Mtet Guidebook 2026 paper II Mathematics set 4 #mtet2026 #education

Added: 2026-05-10

[00:00:00]Hello everyone, welcome to my channel Udisphere. In this video, I would like to discuss about MTE guide book paper 2.

[00:00:07]And here I will discuss mathematics paper 2 and set 4. Good news is set 1 2 3 already discussed and uploaded in the channel. If you have not watched, please go and check all the videos. So let's discuss with the first question they ask here. After reading 34th part of a book, 30 pages were left. How many pages are there in the book? They ask in the question. If you observe here the fraction the book is divided into four part and out of this four part three part already finished reading. Then how many part left? One part is left. And here in the question they said 30 pages were left. That means in one part how many pages were there? There were 30 pages.

[00:00:56]Now if in one part contain 30 pages then four part will contain how many pages just multiply with four. So 30 into four if you multiply how much you'll get you'll get 120. That means option which one? Option C is your correct option 120 pages.

[00:01:18]Next question number 62 they ask here how many prime numbers are there between 100 and 120.

[00:01:27]So prime number that means what the number having two factor that is one and number itself.

[00:01:36]Now here 100 and 120 in between how many numbers are there having two factor?

[00:01:43]If you see here, first will be 101, then second will be 103, third will be 107, fourth will be 109 and fifth will be 113.

[00:02:02]That means how many? Five prime numbers are there between 100 and 120. So option which one? Option C is your correct option. If you see here they are having factors one and the number itself that means 1 0 1 that means only two factor.

[00:02:18]Here also if you observe it is having two factor that is one and the number itself that is 103.

[00:02:25]All are having only two factor. So by definition of prime number we know that if a number having two factor then the number is said to be a prime number.

[00:02:37]Next question number 63. They ask here the sum of the exponent of the prime factors in the prime factorization of it is given 102.

[00:02:49]Let's factoriize here. It is given 102 that is our even number. We have to go with two. So 10 / 2 will be five time and then 2x2 will be one time. Now if you observe here the new number we got 51. It is a odd number and it is also divisible by three. So let's go with three. Now it will be what? 17. Now 17 is a prime number. So we cannot factoriize further.

[00:03:17]So we got here that 102 equal to we got 2 into 3 into 17. But in the question what they ask? They ask sum of the exponent. So remember that exponent means what? It is a power two. Here power how much? One three also having one 17 also 1 * 1. Now they ask their sum 1 + 1 2 2 + 1 3 that means option which one option B is your correct option here.

[00:03:53]Next question number 64 they ask here three numbers are in the ratio it is given 3 ratio 4 ratio 5 and their LCM it is given 2,400.

[00:04:04]Find their ACF is what they ask here.

[00:04:07]Just multiply them. It will be how much?

[00:04:09]12 and 12 into 5 will be 60. So divide here with 60. 0 will be cancel and then if you divide it will go how many times?

[00:04:16]It will go 40 times. So option which one? Option A is your correct option here.

[00:04:21]Next question number 65. They ask here David has every third day off. Every third day off in November. And then John has every fifth day off in November.

[00:04:34]On which date for the first time David and John have day off together?

[00:04:40]That means just take LCM between these two number three and five that is LCM will be 3 into 5 equal to how much? It is our 15 that means November 15. So option B is your correct option here.

[00:04:54]Next question number 66 they ask a bank has rupees 785 in denomination. It is given what? 2 rupees, 5 rupees and 10 rupees coin. The coins are in the ratio. It is given 6 ratio, 9 ratio and 10. So we'll consider there is 6x 9x and 10 x. Now according to the question they have given that means two rupees coins are there. How many 6x? So we'll multiply here 2 into we'll write here 6x plus here 5 rupees coin. So 5 into what? 5 into 9x + 10 into 10 x is equal to how much given here it is given here rupees 700 85 they given in the cushion.

[00:05:43]Next if you multiply here you'll get 12x + 45x and + 100x is equal to how much? 785.

[00:05:55]If you add them how much you'll get 12 and 45 it is how much? It is about 57 and 100 how much?

[00:06:03]157x equal to how much? 785.

[00:06:09]So if you divide x = to how much you'll get? You will get five. That means here 9x we'll put the value here 9 into 5 that is our 45. So if you see here option which one? Option B is your correct option here.

[00:06:25]Next question number 67. They ask here the ratio of boys and girls in a school.

[00:06:31]It is given 12 ratio five given. There are 840 girls in the school. What is the total number of students in the school?

[00:06:41]That means girls number already given.

[00:06:44]Boys number not given in the question.

[00:06:46]First of all, we have to find out uh the boys number and then we will add boys and girls. So we'll get total number of students here in the question they have given their ratio that means boy ratio girl is equal to how much given 12 ratio 5 given and then if we put the value here boy and by girls how many given 840 they have given is equal to how much 12 by 5.

[00:07:13]Now what we can divide here if we cut here five and 840 it will go how many time? It will go one time then six time then eight time. Okay. And then we'll multiply boys equal to what? We will multiply these two value. If we multiply we will get 2016.

[00:07:34]We will get that means number of boys are how many? 2016. Now we'll add boys and girls. Okay. So boys that is are what? 2406 and girls that is given here it is what 840.

[00:07:49]Now we have to add it. If we add 6 + 0 will be 6 it will be our five it will be 8 and 2. So 2 85 6. So option which one that is option C is your correct option here. Next question number 68. The ax here during sale John bought a bag market of 1,200 at 50 uh 25% discount and notebook marked for 80 rupees at 25% discount.

[00:08:20]How much did he save during the sale?

[00:08:23]As we know that it is given percentile.

[00:08:26]So anytime if we remove the percentile we have to multiply with we have to divide with 100. Okay, we have to divide with 100 and into the amount it is given what 1200. So we'll write here 1200 plus again given 25% that means what? 25 by 100 we will write and into amount given 80. If you simplify it here 0 0 we can cancel again 0 0 cancel and then if you multiply 25 into 12 how much? It is our 300 plus here you can cancel 0 0 0 and then if we multiply okay if we multiply how much we'll get here we'll get 20 20 and okay if we multiply and divide by 10 how much we'll get we'll get 20 it will be 200 200 divide by 10 how much 20 then if you add how much we'll get we'll get 320 so option C is your correct option here next question number 69 they ask here after two success exclusive discount of 20% and 35% of an item. It is what sold for 5,200. Find its market price. So market price equal to there is a formula. The formula is what? Selling price into 100 divided by 100 minus discount percent. That is our formula.

[00:09:45]So we will calculate first of all the first discount. Okay. First discount is given 20%. So market price it is given 5,200 into 100 and then what we have to divide with what 100 minus discount person discount person is 20 so 100 minus 20 will be how much is 80 then here 0 we can cancel and then with 8 we can divide will go how many time it goes 6 five time okay and then what we'll get 6,500 we'll get the market price now from here again they given a discount of How much? 35% discount. And we will use the same formula here.

[00:10:24]Selling price will be how much this time? 6,500 into 100. And divide by what? 100 minus discount person. And discount person given 35 this time. So 100 minus 35 how much? It is our 65. So 65 it will be one time. That means 100. And you know that 100 into 100 is how much? It is our 10,000. Okay. It is our 10,000. So option which one? Option E is a correct option here.

[00:10:52]Next question number 70. They ask here the area of a rectangle it is given 6x -4. Which of the following pair could be the length and bread? They ask here.

[00:11:02]Okay. So as you know that formula area equal to what? Length into breadth.

[00:11:06]Length into breadth. If we see here the values that is given 6x - 4 given. So we will take here 2 common. So remaining will be what? 3x - 2. So length will be length will be how much? 2 and breadth is what? Breath is 3x - 2. So which one option D is your correct option here.

[00:11:26]Next question number 71. They ask here the sides of a triangle it is given 3x² - y 2 and second side they have given 4x² - 7 xy + 4 y 2. And third side they have given here - 3x² and + 7 x y + 8 y 2. The perimeter of a triangle is what?

[00:11:50]Perimeter means what? All the three side we have to add. If we add all the three side then we'll get the perimeter of a triangle. So we have to add it. If we add it you can see here that here - 3x² and 3x² they will become zero.

[00:12:07]And next here - 7 xy and here + 7 xy they will become zero. So left one is let's see here 4x² is left here we will write here 4x².

[00:12:19]Then if you observe here 4 y² and - y square how much? 3 y² 3 y square and here it is 8 y². If you add it how much?

[00:12:29]There will be 11 y 2. So if you see here option which one? Option B is your correct option here.

[00:12:38]Next question number 72 they ask here x + y they given if x + y = to given 8 and then they ask 2x - 3 y = 6 then find the value of x they ask here. So if you if we observe here it is only y and here it is 3 y to make it 3 y we can multiply here we can multiply here with 3. So we write here 3x + 3 y = to how much? 24.

[00:13:08]You have to multiply on both side. Okay.

[00:13:10]And next it is given here. Second equation they given here. Okay. We'll give it number one. And second equation they have given here 2x - 3 y is = 6 given. Okay is our number two. If we add them first equation plus second equation if we add here here it is 3 + 2 will be what? 5x and they will become zero is equal to how much it is over 30. Now we can divide. So x = to how much? 6. If you see here option b is your correct option here. Next question number 73.

[00:13:44]They given if a + b and a minus b are respectively the length and breadth of a rectangle then the diagonals of a rectangle is equal to. So if we see here if we see here suppose this is our rectangle. If it is our rectangle, we can see here uh breadth will be what?

[00:14:03]Breath will be it is given here a minus b and it will be your a + b is your length. If we draw the diagonals here, now it is a right angle triangle. Okay.

[00:14:13]So we can use here pythagoras theorem.

[00:14:16]So pythagoras theorem if we apply here that hypotenus okay it will become hypotenus equal to hypotenus square equal to what? There will be what?

[00:14:24]Perpendicular square + base².

[00:14:28]Okay, here will be length and breadth.

[00:14:30]Now if we see here, if we remove the square, so we have to give here root.

[00:14:34]Okay, that is our diagonal hypotenus means it is our diagonal. Okay, we'll write here diagonal. Then this one is square a + b square and then we have to add what? A minus b square. If you see here the formula will be a 2 + 2 a b + b² here will be a 2 - 2 a b + b². So here - 2 a b + 2 a b will be cancel then a square a square will be how many 2 a² and + b² and b square will be 2 b² so we can take here 2 common okay roo<unk>2 and then what a square + b square. So option which one option c is your correct option here.

[00:15:13]Next question number 74 they ask here in the figure given below they said here L is parallel to M.

[00:15:22]Now in the question they said find the value of X + 2 Y. That means we need to find out first Y value and X value.

[00:15:31]If you see here this is the parallel line. Two are parallel line they given here. And if you observe here it is our transversal. And what we know in the if there is a transversal if this is 60 it is also our 60. Why they are 60? Because they are called what? Corresponding angle. And corresponding angles are what? Equal. If it is 60, it is also 60.

[00:15:55]Now as we know this is our straight angle and straight this complete is our straight angle and this straight angle is how much? It is our 180.

[00:16:05]Now if it is 60, if it is 60 then this will be how much? That means 180 minus 60. If you subtract 120, this angle will be 120. That means y = how much we got?

[00:16:18]We got 120. But in the question they given here 2 y. So we'll multiply with two. So 2 y = to how much? It will be our 240.

[00:16:27]Next they ask here first of all we have to find out what x value here. So x and this is this will be your transversal and what we know we know that uh this angle they are called what they are called the consecutive angle and consecutive angle their sum is how much 180. If their sum is 180 and if it is 105 this will be how much? If you subtract from 180 you will get 75. So x value how much? 75. So we got here 75 plus how much? 240.

[00:16:59]So if you add them how much you'll get?

[00:17:01]we will get 315. So option which one?

[00:17:04]Option D is a correct option here.

[00:17:07]Next question number 75 they given here.

[00:17:09]If the figure given below here one A given extra here. So A B C is an equilateral triangle. Okay. Okay. So here given uh AB BC and AC they are equilateral means what? All the three side are equal. If all three side are equal and they make what? they make 60°.

[00:17:28]All angles also equal and they will become what? 60° is for equilateral triangle. Now this angle is 30. X value they ask in the question. Okay. Then this complete angle complete angle is how much? There the straight angle that means 180. And this side it is given 60.

[00:17:46]So let's subtract 60. We'll get how much? We'll get 120.

[00:17:52]Okay. This angle is 120. Next what we know? We know in a triangle they have three interior angle and these three interior angle if you add always you will get 360. That means what? X + sorry 180 we will get okay three interior angle their sum is 180. X + 120 + 30 = to how much? 180. Then if you see here X + if you add them how much you'll get?

[00:18:20]150 = 180. Then if you change the side X equal to how much? 180 minus 150. So x = to how much? 30°. So option which one?

[00:18:30]Option A is your correct option here.

[00:18:33]Next question number 60 uh 76 they given here. Which of the following statement is true here? So option B is your correct option. A circle has infinite number of line of symmetry. So in a circle you can draw you can draw infinite what line of symmetry we can draw here. Okay. So option B is your correct option here. Next question number 77 they ask here the letter that has both line and rotational symmetry that means option A is a correct option H. Next question number 78 they ask here the area of the the area of the parallelogram they ask in the question that is what base into height base into height. So if you see here uh DC if if we take DC as the base so that that means DC into height will be what height will be your DL. So here into DL. So option which one? Option C is your correct option here. Next question number 79 they ask here the length and breadth of a rectangular wire that is given what? 15 cm and 7 cm respectively.

[00:19:37]If the wire is bent into circle the radius of a circle is what they ask in the question. That means here it is given previously it was what rectangle.

[00:19:46]Okay, it was a rectangle and then it forms a circle and they ask for radius value. As we know that uh the same wire they make rectangle and then circle the wire is same. That means what? The perimeter. Okay, perimeter of rectangle.

[00:20:05]Okay, perimeter of rectangle equal to what? Circumference of circle. So perimeter of rectangle formula is what?

[00:20:12]2 into what? L + B. Length plus breadth.

[00:20:15]That means 15 + how much? 7. And circumference of circle formula is 2 pi r.

[00:20:24]If we simplify further here, we'll get 2 into if you add them, how much you'll get? You will get 22. And we know that 2 into pi value is 22 by 7. And they ask r value. So we'll find out r value. If you see here 22, 22 they cancel. 2 and 2 also cancel. So r is equal to how much?

[00:20:45]If you cross multiply you'll get 7 cm.

[00:20:47]So option which one? Option B is your correct option here.

[00:20:53]Next question number 80 they ask here the mode and mean are given by 7 8 respectively. Then the median is what they ask in the question. So there is a formula there is a relation between mean mode and median that is mode mode is equal to the relation is three median minus 2 mean.

[00:21:19]If you put the values here mode given that is 7 is equal to 3 median minus 2 into mean given how much that is given 8. If you simplify here uh 7 + we'll get 2 into 8 how much? 16 that is negative. If we change side we have to plus it 16 equal to 3 median. If you add them how much you'll get? You'll get 23 equal to 3 median. That means median equal to what? 23 by 3. So option which one? Option C is your correct option here.

[00:21:57]Next question number 81. They ask here uh the data of a family size in a town given on the bar graph here and they ask here calculate the average family size of the given data. That means to find out the average family size what we have to count here we have to count here total members. Okay, total members here we have to count count and then total families we have to count. Okay. So then we will divide total members divide by total families then we'll get our answer.

[00:22:29]If you see here families how many families are there? Here it is 5 30 45 40 25 and five. If you add all these if you add all these how much you will get?

[00:22:41]You will get that there is what? 150 families are there.

[00:22:46]Now if you add the members here in this family five family they are having one members that means five into what? One five members plus if you check here 30 families having two members. If you multiply 30 into two how much? It means they are having 60 members.

[00:23:07]Plus 45 family they are having what? 45 family they are having three members. If you multiply 3 into 5 that will be 15 in and hand one 3 into 4 will be 12 and 1 will be 13. So 135 members plus here 40 families having four members. If you multiply 160 members and then again plus 25 families having five members that means 125. Again plus five families having six members that means what? 30 members all together. If you add them, you will get what? 515 members all together. Now if you divide 5 and 515 divide by 150. So if you divide you will get 3.4 and something you will get. So we'll take the round value that is our 3.4. So option C is your correct option here.

[00:24:08]So if you like this video please do subscribe and share a friend. Thank you.

[00:24:12]to have a nice day.