TG TET Maths Model Paper 2026 | Important MCQs with Explanation | Part 2

本站添加: 2026-05-31

[00:00:00]If x ^ 4 + 1x ^ 4 is = to 47, then we are asked to find out the x + 1x. Okay.

[00:00:08]So x ^ 4 + 1x ^ 4 is equ= to 47 given.

[00:00:14]So this can be written as x² + 1x² = 47. What I'm going to do? I'm going to add two on both. So x² + 1x² + 2 = 47 + 2 that is 49. And this whole expression is in the form of a square + b² + 280. This can be written as x² + 1x² = 49. From this x² + 1x² = square root of 49 that is 7. Again adding two on the both sides. So x² + 1x² + 2 = 9 and this LHS can be as x + 1x the whole square is = to 9 and this x + 1x = roo<unk> of 9 that is 3. So what is the value of x + 1x that is 3. So first option is the correct answer for this question. Now let us go with the next question. The area of triangle for the three points 0a 6 4a 0 and origin. Okay. So for this we can use that area of triangle that is 1x2 * of mod of x and that all formula we can use. But if you have visualize this points on the cartisian plane so we get the answer very easily. First point is what 0a 6 0a 6 lies on yaxis and second point is what? 4 comma 0 lies on x-axis and origin. This is on origin.

[00:01:54]And by joining these three points, we get a triangle. And in this triangle, this is a right angle triangle whose base is 4 units. Height is 6 units. So area of triangle is equal to half into base 4 into height 6. So what you get? You get 12 square units.

[00:02:14]That is the second option is a correct answer. Okay. If you have visualized these points in the cartisan plane, we can get the answer very easily. Now let us see the next question. The value of log sin 30 plus log sin cos 60 minus log tan 6. Okay. So we know that log a plus log b can be written as log of a into b by using this formula. This can be written as log of sin 60 into cos 60 by tan 60 we can write. Okay. Co base is 2. So we know that values of sin 60 it is <unk>3x2 and this is cos 60 1x2 by <unk>3 <unk>3 roo<unk>3 get cancel. This can be written as log of 1x 4 to the base 2. So 1x 4 can be written as 2 ^ of -2 to the base 2. This can be written as -2 * of log 2 base 2. We know that value of log a base a is 1. By using this it value is -2. So third option is a correct answer for this question. Okay.

[00:03:30]Now let us next question.

[00:03:35]Volume of a sphere of radius is 3.5 cm.

[00:03:39]Okay. We have given that radius of a sphere as a 3.5 cm and we are asked to find out the volume. So volume of sphere is what 4x3 I rq by using this formula 4x3 * of I is what? 22x 7 into 3.5 3.5 can be written as uh 3.5 means 35 by 10.

[00:04:02]So this is uh 52 5 that is 7 by2 you can return. So uh r cube means what? 7x2 whole cube that mean 7x2 into 7x2 into 7x2. So this denominator 7 numerator 7 get cancel.

[00:04:20]Okay 2 4 4 get cancel 2 1 2 11 we get.

[00:04:25]So what we get? We get 11 into 7 into 7 by uh denominator 3. So on multiplying this we'll get 49 49 into 11 539 539 by 3 is the answer. So that is the first option is the correct one. Now let us go ahead with the sum. Next question. Okay.

[00:04:48]Now next question. Okay. If alpha, beta and gamma are the zeros of this polinomial then we are asked to find out the sum of the zeros product of the sum of the product of two zeros at once and the product of the okay we know that standard form of cubic equation cubic col is a xq + b x² + c x + d and if alpha beta gamma are zeros of this one so alpha plus beta plus gamma will be obtained by minus b by a so here b is what - 5 so minus of - y by a is 2 so 5 by 2 okay alpha + beta + gamma is equals to 5 by 2 and sum of the product of two zeros at first this alpha into beta and beta into gamma and alpha into gamma is equals to c by a so here c means what cofficient of x terms okay that is -4 by 2 that is -2 and product of the roots alpha Beta gamma is also - d by 8. So d is what 8 - d is what? - 8 by 2 that is -4.

[00:06:03]Okay. So if you observe answer options 5 by 2 - 2 - 4 that is of second option is a correct one. Okay. Now let us say this next question. Which of the following is not true? Okay. Mode is not affected by the extent. Mode is not affected by the extent. This is also true statement. But we are asking not not true that is false statement we need to select. So first option is not corrected. Okay. Mean is simply by the every observation of the value. Yes. Mean is influenced by the every observation and median is unaffected by the ext. Median is unaffected by the extreme that is also correct and range is central tendency of the value. So this is a false statement because central tendencies we have three methods of central tendencies that are mean, median, mode. So range is not considered as a measure of central tendency. So false statement is a fourth one. So fourth option is a correct one as suitable answer for this question.

[00:07:04]Okay. So now let us next question. The length of the diagonal of a square whose perimeter and area are numerically equal. That means we have given that area of square is equal to perimeter of square. Area of square is what? A square that is equal to 4 perimeter of the square is 4 into a side is a from this a square is equal to 4 into a a into a can be 4 into a from this a= transposing this a becomes a denominator. So a a get cancel. So we get a a= to 4. So each side of square is what four you got. If each side of square is a units and it's a diagonal will be obtained by <unk>2 a.

[00:07:46]So here also 4 <unk>2 is the suitable answer for this question. So first option is the correct one. Now let us see this next question. Sum of the first n whole numbers sum of the first n whole numbers. Sum of first n whole numbers formula is n into n minus 1 by 2 by using this formula. This is 100 into 100 - 1 that is 99 by 2 1 are 250 are 50 into 99 that is 4950 that is the third option is the correct one for this question. Now let us say this next question. The curve surface area of right circular cone whose radius is 3 cm and height is 4 cm. The radius of this base of this circular con phone is what? 3 cm. Height is 4 units. So we need to find out the slant height. Slant height will be obtained by square root of r² + h² r² is what? 3² + 4² that is square root of 25. So slant height is what?

[00:08:44]Five we got. What we need to find out?

[00:08:45]We need to find out surface area surface area is RL 5 means 22x 7 into R 3 into 5. So when multiplying this we get 330 by 7 330 by 7 that is the first option is the correct one. Okay. Now let us see this next question. H contains calcium carbon and oxygen in the ratio of 10 is to 3 to 12 iron in the stick of chart 4 g of presence. Then weight of char.

[00:09:22]Okay. Here we have given that as per the ratio weight of the carbon is three parts. So this three part represents 4 g from this one part given as 4x3 g and total weight that we are asking. So total weight means what? First one is 10 parts. Uh second one is three part and oxygen is 12 parts. So and adding this all you will get 25 parts value weight that we are asking to find out. One part weight is what? 4x3 g. So 25 part weight is what? 25 into 4x3 that is 100 by 3 g.

[00:10:00]So if you convert into decimals this will be 33 g that. So first option is the correct one. Okay. Now let us say this next question.

[00:10:11]The mean of p and 1x p is given as a q.

[00:10:14]Then we are asked to find out the mean of p square and 1x p square. So what we have given mean given mean of P and 1x P means what? Sum of observations by number of observations that is given as an q from this p + 1x p is equals to 2 q. So and applying squaring on both sides p + 1x p square gives you 2 the whole square. This can be + p² + 1x p 1x p² + 2 * of p into 1x p that gives you 4 q². Okay. P get cancel. So p² + 1x p² is equ= to 4 q ² - 2. Okay. So what we are asked to find out mean of this. So means what? Sum of observations by two. Sum of observations what we got?

[00:11:09]4 Q ² - 2 by 2 and taking 2 as a common in the numerator. So 2 q ² - 1 by 2 we will get the answer. So required answer is what 2 ² - 1 that is of fourth option is the correct answer. Okay. Now let us say this next question. In the next question we have given that if the letter is selected from the third computer randomly then probability of getting the OS. Firstly let us see that how many letters are there in the word computer. In the computer we have see 1 2 3 4 5 6 7 8 letters are there. Total eight letters are there. In this how many os are there? O E I O U are said the O of English alphabet. In this what are the OL that we have? O U and E three O is three. So required probability probability of getting O means number of O by total letters that is 8 3 by 8 is the correct answer. So that is the first option is a correct answer for this question. Now let us this next question.

[00:12:18]Okay. A shopkeeper bought five articles for 4 rupees and sold four articles for 5 rupees then profit percentage that we have given. So firstly let us take cost price and selling price. What we know?

[00:12:31]We know that cost price of five articles five times of cost price of one article given us a four rupees and selling price of four articles that is four times of selling price of one article given as 5 rupees. So we know that LCM of four and five is 20. So I need to make this cost price of 20 selling price of 20 that so to that if I multiply by four on both sides this should be multiplied by five on both sides. So 20 4 5 are 20 20 cost price of 20 articles is what? 4 16 that you'll get. Okay. So selling price of 20 is equals to 25 rupees that you get. So here what is the profit? Profit 25 - 16 that is 9 by cost price is 16 into 100.

[00:13:26]So 4 4 are 42 25 are 25 9 are that is 225 by 4. If you convert it into mix refraction this will be as 56 1x2 1x4 percentage that is the second option is the correct one. Okay. Now let us last problem in this video. If from the figure line L is par to line M and N is a transposer. This is a line L. This is m and this is n is a transpersonal. Then we are asked to find out the value of x + 5 y + z + 3°. Okay. So if you observe a diagram this y and 30 are corresponding angles. So y value we get as 30 and we know the relation between x and y as 180° because these are adjacent angles. These are linear pair angles.

[00:14:19]Sum of them is equals to 180°. X + 30° = to 180. From this X = 180 - 30 that is uh 150° C. Okay. X = to 150°. Now Z and 30° are vertically opposite angle. So Z value will be 30°. And what we are asking to find out? We are asking to find out X + 5 + Z + 3°. X value as 150.

[00:14:46]Okay. and Z Y into 5 into Y value is 30 plus Z value 30 + 3. So 150 + 5 into 30 150 + 30 less 3 150 + 150 300 300 + 33 330 30 + 33 33° that will the answer. So third option is the correct. So likewise we can solve this problem very easily.