# Advanced Problems in Mathematics for JEE Advanced

## Advanced Problems in Mathematics for JEE Advanced

Hello Students,

Vedantu provides solutions to JEE Advanced 2021 Paper 1 and Paper 2. These solutions come in PDF format with the free download option. These can also be availed online at Vedantu’s learning portal. Both the Question Papers for JEE Advanced are compulsory for the students who clear JEE Main. These solved Paper 1 and Paper 2 have solutions of all the three sections each, which are Mathematics, Physics and Chemistry. JEE Advanced doesn’t have a fixed exam pattern. The number of questions asked in the exam paper varies every year with a surprise element. Variations of the questions remain almost the same and practising these solved papers will help you understand various types of questions asked.

JEE Advanced 2021 Question Paper – IIT Kharagpur has released JEE Advanced question paper 2021 officially. Candidates can download it from the links given below or from the official website, jeeadv.ac.in. JEE Advanced question paper has been released for all subjects in Paper 1 and Paper 2, i.e for Physics, Chemistry and Mathematics. Candidates can use these question papers to cross-check their answers once the official JEE Advanced answer key is out. It can be also used to know the type of questions asked in the exam. Know more about JEE Advanced 2021 question paper from this page.

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## Advanced Problems in Mathematics

Important Trigonometry Questions

Q : If cos θ = , then tan θ is equal to.

(A)

(B)

(C)

(D) 3

Correct Answer : D

Q : If 2sin2 θ – 3 sin θ + 1 = 0, θ being positive angle, then the values of θ are :

(A)

(B)

(C)

(D)

Correct Answer : A

Q : If tan α = 2, then the value of

αα

αα

is :

(A)

(B)

(C)

(D)

Correct Answer : C

Q : What is the value of

is:

(A) 3

(B) 2

(C) 1

(D) 0

Correct Answer : C

Q : A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend and angle twice as before. The height of the tower is

(A) 80 m

(B) 100 m

(C) 160 m

(D) 200 m

Correct Answer : A

Q : If sinθ – cosθ = 7/13 and 00 < θ < 900 , then the value of sinθ + cosθ is :

(A) 17/13

(B) 13/17

(C) 1/13

(D) 1/17

Correct Answer : A

Q : What is the value of

(A) 0

(B) 1

(C) -1

(D) 2

Correct Answer : B

Q : If θ

, then what is the value of sec θ sin θ?

(A)

(B)

(C)

(D)

Correct Answer : A

Q : If x cos2300. sin600=

then the value of x :

(A)

(B)

(C)

(D)

Correct Answer : B

Q : The value of

.

(A)

(B)

(C)

(D) 1

Correct Answer : D

Q : What is the value of the following

(A) cosec A

(B) cos A

(C) secA

(D) sinA

Correct Answer : C

Q : If θ

then find cos2θ :

(A)

(B)

(C)

(D)

Correct Answer : B

Q : If 5cosθ – 12sinθ=0 then value of

(A)

(B)

(C)

(D)

Correct Answer : D

Q : If 4sin2 θ – 1 = 0 and angle θ is less than 900. The value of cos2 θ + tan2 θ is:

(Take 00 < θ < 900)

(A)

(B)

(C)

(D)

Correct Answer : A

Mensuration Questions with Answers

Q : Length of a rectangle is 53 metre, while its breath is 28 metre. Cost of covering it with grass bed is Rs.27 sq meter. Find total expenditure?

(A) Rs. 40,098

(B) Rs. 40,048

(C) Rs. 40,058

(D) Rs. 40,088

(E) None of these

Correct Answer : E

Q : Base of a right-angle triangle is 9 cm and its area is 81 sq cm. Find its height.

(A) 36 cm

(B) 9 cm

(C) 27 cm

(D) None of these

Correct Answer : D

Q : Difference between the circumferences of two circles is 132 cm and radius of the smaller circle is 14 cm. Find the radius of the larger circle?

(A) 14 cm

(B) 21 cm

(C) 30 cm

(D) None of these

Correct Answer : D

**Advanced Problems in Mathematics**

Q : Poles are to be created along the boundary of a rectangular field in such a way that distance between any two adjacent poles is 1.5 metres. The perimeter of the field is 21 metres and length and the breadth are in the ratio of 4:3 respectively. How many poles will be required?

(A) 14

(B) 16

(C) 15

(D) 20

Correct Answer : A

Q : The ratio of length and breadth of rectangle is 5:2 respectively. The respective ratio of its perimeter and area is 1:3 (irrespective of the unit). What is the length of the rectangle?

(A) 27 units

(B) 32 units

(C) 21 units

(D) None of these

Correct Answer : C

Q : The length of a rectangle, which is 25 cm is equal to the length of a square and the area of the rectangle is 125 square cm less than the area of the square. What is the breadth of the rectangle?

(A) 15 cm

(B) 20 cm

(C) 12 cm

(D) 14 cm

Correct Answer : B

Q : The area of a rectangle with 10 cm length is equal to the area of a circle. Find the circumference of the circle.

(A) 36 cm

(B) 34 cm

(C) 26 cm

(D) cannot be determined

Correct Answer : D

Q : If the length of a rectangle is increased by 20% and the breadth is decreased by 10%. What will be the effect on its area?

(A) 8% increase

(B) 8% decrease

(C) 2% increase

(D) 2% decrease

Correct Answer : A

Q : The ratio of length and breadth of a rectangular plot is 71:16 respectively. The area of the plot is 17324 sq.metres. What is the perimeter of the plot?

(A) 284 metres

(B) 528 metres

(C) 264 metres

(D) 614 metres

Correct Answer : B

Q : If area of a circular jogging track is 3850 sq.metres. What is the circumference of the jogging track?

(A) 225 metres

(B) 214 metres

(C) 220 metres

(D) 235 metres

Correct Answer : C

Q : Ratio between areas of two squares is 36:25. What would be the ratio between their perimeter.

(A) 5:4

(B) 6:5

(C) 4:6

(D) 8:7

Correct Answer : B

Q : A wheel can travel 22 km. in 100 rounds. Find the radius of that wheel.

(A) 42 mtr

(B) 28 mtr.

(C) 35 mtr

(D) 49 mtr

Correct Answer : C

Q : A cow is tied with a 14 ft. long rope in the centre of a field. If the cow can graze the grass of 100 ft2 area per day. What will be the time taken by the cow in grazing the grass of whole field?

(A) 2 Days

(B) 18 Days

(C) 24 Days

(D) 6 Days

Correct Answer : D

Q : A rectangular plot has the ratio of 5:3 between length and breath. If the perimeter of the plot is 320 mtr. What’s the area of the plot?

(A) 6000 sq.mtr.

(B) 12000 sq.mtr.

(C) 4500 sq.mtr.

(D) 18000 sq.mtr.

Correct Answer : A

Q : Ratio of length, breath and height of a room is 5:4:2. Area of four wall is 144 square meter. Find diagonal of the floor.

(A) 2√41 mtr

(B) 3√41 mtr

(C) 2√42 mtr

(D) 2√41 mtr

Correct Answer : A

Q : Area of a rectangle is 4 times than that of a square. Breath of rectangle is 12cm. and length of side of square. What is the length of the side of square?

(A) 10 cm

(B) 12 cm

(C) 14 cm

(D) 16 cm

Correct Answer : B

Q : Diagonal of a square is 12√2. Find the ratio between the area of this square and that of square drawn on diagonal.

(A) 2:1

(B) 1:1

(C) 1:2

(D) 1:3

Correct Answer : C

Q : Ratio between the length and breadth of a rectangular field is 9:4. Rs.14400 are spent on the implantation of grass on this field. If the rate of implantation is Rs. 4 per meter square. What is the breath of the field?

(A) 38 mtr

(B) 48 mtr

(C) 42 mtr

(D) 40 mtr

Correct Answer : D

Q : Length and breadth of a rectangular field is 140 m. and respectively. Poles have to be fixed around this field at the distance of 5 m. How many such poles are required?

(A) 88

(B) 40

(C) 92

(D) 41

Correct Answer : C

Q : A carpet is to be laid in a room of 12m ×8m. measurement. Breath of the carpet is 3m. What should be the length of this carpet?

(A) 34 mtr

(B) 32 mtr

(C) 36 mtr

(D) 40 mtr

Correct Answer : B

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