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The number of proper subsets of the set A = {a, b, c, d} is

Find the value of $3\frac{4}{7}\times 2\frac{2}{5}\times 1\frac{3}{4}$

Let ‘n’ be the smallest positive integer having exactly 21 positive integer divisors including 1 and the number itself, then the units digit of ‘n’ is___

Find the unknown angle x in the figure.

In Manali, the temperature was – 5°C on Monday and then it dropped by 2°C on Tuesday. On Wednesday, it rose by 4°C. What was the temperature on wednesday?

Out of (-7),(-5),(-3),1,4,7,find a pair of integers whose sum is:

a) -2 b) 2 c) 0

The line segment PQ has two point X and Y lying on it as shown :

The length of PQ is 30 cm

If the ratio between PX and YQ is 4 : 5 and between XY and YQ is 1 : 5 , Then find the length of XY.

For any integer $b$, $b$ ÷ (-1) is ______.

In the given figure, $\angle x={20}^{\circ },\angle y={160}^{\circ },\angle w={105}^{\circ },\angle z={75}^{\circ }$

Which of the following is correct?

An elevator descends into a mine shaft at the rate of 6m per minute . If it begins to its descend from 15 m above the ground level and what will be it's position after 45 m

The attendance report of a class for 150 days is as follows:

$\begin{array}{cc}\text{Student}& \text{Attendance}\\ 1& 146\\ 2& 142\\ 3& 147\\ 4& 149\\ 5& 146\\ 6& 145\\ 7& 147\\ 8& 146\\ 9& 145\\ 10& 150\\ 11& 143\\ 12& 145\\ 13& 144\\ 14& 142\\ 15& 148\end{array}$

What is the probability that a student has 98% or more attendance?

Question 4

Find the missing values:

$$\begin{array}{ccc}Base& Height& Areaoftriangle\\ 15cm& \dots & 87c{m}^2\\ \dots & 31.4mm& 1256m{m}^2\\ 22cm& \dots & 170.5c{m}^2\end{array}$$

Which of the following is/are true regarding a solid?

Pick the odd one out from the alphabets given, based on the number of lines of symmetry:

Which of the following is a measure of central tendency?

A pentagonal pyramid has ___ edges.

A geometrical figure that has length, breadth and height is called a___.

$△$ABC is drawn with the length of side AB being 5 cm. If $\angle$A is 55${}^{\circ }$ and $\angle$C is 75${}^{\circ }$, then the perimeter of this triangle is

Simplify $(x+7)(x+7)$.

$-2-3=?$

An angle is ${30}^{\circ }$ more than half of its complement. Find the angle.

The degree of the polynomial $x^3+1-7x^8$ is

Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal.

(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.

(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is ${40}^{\circ }$?

$\begin{array}{cccccc}Numberofspokes& 4& 6& 8& 10& 12\\ Anglebetweenapairofconsecutivespokes\left(Indegrees\right)& 90& 60& & & \end{array}$
[3 MARKS]

Question 77

State whether the statement is True or False.

If M is the mid-point of a line segment AB, then we can say that AM and MB are congruent.

The value of $4^3\times 2^3$ is

$△$ABC is constructed such that AB = 4 cm, BC = 5 cm and $\angle$A = 70${}^{\circ }$. Taking side BC as base, another triangle BCD is constructed such that length of side BD is 3 cm and length of side CD is 3 cm. Then $\angle$DBC + $\angle$DCB equals

An object is travelling from A to B along the given path. The distance from A to C = 50 meters, the distance from C to D was travelled in 2 seconds at 20 m/s and E to B was travelled in 3 seconds at 36 km/hr. Distance from D to E = 70 meters. The object took 20 seconds to cover the entire distance. Select the correct statement(s).

Sum of two integers is $-32.$ If one of them is $26,$ then find the other.

If $x^2$ + $y^2$ = 14 and xy = 3, find the value of $2{(x+y)}^2-5{(x-y)}^2$.

Use the signs $>,<$ or $=$ in the blank to make the statement true.

8 -13 -15 __ -15 -39 + 6

The monthly income of a man is ₹ 28,000. He gives $\frac{1}{5}$ of it to his wife and $\frac{2}{5}$ of the remaining he spends on household expenses.

1) How much does he give his wife?

2) What is the amount that is left with him?

If $(-2{)}^x=-128$, then find the value '$x$'.

Ashin invested an amount of Rs. 13,900 divided into two different schemes A and B at the simple interest rate of 14% per annum and 11% per annum respectively. If the total amount of simple interest earned in 2 years is Rs. 3508, what was the amount invested in Scheme B (in rupees)?

In the notation ${(-4)}^5$, 5 is called __.

In the process of construction of ${45}^{\circ }$, which angle would be constructed first?

Identify proper fractions from the following.

A pole is divided in the ratio 7 : 8. If the longer part measures 176 cm, then the measure of the shorter part is _____ cm.

If $\Delta \text{ABC}\sim \Delta \text{PQR}$, identify the pairs of corresponding sides.

John is driving a car at 30 km/hr speed. He drove for half an hour and then he changed his speed to 60 km/hr and drove for another half an hour. What is the total distance covered by John and also find its average speed? [5 MARKS]

The mixed fraction representation of
$\frac{7}{3}\text{is \_\_\_\_\_.}$

In the equation $\frac{2x}{9}=8$, what is the value of $x$ which balances the equation?

There is a frame with a portrait in it. The length and breadth of the frame are in the ratio 8 : 7.

If the entire frame is 450 cm in perimeter, find the length of the frame.

A boy first goes 24 m north and then some distance to the east ,if the distance between the starting point and the ending point is 25 m, then find the distance he travelled due east

Calculate $\sqrt{182.25}$ = ?

The below question consists of four figures a, b, c and d and followed by answer figures marked as (A), (B), (C) and (D) each consisting of two figures marked a and d. Select a figure from the answer sets which suitable in the problem figure such that c is related to figure d and in the same way figure a is related to figure b.

The area of a right triangular region is 129.5 cm² . If one of the sides containing the right angle is 14.8 cm . find the other one