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(Total price for the previous shopping was 3x + 4y, where x is cost of one pant and y is the cost of one shirt)

What will be the expression for the sum of numbers p and q, which is subtracted from their product ?

What is the probability of getting a sum of 11 when a pair of dice is rolled?

A circular garden has a water body which is in the shape of a circle with diameter 14 m.The remaining part of the garden is covered with grass and this portion is 7 m wide. Find the area of the lawn in $m^2$

In a quadrilateral MIST, MI = 3.5 cm, IS = 6.5 cm, $\angle M$ = ${75}^{\circ }$, $\angle I$ = ${105}^{\circ }$ and $\angle S$ = ${120}^{\circ }$. Which of the given line segments could be drawn first to construct the quadrilateral ?

The standard form of the number $12345$ is

(a) $1234.5\times {10}^1$
(b) $123.45\times {10}^2$
(a) $12.345\times {10}^3$
​​​​​​​(a) $1.2345\times {10}^4$

Two right-angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle. What is this condition called?

Question 105

State whether the statement is True or False.

Integers are closed under division.

Two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the

a) RHS congruence criterion
b) ASA congruence criterion
c) SAS congruence criterion
d) AAA congruence criterion

In triangle DEF, an exterior angle at F is represented as 8x + 15. If the two non-adjacent interior angles are represented as 4x + 5 and 3x + 20, find the value of x.

Question 124

Nancy obtained 426 marks out of 600 and the marks obtained by Rohit are 560 out of 800. Whose performance is better ?

Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side of the triangle on which it is constructed. The angle opposite to the blue colour square is the right angle. If the largest side 5 cm, then find the sum of the area of the yellow square and brown square.

Construct a triangle ABC in which BC is 3 cm, $\angle$ B is ${60}^{\circ }$ and AC - AB = 1 cm. [3 MARKS]

The drawing below (figure), show angles formed by the goalposts at different positions of a football player. The greater the angle the better chance the player has of scoring a goal, e.g. The player has a better chance of scoring a goal from position A than from position B.

Seven football players are practising their kicks. They are lined up in a straight line in front of the goalpost [figure (ii)]. Which player has the maximum chance of hitting the goal ?

Question 21
In which of the following cases, a unique triangle can be drawn?
a) AB = 4 cm, BC = 8 cm and CA = 2 cm
b) BC = 5.2 cm, \angle B = 90^\circ and \angle C = 110^\circ
c) XY = 5 cm, \angle X = 45^\circ and \angle Y = 60^\circ
d) An isosceles triangle with the length of each equal side 6.2 cm

Question 71

Are the rational numbers $\frac{-8}{28}$ and $\frac{32}{-112}$ equivalent? Give reason.

The coordinates of A, B, C are (6, 3), (–3, 5) and (4, – 2) respectively and P is any point (x, y). Show that the ratio of the areas of triangle PBC and ABC is .
| $\frac{x+y-2}{7}$| [4 MARKS]

What is the last digit of $6^{109}$?

A closed figure made by joining three non-collinear points is called

The perimeter of a rectangle is 28x³ + 16x² + 8x + 4. One of its side is 8x²+ 4x. Find the other side.

Answer should be 14x³+2

Question 50

In questions 24 to 59, fill in the blanks to make the statements true.
25 mL is ___ % of 5 L.

$(x+y)(x-y)(x^2+y^2)=$

Find the value of x in the equation $3x+\frac{9}{3}=5x+\frac{5}{9}.$

Simplify ${12}^{-8}\times 5^{-8}$.

A man makes a cuboid of plastic of dimension 5cm, 2cm, 5cm. Find the volume to be added to the original cuboid to form a perfect cube? [2 MARKS]

In a marathon of 5 km, Manish can run for 2 km. If Kushagra ran for $\frac{1}{2}$ of the total length of the marathon, who covered more distance?

The image of the point (-5,-6) when reflected in the x axis is

Which of the following statements is true?

___ is the most frequently observed value.

Rina and Tina bought half a dozen apples and two chocolates one for each. What is the amount (in ₹) they spent if each apple cost ₹ x and each chocolate ₹ y?

Question 81

Change the statement, converting expression into statement in ordinary language:

The number of students dropping out of school last year was m. Number of students dropping out of school this year is m - 30.

Consider the figure below:

If $\Delta BOC\cong \Delta AOD$ , and $\angle$ $DOA={30}^o$, then what is the measure of $\angle BCO$ (in degrees) ?

Question 126

Ambika got 99% marks in Mathematics, 76% marks in Hindi, 61% in English, 84% in Science and 95% in Social Science. If each subject carries 100 marks, then find the percentage of marks obtained by Ambika in the aggregate of all the subjects.

If 50 is subtracted from me, the result is 4. Who am I?

The population of a town is 5a${}^2$+3ab-9. If there are -2a${}^2$+ab males then find the number of females in the town.

Find the number of letters(upper case) in English alphabet which have rotational symmetry. Answer in terms of a number___

In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, Find x.

In the given figure two parallel lines l,m are intersected by a tranversal. If $\angle 4={45}^{\circ }$ then $\angle 5$ is

The area of a rectangular piece is 36 cm². If its width is 4 cm, find its length.

Ted and Ned cut their share of pizza into 8 slices each, leaving a total of 16 slices. Ted takes 8 slices. What is the fraction of slices Ted takes?

Ravi and his son scored 14.5 and 16.5 in a game. What is the product of their scores?