IIT JEE & NEET Question Bank with Solution: 09/04/21

Trigonometric Functions

This MCQs are based on the Mathematics Part I Textbook of Maharashtra (click here for reference).
For more questions with explanation of Trigonometric Functions (click Trigonometric Functions).

Q.1. If $sin to the power of negative 1 end exponent space open parentheses 1 minus x close parentheses minus 2 space sin to the power of negative 1 end exponent x space equals space straight pi over 2$ then x is

(A) $negative 1 half$

(B) 1

(C) 0

(D) $1 half$

Q.2. The principal solution of $c o t space x space equals space minus square root of 3$ are________.

(A) $straight pi over 6 comma space fraction numerator 5 straight pi over denominator 6 end fraction$

(B) $fraction numerator 5 straight pi over denominator 6 end fraction comma space fraction numerator 7 straight pi over denominator 6 end fraction$

(C) $fraction numerator 5 straight pi over denominator 6 end fraction comma space fraction numerator 11 straight pi over denominator 6 end fraction$

(D) $straight pi over 6 comma space fraction numerator 11 straight pi over denominator 6 end fraction$

Q.3. The polar co-ordinates of a point whose cartesian co-ordinates are $open parentheses negative fraction numerator 1 over denominator square root of 2 end fraction comma negative fraction numerator 1 over denominator square root of 2 end fraction close parentheses$ are __________.

(A) $open parentheses 1 comma straight pi to the power of c over 4 close parentheses$

(B) $open parentheses 1 comma fraction numerator 5 straight pi to the power of straight c over denominator 4 end fraction close parentheses$

(D) $open parentheses square root of 2 comma 200 to the power of degree close parentheses$

Q.4. If $sin to the power of negative 1 end exponent space 4 over 5 space plus space cos to the power of negative 1 end exponent space 12 over 13 space equals space sin to the power of negative 1 end exponent space alpha comma$ then $alpha space equals$ ________.

(A) $63 over 65$

(B) $62 over 65$

(D) $60 over 65$

Q.5. If $tan to the power of negative 1 end exponent space open parentheses 2 x close parentheses space plus space tan to the power of negative 1 space end exponent open parentheses 3 x close parentheses space equals space straight pi over 4$ , then x = _______.

(A) 1

(B) $1 over 6$

(D) $3 over 2$

Q.6. The principal value branch of $s e c to the power of negative 1 end exponent x$ is_________.

(A) $open square brackets negative straight pi over 2 comma space straight pi over 2 close square brackets minus space open curly brackets 0 close curly brackets$

(B) $open square brackets 0 comma space straight pi close square brackets minus space open square brackets straight pi over 2 close square brackets$

(D) $open parentheses negative straight pi over 2 comma space straight pi over 2 close parentheses$

Q.7. If in $increment A B C$ with usual notations a = 18, b = 24, c = 30 then $sin space A over 2$ is equal to

(A) $fraction numerator 1 over denominator square root of 5 end fraction$

(B) $fraction numerator 1 over denominator square root of 10 end fraction$

(D) $fraction numerator 1 over denominator 2 square root of 5 end fraction$

Q.8. If sum of all the solution of the equation $8 space cos space x space. space open square brackets cos open parentheses straight pi over 6 plus x close parentheses. cos open parentheses straight pi over 6 minus x close parentheses minus 1 half close square brackets equals space 1$ in $open square brackets 0 comma space straight pi close square brackets$ is $k straight pi$ , then k is equal to

(A) $13 over 9$

(B) $8 over 9$

(D) $2 over 3$

Q.9. If $cos space p space theta space equals space cos q theta comma space p space not equal to space q$ , then ________.

(A) $theta space equals space fraction numerator 2 n straight pi over denominator p plus-or-minus q end fraction$

(B) $theta space equals space 2 n straight pi$

(D) $n straight pi space plus-or-minus straight q$

Q.10. The number of solution of sin x + sin 3x + sin 5x = 0 in the interval $open square brackets straight pi over 2 comma space fraction numerator 3 straight pi over denominator 2 end fraction close square brackets$ is

(A) 2

(B) 3

(D) 5

Q.11. In $increment A B C comma$ If a = 13, b = 14 and c = 15, then $sin open parentheses A over 2 close parentheses equals$ ________.

(A) $1 fifth$

(B) $square root of 1 fifth end root$

(D) $2 over 5$

Q.12. The general solution of the trigonometric equation $tan squared theta space equals space 1$ is _______.

(A) $theta space equals space n straight pi space plus-or-minus space straight pi over 3 comma space straight n space element of space straight Z$

(B) $theta space equals space n straight pi space plus-or-minus space straight pi over 6 comma space straight n space element of space straight Z$

(C) $theta space equals space n straight pi space plus-or-minus space straight pi over 4 comma space straight n space element of space straight Z$

(D) $theta space equals space n straight pi comma space straight n space element of space straight Z$

Q.13. $2 space tan to the power of negative 1 end exponent space open parentheses 1 third close parentheses space plus space tan to the power of negative 1 end exponent space open parentheses 1 over 7 close parentheses space equals$ ________.

(A) $tan to the power of negative 1 end exponent space open parentheses 4 over 5 close parentheses$

(B) $straight pi over 2$

(D) $straight pi over 4$

Q.14. tan $open parentheses 2 tan to the power of negative 1 end exponent open parentheses 1 fifth close parentheses minus straight pi over 4 close parentheses equals$ ________.

(A) $17 over 7$

(B) $negative 17 over 7$

(D) $negative 7 over 17$

Q.15. The principal solution of equation $sin theta space equals space fraction numerator negative 1 over denominator 2 end fraction$ are_______.

(A) $fraction numerator 5 straight pi over denominator 6 end fraction comma space straight pi over 6$

(B) $fraction numerator 7 straight pi over denominator 6 end fraction comma space fraction numerator 11 straight pi over denominator 6 end fraction$

(D) $fraction numerator 7 straight pi over denominator 6 end fraction comma space straight pi over 6$

Q.16. The principal solution of equation $c o t space theta space equals space square root of 3$ ________.

(A) $straight pi over 6 comma space fraction numerator 7 straight pi over denominator 6 end fraction$

(B) $straight pi over 6 comma space fraction numerator 5 straight pi over denominator 6 end fraction$

(D) $fraction numerator 7 straight pi over denominator 6 end fraction comma space straight pi over 6$

Q.17. The general solution of sec x = $square root of 2$ is ________.

(A) $2 n straight pi space plus-or-minus space straight pi over 4 comma space straight n space element of space straight Z$

(B) $2 n straight pi space plus-or-minus space straight pi over 2 comma space straight n space element of space straight Z$

(C) $n straight pi space plus-or-minus space straight pi over 2 comma space straight n space element of space straight Z$

(D) $2 n straight pi space plus-or-minus space straight pi over 3 comma space straight n space element of space straight Z$

Q.18. If polar co-ordinates of a point are $open parentheses 2 comma straight pi over 4 close parentheses$ , then its cartesian co-ordinates are ________.

(A) $open parentheses 2 comma space square root of 2 close parentheses$

(B) $open parentheses square root of 2 comma space 2 close parentheses$

(D) $open parentheses square root of 2 comma space square root of 2 close parentheses$

Q.19. If $square root of 3$ cos x - sin x = 1, then general value of x is ______.

(A) $2 n straight pi plus-or-minus space straight pi over 3$

(B) $2 n straight pi plus-or-minus straight pi over 6$

(C) $2 n straight pi plus-or-minus straight pi over 3 minus straight pi over 6$

(D) $n straight pi space plus space open parentheses negative 1 close parentheses to the power of straight n space straight pi over 3$

Q.20. In $increment$ ABC if $angle A space equals space 45 to the power of degree$ , $angle B space equals 60 to the power of degree$ , then the ratio of its sides are________.

(A) $2 space bold colon space square root of 6 space bold colon bold space square root of bold 3 bold space plus space 1$

(B) $square root of 2 space bold colon space 2 space bold colon space square root of 3 space plus 1$

(D) $2 space bold colon space 2 square root of 2 space bold colon space square root of 3 space plus space 1$

Q.21. $cos space open square brackets tan to the power of negative 1 end exponent 1 third plus tan to the power of negative 1 end exponent 1 half close square brackets$ = ________.

(A) $fraction numerator 1 over denominator square root of 2 end fraction$

(B) $fraction numerator square root of 3 over denominator 2 end fraction$

(D) $straight pi over 4$

Q.22. In $increment A B C comma$ if $c squared space plus space a squared space minus space b squared space equals space a c comma$ then $angle B equals$ ________.

(A) $straight pi over 4$

(B) $straight pi over 3$

(D) $straight pi over 6$

Q.23. In ABC, ac cos B - bc cos A = _______.

(A) $a squared space minus space b squared$

(B) $b squared space minus space c squared$

(D) $a squared space minus space b squared space minus space c squared$

Q.24. If in a triangle, the angle are in A.P. and $b space bold colon space c space equals space square root of 3 space bold colon space square root of 2$ then A is equal to ________.

(A) $30 to the power of degree$

(B) $60 to the power of degree$

(C) $75 to the power of degree$

(D) $45 to the power of degree$

Q.25. The value of cot $open parentheses tan to the power of negative 1 end exponent space 2 x space plus space c o t to the power of negative 1 end exponent space 2 x close parentheses$ is________.

(A) 0

(B) 2x

(D) $straight pi space minus space 2 straight x$

Q.26. $cos to the power of negative 1 end exponent space open parentheses cos fraction numerator 7 straight pi over denominator 6 end fraction close parentheses equals$ ________.

(A) $fraction numerator 7 straight pi over denominator 6 end fraction$

(B) $fraction numerator 5 straight pi over denominator 6 end fraction$

(D) $fraction numerator 3 straight pi over denominator 2 end fraction$

Q.27. The principal value of $sin to the power of negative 1 end exponent space open parentheses negative fraction numerator square root of 3 over denominator 2 end fraction close parentheses$ is _________.

(A) $open parentheses negative fraction numerator 2 straight pi over denominator 3 end fraction close parentheses$

(B) $fraction numerator 4 straight pi over denominator 3 end fraction$

(D) $negative straight pi over 3$

Q.28. If $tan space theta space plus space tan space 2 theta space plus space tan space 3 theta space equals space tan theta space tan space 2 theta space tan 3 theta$ , then the general value of the $theta$ is __________.

(A) $n straight pi$

(B) $fraction numerator n straight pi over denominator 3 end fraction$

(D) $fraction numerator n straight pi over denominator 2 end fraction$

Q.29. The principal solution of $s e c space x space equals space fraction numerator 2 over denominator square root of 3 end fraction$ are

(A) $straight pi over 3 comma space fraction numerator 11 straight pi over denominator 6 end fraction$

(B) $straight pi over 6 comma space fraction numerator 11 straight pi over denominator 6 end fraction$

(D) $straight pi over 6 comma space fraction numerator 11 straight pi over denominator 4 end fraction$

Q.30. If any $increment A B C$ , if a cos B = b cos A, then the triangle is ________.

(A) Equilateral triangle

(B) Isosceles triangles

(D) Right angled

Q.31. The principal solution of $cos to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses$ is

(A) $straight pi over 3$

(B) $straight pi over 6$

(C) $fraction numerator 2 straight pi over denominator 3 end fraction$

(D) $fraction numerator 3 straight pi over denominator 2 end fraction$

Q.32. In $increment A B C comma$ if a = 2, b = 3 and $sin space A space equals space 2 over 3$ , then $angle B space equals$ ________.

(A) $straight pi over 4$

(B) $straight pi over 2$

(D) $straight pi over 6$

Q.33. The general solution of tan 3x = 1 is

(A) $x space equals space n open parentheses straight pi over 3 close parentheses plus open parentheses straight pi over 12 close parentheses comma space n space element of space Z$

(B) $x space equals space n straight pi comma space straight n space element of space straight Z$

(C) $x space equals n straight pi space plus space straight pi over 4 space comma space straight n space element of space straight Z$

(D) $x space equals space n straight pi space plus-or-minus space straight pi over 4 space comma space straight n space element of space straight Z$

Q.34. The number of principal solution of $tan space 2 theta space equals space 1$ is

(A) One

(B) Two

(D) Four

Q.35. In $increment A B C semicolon$ with usual notations b = 2c and B = 3C, then sin A=

(A) $fraction numerator square root of 3 over denominator 2 end fraction$

(B) 1

(D) $fraction numerator 1 over denominator square root of 2 end fraction$

IIT JEE & NEET Question Bank with Solution

Tabs

Saturday, September 4, 2021

HSC Trigonometric Functions Solved MCQ : Maharashtra Board