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There are $50$ numbers. Each number is subtracted from $53$ and the mean of the numbers so obtained is found to be $-\mathrm{3.5.}$ The mean of the given numbers is :

Consider the following statements:
When two straight lines intersect:
(i) adjacent angles are complementary
(ii) adjacent angles are supplementary
(iii) opposite angles are equal
(iv) opposite angles are supplementary

Question 55

Fill in the blanks to make the statement true.

88 $\times$ ___ = -88

1. 17

In a trapezium PQRS, as shown in the figure, $PQ||SR||TU.IfTP=\frac{1}{2}PS,$ then the ar(PQRS) is equal to

What is the total surface area of a hemisphere?

In the figure, ∠x = 62^o, ∠XYZ =54^o. if YO and ZO are the bisectors of ∠XYZ and ∠XZY respectivel of ΔXYZ, then ∠YOZ is

cos$1^{\circ }$ $\times$ cos$2^{\circ }$ $\times$ cos$3^{\circ }$ $\times$……..$\times$ cos ${180}^{\circ }$ is equal to ____.

Assertion : In $\Delta ABC$, median AD is produced to X such that AD = DX. Then, ABXC is a parallelogram.

Reason : Diagonals AX and BC bisect each other at right angles.

Which of the following is correct?

If $3^{x-1}$ =9 and $4^{y+2}$ =64, what is the value of $\frac{x}{y}$

If $\Delta ABC$ $\cong$ $\Delta DEF$ by S.S.S. congruence, then which of the following options is correct?

In the given figures, mark the figures which are on the same base but not between same parallels.

The altitude AD of in $\Delta$ABC is 10 cm. The $\angle$A is an obtuse angle and BD = 10 cm, CD = 10$\sqrt{3}$ cm. Find $\angle$A.

The wheel of a cart is making 4 revolutions per second. If the diameter of the wheel be 84 cm, find its speed.

Person A is at number 9 on a number line. He moves 2 steps to left and then another 5 steps to the left, where is he standing now?

Raghu had to make a cylindrical aluminium tube. What is the area of the aluminium sheet required to make the tube, if the length of the tube is 1 m and the base radius is 3.5 cm? (Take $\pi =\frac{22}{7}$)

Madhav and Rama have feedback forms from 50 participants of a workshop in which participants have commented about different sessions. They want to know how the workshop was. What kind of data they are handling?

Find the area of a parallelogram ABCD in which AB = 3 cm and BC = 4 cm and AC = 5 cm using Heron's formula.

Question 7 (ii)

To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.

$\begin{array}{cc}\text{Opinion}& \text{Number of students}\\ \text{like}& 135\\ \text{dislike}& 65\end{array}$

Find the probability that a student chosen at random

(ii) does not like it

The lengths of the sides of a triangle are in ratio 3:4:5. Find the area of the triangle if its perimeter is 144cm

A cylindrical tank has a capacity of 6160 $m^3$. Find its depth if its radius is 14 m. Calculate the cost of painting its curved surface (outer) at the rate of Rs. 3 per $m^2$.

‘-p’ and ‘q’ are the zeroes of the polynomial

$x^2–bx+c$.

The zeroes of the polynomial $x^2–bxy+c{y}^2$are

Given below is the frequency distribution of marks of 70 students of Class-$9^{th}$

Simplify : $\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}.$

A hemispherical bowl is made of steel,0.25 cm thick.The inner radius of the bowl is 5 cm.Find the outer curved surface area of the bowl.

√3 +√2 /√3 -√2 = a + b√5. Find a and b

In ∆ triangle ABC, D and E are the midpoints of side AB and AC. State which of the following are correct option(s).

In which quadrant will the point, (-3,-1) lie in the cartesian plane?

Find the area (in cm${}^2$) of the shaded part in the figure given below. [Take $\pi =\frac{22}{7}$ and all the dimensions are in $cm$]

1. 10.5