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The maximum length of a pencil that can be kept in a rectangular box of dimensions $12cm\times 9cm\times 8cm$, is

(a) $13cm$

(b) $17cm$

(c) $18cm$

(d) $19cm$

Question 4

The width of each of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper class limit of the highest class is:



A) 15

B) 25

C) 35

D) 40

Find the solution for the following pair of equations

$2x+y=8$

$3x-2y=5$

Rashid
spent Rs 35.75 for Maths book and Rs 32.60 for Science book. Find the
total amount spent by Rashid.

What are the resultant coordinates of (x, y) when it is reflected through the origin?

If 5 is subtracted from three times a number, the result is 16. Find the number.

A trader dealing in pressure cooker reduced the price by 20% as a result of which his sale went up by 80%. What was the net effect on his sales income?
(A)44% decrease
(B)44% increase
(C)66% increase
(D)66% decrease

$6^2$ + $7^2$ + $($___${)}^2$ = ${43}^2$

Find the mean age in years from the frequency distribution given below:

$\begin{array}{cc}\text{Class interval of age in years}& \text{Frequency}\left(f_i\right)\\ 25-29& 4\\ 30-34& 14\\ 35-39& 22\\ 40-44& 16\\ 45-49& 6\\ 50-54& 5\\ 55-59& 3\\ \text{Total}& 70\end{array}$

Which of these are examples of direct proportion?

(i) Cost price to grocery.

(ii) Time required in completing a work to the number of workers doing that work.

(iii) Distance covered and time taken to cover that distance when speed is constant.

$\text{Find the rate of disocunt being given on a shirt whose selling price is Rs,546 after deducting a discount of Rs.104 on its marked price.}$

A teacher wants to arrange 2800 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 96 were left out after the arrangement.

Fill up the blanks to make the following statements true:

(a) Sum of the angles of triangle is ___________.

(b) An exterior angle of a triangle is equal to the sum of ___________ opposite angles.

(c) An exterior angle of a triangle is always ___________ than either of the interior opposite angles.

(d) A triangle cannot have more than ___________ right angle.

(e) A triangle cannot have more than ___________ obtuse angle.

If the price of cooking oil increases by 25%, then by how much percentage should a family reduce its consumption of cooking oil so that their expenditure on cooking oil remains the same?

Represent on the number line.

Let the GCD = $x+1$ and LCM = $x^6-1$ for given two polynomials. Then, if $f\left(x\right)=x^3+1$. what is $g\left(x\right)$?

By using the formula, find the amount and compound interest on:

Three years ago, the population of a town was 50000. If the annual increase during three successive years be at the rate of $5\%,4\%and3\%$ respectively, what is its present population?

The graph below shows average height of girls at different ages. At what age will the height of the girl be 65 inches?

​​​​​​​

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

(i) 243

(ii) 256

(iii) 72

(iv) 675

(v) 100

If the seventh term from the beginning and the end in the expansion of ${(\sqrt[3]{32}+\frac{1}{\sqrt[3]{33}})}^n$ are equal, then the value of $\sum _{r=0}^5{}^n{C}_r$ is equal to

The LCM of $x^5$, $x^3$, $x^2$ is___

From the given figure, the volume of x is___

Factorise $a^2-81(b-c{)}^2$

Area of $\Delta PQR$ is $100c{m}^2$ as shown in the figure below. If altitude QT is 10 cm, then its base PR is

Question 16

Write the correct answer from the given four options.

Which among ${43}^2$, ${67}^2$, ${52}^2$, ${59}^2$ would end with digit 1?

a) ${43}^2$

b) ${67}^2$

c) ${52}^2$

d) ${59}^2$

In a certain code, $FORGIVE$ is written as $DPPHGWC$. How would $REQUEST$ be written in that code?

In a college, the ratio of the number of boys to the number of girls is 8:5. If the number of boys is 243 more than the number of girls, then what is the fraction of the number of girls in the college to the total number of students?

Statement 1: Profit is defined as the positive difference between selling price and cost price (S.P > C.P).

Statement 2: Loss is found when (C.P > S.P)

The sum of all the exterior angles of a triangle is ___ (in degrees)​.

Mr. Thomas invested an amount of ₹13,900 and divided it 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?

Question 47

Histogram given below shows the number of people owning the different number of books.



The total number of people surveyed are ___,

Question 9

In the following question, out of the four options, only one is correct. Write the correct answer:

The value of $(-2{)}^{2\times 3-1}$ is :
(a) 32
(b) 64
(c) -32
(d) -64