EMRS PGT Mathematics Mock Test - 1 - EMRS MCQ

1) 8, 4, 3, 7, 1, 5, 2, 6

2) 5, 2, 7, 3, 4, 1, 8, 6

3) 3, 1, 6, 8, 4, 5, 2, 7

4) 1, 4, 8, 3, 2, 5, 7, 6

'POLITICS' is a meaningful English word.

Hence, '1, 4, 8, 3, 2, 5, 7, 6' is the correct answer.

The logic followed is:

It is given that Rajat has 64% marks in 10th, an age of 27 years, and work experience of 5 years.

It is clearly mentioned in the criteria that 10th marks should be greater than 60% for job Quality check Engineer and greater than 65% for job Software Engineer.

Rajat got 64% marks in 10th and has work experience of 5 years.

Therefore, Rajat qualifies for the job of Quality check Engineer.

Hence, the correct answer is "Quality check Engineer".

Given:

Efficiency of Amit = 2 × Efficiency of Ramit

Concept used:

Total work = Efficiency × Time period

Calculation:

The efficiency of Amit = 2

Efficiency of Ramit = 1

Total work = (2 + 1) × 28 = 3 × 28 = 84

Number of days Ramit takes to complete the whole work = 84/1 = 84

∴ The number of days in Ramit will complete the work is 84 days.

The logic followed is:

Similarly,

Hence, the correct answer is "15".

The logic followed is:

middle number = sum of the bottom number - top number

In fig 1:

10 = (7 + 9) - 6

10 = 16 - 6

10 = 10

In fig 2:

10 = (5 + 8) - 3

10 = 13 - 3

10 = 10

Similarly,

? = (9 + 6) - 4

? = 15 - 4

? = 11 

Hence, the correct answer is "11".

The correct answer is Special keys​.

Key Points

• A keyboard key that moves the cursor (pointer) around the screen.
• The four arrow keys, as well as the PageUp, PageDown, Home, and End keys, are among them. Keys for navigating.
• These keys are used to navigate documents and webpages, as well as to modify text.
• The arrow keys, Home, End, Page Up, Page Down, and Insert are among them.
• To close the current open program or window, simultaneously press the Ctrl and F4 keys on the keyboard.
• Users can also simultaneously press the Alt and spacebar keys, then arrow down to the Close or Exit option in the menu and click Enter.

Important Points

• A special key, sometimes known as a media key or multimedia key, is a keyboard key that performs a function not available on a standard 104-key keyboard.
• A function key is a type of soft key that can be programmed on a computer or terminal keyboard to cause an operating system command interpreter or application software to do specified activities.

Age of learner is proportional to the cognitive ability of the learner, thus teaching aids should be selected on the basis of the age. Use of any kind of teaching aid can only be helpful in serving the purpose, if it runs parallel to the cognitive ability of the learner.
The use of teaching aids facilitates the objective of teaching by assisting teachers in differentiating instruction. Hence, they must be chosen keeping in view what the teacher intends to teach the students.
The teaching aids also must be carefully chosen to match the intellectual level of the students. In case of students with intellectual disabilities, different kind of teaching aids are to be used, instead of those used for normal intellectual abilities.

Mrs. Shalini is using a black board. A black board is a visual aid, thus Mrs.Shalini is using a visual aid. Visual aids, like the black board, are important teaching aids which can facilitate learning. The black board is the most basic and important visual aid for a classroom. Visual aids are visual communication of ideas and apart from black boards, other visual aids include PPTs, flip charts etc.

As we know that the length of the perpendicular from point P(x₁,y₁,z₁) from the plane


Here, P(2,3,-5) is the point and equation of plane is x+2y - 2z = 9

Therefore, the perpendicular distance is :

We have:
limx→0 ln(1+ax)]/x=a
lim x→0 ln(1+ax)/ax=a
and then:
lim x→0 [ln(1+ax)-ln(1+bx)]/x
= a-b

The equation of the circle  with centre at (h,k) and radius equal to a is (x−h)² +(y−k)² = a²
 When the circle passes through the origin  and centre lies on x− axis 
⇒h = a and k = 0
Then the equation (x−h)²+(y−k)²=a² becomes (x−a)²+y²=a²
If a circle passes through the origin and centre lies on x−axis then the abscissa will be equal to the radius of the circle and the y−co-ordinate of the centre will be zero Hence, the equation of the circle will be of the form 
(x±a)²+y²=a²⇒x²+a² ±2ax+y²=a²
=x² +y² ±2ax=0 is the required equation of the circle.

Shortest distance between two skew lines is The line segment perpendicular to both the lines .

If AB = BA = I , then A and B are inverse of each other. i.e. A is invers of B and B is inverse of A.

C₁C₂ < r₁+ r₂

The number of possible entries of 2 × 2 matrix is 4 Every entry has two choice, 0 or 1.

Thus, the total no. of choices is,

2 × 2 × 2 × 2 = 2⁴

= 16

The equation y = 2x − x² i.e. y – 1 = - (x - 1)² represents a downward parabola with vertex at (1, 1) which meets x – axis where y = 0 .i .e . where x = 0 , 2. Also , the line y = - x meets this parabola where – x = 2x − x² i.e. where x = 0 , 3. 
Therefore , required area is :

9x² + 5y² - 30y = 0
9x² + 5(y−3)² = 45
We can write it as : [(x-0)²]/5 + [(y-3)²]/9 = 1
Compare it with x²/a² + y²/b² = 1
e = [(b² - a²)/b²]^½
e = [(9-5)/9]^1/2
e = (4/9)^½
e = ⅔

A 3-digit no.: _ _ _
Possible digits: 0, 1 ,2, 3, 4, 5, 6, 7, 8, 9
In the first place there are 9 possible digits (0 cannot be the 1st digit)
In the second and third place there are 10 possible digits.
Total no. of 3-digit numbers = 9 *10 *10 = 900 
For 3-digit no. without digit 7,
Possible digits: 0, 1 ,2, 3, 4, 5, 6, 8, 9
In the first place there are 8 possible digits (0 cannot be the 1st digit)
In the second and third place there are 9 possible digits.
Total no. of 3-digit numbers = 8 *9 *9 = 648 
No. of 3-digit numbers with at least one digit 7 = 900 – 648 = 252

A square matrix A for which Aⁿ= 0 , where n is a positive integer, is called a Nilpotent matrix.

We have: 

z = -i
Comlex number z is of the form x + iy
x = 0, y = -1
arg(z) = π − tan−1|y/x|
⇒ π − tan−1|-1/0|
= π - (π/2)
⇒  π - π/2
⇒ π/2

(i) |a – a| = 0 < 1 is always true
(ii) a R b ⇒ |a – b| < 1 ⇒ |-(a – b)| < ⇒ |b – a| < 1 ⇒ b R a.
(iii) 2R 1 and
But, 2 is not related to 1/2. So, R is not transitive. 

Geometric mean of two numbers a and b is √ab
As two numbers are 14 and 56
Geometric mean is √14×56
= ± √2×7×2×2×2×7
= ±(2×2×7)
= ±28

The determinant of a matrix A and its transpose always same.

a + b = a₁ +a_2n = a₂ + a_2n-1 = and ab = g₁g_2n = g₂g_2n-1 .... and

Suppose that the Reqd. Limit L = lim x→0 (sinx − x)/x³.
Substiture x = 3y , so that, as x→0 , y→0.
∴ L = lim y→0 sin3y − 3y/(3y)³,
= lim y→0 (3siny − 4sin3y)− 3y)/27y³,
= lim y→0 {3(siny − y)/27y³) − (4sin³y/27y³)},
⇒ L = lim y→0 1/9 * (siny − y)/y³) − 4/27* (siny/y)³...(∗)
.Note that, here,
= lim y→0(siny − y)/y³)
= lim x→0 (sinx−x)/x³) = L.
Therefore, (∗) ⇒ L = 1/9*L − 4/27
or,  8/9L = −4/27
Hence, L = −4/27*9/8
=−1/6

Required area :

then projection of vector a on vector b is given by :