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Trigonometric Ratios & Identities — NDA Mathematics PYQs

295 previous year questions from Trigonometric Ratios & Identities with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

295 questionsMathematicsSolutions on every page
1

If lies in the fourth quadrant and 3 +4=0 , then what is the value of 2 + 2 ?

NDA 2026 Solution View → 2

If + =0= + , then what is a value of 2 + 2 +2 ( + ) ?

NDA 2026 Solution View → 3

If 2 4 = 2 + 2 , then which one of the following is a possible value of ( + ) ?

NDA 2026 Solution View → 4

If x= - and y= + , then which one of the following is correct ?

NDA 2026 Solution View → 5

If = 1 3 , then what is the value of ( 2 ) ( 3 2 ) ?

NDA 2026 Solution View → 6

If A and B are acute angles such that 2A+2B= , then what is the maximum value of A B ?

NDA 2026 Solution View → 7

x+ 3 x is maximum when x is equal to

NDA 2026 Solution View → 8

In a triangle ABC , A= B+ C then what is ( B 2 )+ ( B 2 ) equal to ?

NDA 2026 Solution View → 9

If and are complementary angles such that - = 6 and m =n , then what is ( m+n m-n ) equal to ?

NDA 2026 Solution View → 10

For the following two (02) items: Let A + B = p and A + B = q . What is p^2 - q^2 p^2 + q^2 equal to?

NDA 2025 Solution View → 11

For the following two (02) items: Let p = cosec , 20° and q = cosec , 70° . What is p^2 + q^2 p^2 q^2 equal to?

NDA 2025 Solution View → 12

For the following two (02) items: Let A + B = p and A + B = q . What is p q equal to?

NDA 2025 Solution View → 13

For the following two (02) items: Let p = cosec , 20° and q = cosec , 70° . What is ( 3 ,p 4 - q 4 ) equal to?

NDA 2025 Solution View → 14

Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r = (-95°) . What is (p + q + r) equal to?

NDA 2025 Solution View → 15

Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r = (-95°) . What is (pq + qr + rp) equal to?

NDA 2025 Solution View → 16

Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r = (-95°) . What is (p^2 + q^2 + r^2) equal to?

NDA 2025 Solution View → 17

Consider the following for the two (02) items that follow: Let p = | - ( - 90°)| . What is the maximum value of p ?

NDA 2025 Solution View → 18

Consider the following for the two (02) items that follow: Let p = | - ( - 90°)| . What is the minimum value of p ?

NDA 2025 Solution View → 19

Consider the following for the three (03) items that follow: Let p = 2 - and q = - 2 . What is (p/q) equal to?

NDA 2025 Solution View → 20

Consider the following for the three (03) items that follow: Let p = 2 - and q = - 2 . What is (p + q) equal to?

NDA 2025 Solution View → 21

Consider the following for the three (03) items that follow: Let p = 2 - and q = - 2 . What is ^2 equal to?

NDA 2025 Solution View → 22

Consider the following for the two (02) items that follow: Let 2 + = 2 , where 0 What is equal to?

NDA 2025 Solution View → 23

Consider the following for the two (02) items that follow: Let 2 + = 2 , where 0 What is 2 2 + 2 equal to?

NDA 2025 Solution View → 24

In a triangle ABC , A + B + C =k What is the value of A B C ?

NDA 2024 Solution View → 25

What is 12^ 48^ equal to?

NDA 2024 Solution View → 26

Consider the following numbers: A. 22.5^ B. 22.5^ C. 22.5^ - 22.5^ How many of the above are irrational numbers?

NDA 2024 Solution View → 27

What is the maximum value of the a x+b x+c ?

NDA 2024 Solution View → 28

If p ( -30^ )=q ( +120^ ) , then what is (p+q) (p-q) equal to? equal to?

NDA 2024 Solution View → 29

If x = y ( 2 3 - ) = z ( 2 3 + ) then what is x+y+z equal to?

NDA 2024 Solution View → 30

If A B C is a triangle, then what is the value of the determinant | array ccc C & ~B & 0 ~A & 0 & ~B 0 & ( ~B + C ) & C array | ?

NDA 2024 Solution View → 31

What is ( 9^ - 9^ ) equal to?

NDA 2024 Solution View → 32

ABC is a triangle such that angle C =60^ , then what is A + B ( A - B 2 ) equal to?

NDA 2024 Solution View → 33

If f( )= 1 1+ and + = 5 4 , then what is the value of f( ) f( ) ?

NDA 2024 Solution View → 34

If and are the roots of the equation x^2-6 x+8=0 , then what is the value of (2 +2 ) ?

NDA 2024 Solution View → 35

What is the value of 65^ +2 45^ -2 40^ - 25^ ?

NDA 2024 Solution View → 36

What is 17^ - 17^ 17^ + 17^ equal to?

NDA 2024 Solution View → 37

What is 3 10^ - 10^ 25^ 25^ equal to?

NDA 2024 Solution View → 38

What is the value of 10^ 50^ + 50^ . 250^ + 250^ 10^ equal to?

NDA 2024 Solution View → 39

If = 1 7 , = 1 10 ; 0 , 2 then what is the value of ( +2 ) ?

NDA 2023 Solution View → 40

A function is defined by f(x)= + ^2 x What is the period of the function?

NDA 2023 Solution View → 41

Let p= ( 5 ) ( 2 5 ) and q= ( 4 5 ) ( 8 5 ) . What is the value of p+q ?

NDA 2023 Solution View → 42

Let p= ( 5 ) ( 2 5 ) and q= ( 4 5 ) ( 8 5 ) . What is the value of p q ?

NDA 2023 Solution View → 43

Let p= 1 3 - 3 x x and q=1-3 ^2 x, 0 x , x 2 . What is pq equal to

NDA 2023 Solution View → 44

Let x+ y= 3 ( y- x) ; x+y= 2 , 0 x, y 2 What is a value of 3 x+ 3 y ?

NDA 2023 Solution View → 45

Let x+ y= 3 ( y- x) ; x+y= 2 , 0 x, y 2 What is a value of ^3 x+ ^3 y ?

NDA 2023 Solution View → 46

Let p= 1 3 - 3 x x and q=1-3 ^2 x, 0 x , x 2 . For how many values of x does 1 p become zero?

NDA 2023 Solution View → 47

Paragraph: Given that x+ x+ x+ x+ x+ cosec x=7 Question: The given equation can be reduced to

NDA 2023 Solution View → 48

Paragraph: Let be the GM of and ; be the AM of and Question: What is 2 equal to?

NDA 2023 Solution View → 49

Paragraph: Given that x+ x+ x+ x+ x+ cosec x=7 Question: If 2 x=a-b c , where a and b are natural numbers and c is prime number, then what is the value of a - b +2 c ?

NDA 2023 Solution View → 50

Paragraph: Let f(x)= [ ^2 ] x+ [- ^2 ] x where [.] is a greatest integer function. Question: What is f ( 2 ) equal to?

NDA 2023 Solution View → 51

If f(x)=x (4 x^2-3 ) , then what is f( ) equal to?

NDA 2023 Solution View → 52

Paragraph: Let f(x)= [ ^2 ] x+ [- ^2 ] x where [.] is a greatest integer function. Question: What is f ( 4 ) equal to?

NDA 2023 Solution View → 53

Paragraph: Let be the GM of and ; be the AM of and Question: What is the value of of 2 ?

NDA 2023 Solution View → 54

What is the value of cosec (- 73 3 ) ?

NDA 2022 Solution View → 55

What is the value of ( 5 17 )+ ( 7 17 )+2 ( 11 17 ) ( 17 ) ?

NDA 2022 Solution View → 56

What is the value of ( 3 8 ) ?

NDA 2022 Solution View → 57

What is the value of ^2 165^ + ^2 165^ ?

NDA 2022 Solution View → 58

If x= 25 24 and x lies in the fourth quadrant, then what is the value of x+ x ?

NDA 2022 Solution View → 59

What is 36^ - 72^ equal to?

NDA 2022 Solution View → 60

If f( )= ^2 -1 , then what is f( )+f( ) 1-f( ) f( ) equal to?

NDA 2022 Solution View → 61

What is the value of (2 n + 5 6 ) (2 n - 5 6 ) , where n Z ?

NDA 2022 Solution View → 62

In a triangle A B C , A- B- C=0 What is angle B equal to?

NDA 2022 Solution View → 63

If (45^ + )=1+ 2 , where - 4 4 , then what is the value of 2 ?

NDA 2022 Solution View → 64

Let 2 = 3 , where is acute angle. What is the value of 1+4 ? ( . given that . 18^ = 5 -1 4 )

NDA 2022 Solution View → 65

If =- 5 12 , then what can be the value of ?

NDA 2022 Solution View → 66

What is the value of ^4 7 8 + ^4 5 8 ?

NDA 2022 Solution View → 67

What is ^2 ( 4 + )- ^2 ( 4 - ) equal to?

NDA 2022 Solution View → 68

If + =1- , where then which of the following is one of the values of ( + ) ?

NDA 2022 Solution View → 69

If (1+ )(1+ 9 )=2 , then what is the value of (10 ) ?

NDA 2022 Solution View → 70

What is the value of 0^ + 10^ + 20^ + 30^ + .+ 360^ ?

NDA 2022 Solution View → 71

What is the maximum value of the function f(x)= 1 x+ x , where 0 x 2 ?

NDA 2022 Solution View → 72

What is the maximum value of 3( x- x)+4 ( ^3 x . .- ^3 x ) ?

NDA 2022 Solution View → 73

If + = 4 and 2 =1 , then what is 2 equal to?

NDA 2022 Solution View → 74

What is value of ^2 15^ + ^2 15^ ?

NDA 2022 Solution View → 75

Let the equation x cosec x=p have a solution, where p is a positive real number. What should be the smallest value of p ?

NDA 2021 Solution View → 76

Let A B C be a triangle. If 2 A+ 2 B+ 2 C=-1 then which one of the following is correct?

NDA 2021 Solution View → 77

Let x+ y= x+ y for all x, y R . What is ( x 2 + y 2 ) equal to?

NDA 2021 Solution View → 78

If (A+B)=1 and 2 (A-B)=1 , where 0 A, B 2 , then what is A: B equal to?

NDA 2021 Solution View → 79

What is 2 x 4 x- 4 x 6 x- 6 x 2 x equal to?

NDA 2021 Solution View → 80

16. If x=- 3 4 and x is in the second quadrant, then what is the value of x x ?

NDA 2021 Solution View → 81

What is the value of the following? 31^ 33^ 35^ ________ 57^ 59^

NDA 2021 Solution View → 82

What is the range of the function f(x)=1- x defined on entire real line?

NDA 2021 Solution View → 83

What is the value of the following? ( 24^ + 66^ ) ( 24^ - 66^ )

NDA 2021 Solution View → 84

What is (1+ - cosec )(1+ + ) equal to?

NDA 2021 Solution View → 85

What is 1+ ^2 1+ ^2 - ( 1- 1- )^2 equal to?

NDA 2021 Solution View → 86

If 7 +24 =25 , then what is the value of ( + ) ?

NDA 2021 Solution View → 87

What is the value of the following? cosec ( 7 6 ) ( 5 3 )

NDA 2021 Solution View → 88

If 3 =4 , then what is the value of (45^ + . ) ?

NDA 2021 Solution View → 89

If A= 1 7 , then what is 2 A equal to?

NDA 2021 Solution View → 90

What is the maximum value of 2 x 2 x ?

NDA 2021 Solution View → 91

Paragraph: Read the following information and answer that follow: Let a ^2 x+b ^2 x=c ; b ^2 y+a ^2 y=d and p x=q y . Question: What is ^2 x equal to ?

NDA 2020 Solution View → 92

Paragraph: Read the following information and answer that follow: Let a ^2 x+b ^2 x=c ; b ^2 y+a ^2 y=d and p x=q y . Question: What is p^2 q^2 equal to?

NDA 2020 Solution View → 93

Paragraph: Read the following information and answer Let t_n= ^n + ^n . Question: What is t₃-t₅ t₅-t₇ equal to?

NDA 2020 Solution View → 94

Paragraph: Read the following information and answer: Let = =15^ . Question: What is the value of 7 - 7 ?

NDA 2020 Solution View → 95

If x+ y= y- x , where 0 y x 2 , then what is ( x-y 2 ) equal to?

NDA 2020 Solution View → 96

Paragraph: Read the following information and answer: Let = =15^ . Question: What is ( +1^ )+ ( +1^ ) equal to?

NDA 2020 Solution View → 97

Paragraph: Read the following information and answer: Let 3 A A =K , where A 0 and K 1 3 . Question: What is ^2 A equal to?

NDA 2020 Solution View → 98

Paragraph: Read the following information and answer: Let 3 A A =K , where A 0 and K 1 3 . Question: For real values of A, K cannot lie between

NDA 2020 Solution View → 99

Paragraph: Read the following information and answer that follow: Let a ^2 x+b ^2 x=c ; b ^2 y+a ^2 y=d and p x=q y . Question: What is d-a b-d equal to?

NDA 2020 Solution View → 100

Paragraph: Read the following information and answer Let t_n= ^n + ^n . Question: What is the value of t₁₀ where =45^ ?

NDA 2020 Solution View → 101

If = 17^ - 17^ 17^ + 17^ , then what is the value of ?

NDA 2020 Solution View → 102

Paragraph: Read the following information and answer: A B C D is a trapezium such that A B and C D are parallel and B C is perpendicular to them. Let A D B= , A B D= , B C=p and C

NDA 2020 Solution View → 103

Paragraph: Read the following information and answer Let t_n= ^n + ^n . Question: What is t₁^2-t₂ equal to?

NDA 2020 Solution View → 104

A and B are positive acute angles such that 2 B=3 ^2 A and 3 2 A=2 2 B . What is the value of (A+2 B) ?

NDA 2020 Solution View → 105

Paragraph: Read the following information and answer: Let = =15^ . Question: What is the value of + ?

NDA 2020 Solution View → 106

The value of ordinate of the graph of y=2+ x lies in the interval

NDA 2020 Solution View → 107

What is 3 x+ 3 x+4 ^3 x-3 x+3 x-4 ^3 x equal to ?

NDA 2020 Solution View → 108

What is the value of 8 10^ 20^ 40^ ?

NDA 2020 Solution View → 109

What is the maximum value of x x ?

NDA 2020 Solution View → 110

What is the minimum value of 3 (A+ 3 ) where A R ?

NDA 2020 Solution View → 111

What is the value of 48^ - 12^ ?

NDA 2020 Solution View → 112

If cosec = 29 21 where 0 90^ , then what is the value of 4 +4 ?

NDA 2019 Solution View → 113

Consider the following statements: 1. + can never be equal to 1.5 . 2. + can never be less than 2 . Which of the above statements is/are correct?

NDA 2019 Solution View → 114

What is ( + )-2 + ( - ) equal to ?

NDA 2019 Solution View → 115

If A - B =x and B - A =y , then what is the value of (A-B) ?

NDA 2019 Solution View → 116

If angle C of a triangle A B C is a right angle, then what is A + B equal to?

NDA 2019 Solution View → 117

What is ( A 2 )- ( A 2 ) equal to?

NDA 2019 Solution View → 118

What is 80^ + 40^ - 20^ equal to?

NDA 2019 Solution View → 119

What is A + cosec A equal to?

NDA 2019 Solution View → 120

Paragraph: Consider the function f(x)=g(x)+h(x) where g(x)= ( x 4 ) and h(x)= ( 4 x 5 ) Question: What is the period of the function g(x) ?

NDA 2019 Solution View →
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