move to reach -13?
iv. If we are at -6 on the number line, in which direction should we move to reach -1?

A is translated to A' by ___.

Question 2
ABC is a triangle, right angled at C. If AB = 25 cm and AC = 7 cm, find BC.

A person walks at the rate of 4 km per hour. How long will he take to go around a square Park 5 times, whose area is 2500 m square?

Question 9(a)
Replace the blank with an integer to make it a true statement.
(- 3) $\times$ ___ = 27

If the radius of a circle is three times the even prime number, the diameter of the circle is ______.

If the length of a rectangle is 10/3cm more than the breath which is equal to the side of a square whose perimeter is 24cm then the area of the rectangle is :

Mr. Thomas invested an amount of ₹13,900 divided in two different schemes A and B at the simple interest rate of $14\%$ p.a. and $11\%$ p.a. respectively. If the total amount of simple interest earned in 2 years be ₹ 3508, what was the amount invested in Scheme B?

The area of the triangle shown in the figure given below is _____.

A water tank has steps inside it. A monkey is sitting on the top most step (i.e., the first step). The water level is at the ninth step .

(1) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level ?

(2) After drinking water , he wants to go back . For this he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step ?

(3) If the no. Of steps moved down is represented by negative integers and the no. Of steps moved up by positive integers , represent his moves in part 1 and 2 by completing the following; (1) -3+2-..... = -8 (2) 4-2+....... =8. In 1 the sum (-8) represent going down by eight steps. So, what will the sum 8 in 2 represent ?

Question 54

In questions 24 to 59, fill in the blanks to make the statements true.
To convert a fraction into a percent, we ___ it by 100.

A submarine is travellingat a speed of 220 mph at a depth of 1600 miles from sea level . To avoid detection ,it further goes down 220 miles . Later when it reaches safe zone , it ascends 440 miles . Finally ,what is the depth of submarine from sea level ?

Express $512\times 729$ in exponential form:

Number of lines of symmetry in a circle are

Which among the following is/are proper fraction(s)?

The runs scored by a batsman in 10 matches are 34, 65, 23, 11, 28, 56, 87, 54, 98 and 12 respectively.
What is the median of the runs scored in these 10 matches?

Question 112

In the given figure, two parallel lines l and m are cut by two transversal p and q. Determine the values of x and y .

A table marked at Rs.15000 is available for Rs.14400. What is the discount %?

Which number completes the below pattern of integers?

-12, -9, -6, -3

Which of the following should be the FIRST sentence after rearrangement?

Draw an angle ${125}^{\circ }$ and take point A on one of its arm and B on the second arm such that OA = OB. Draw the perpendicular bisector of OA and OB. [4 MARKS]