IIT JEE & NEET Question Bank with Solution: 09/08/21

This MCQs are based on the Mathematics Part I Textbook of Maharashtra (click here for reference).
NCERT Straight Line (click on the link).

Q.1. The joint equation of the pair of lines passing through (2, 3) and parallel to the coordinate axes is

(A) xy - 3x - 2y + 6 = 0

(B) xy + 3x + 2y + 6 = 0

(D) xy - 3x - 2y - 6 = 0

Q.2. If the lines represented by $k x squared space minus space 3 x y space plus space 6 y squared space equals space 0$ are perpendicular to each other, then _______.

(A) k = 6

(B) k = -6

(D) k =-3

Q.3.If $m subscript 1$ and $m subscript 2$ are slope of the lines represented by $open parentheses s e c squared theta minus sin squared theta close parentheses space x squared space minus 2 space tan space theta space x y space plus space sin squared theta y squared space equals space 0 comma$ then $open vertical bar m subscript 1 minus m subscript 2 close vertical bar equals$

(A) 1

(B) 3

(C) 2

(D) 4

Q.4. The combined equation of the co-ordinate axis is _______.

(A) x + y = 0

(B) xy = k

(C) xy = 0

(D) x - y = k

Q.5. If the slope of one of the two lines $x squared over a plus fraction numerator 2 x y over denominator h end fraction plus y squared over b equals 0$ is twice that of the other, then $a b bold colon h squared equals$ ________.

(A) $1 space bold colon space 2$

(B) $2 space bold colon space 1$

(D) $9 bold space bold colon space 8$

Q.6. If an equation hxy + gx + fy + c = 0 represents a pair of lines, then

(A) fg = ch

(B) gh = cf

(D) hf = -cg

Q.7. The joint equation of the lines through the origin and perpendicular to the pair of lines $3 x squared space plus space 4 x y space minus space 5 y squared equals space 0$ is________.

(A) $5 x squared space plus space 4 x y space minus 3 y squared space equals space 0$

(B) $3 x squared space plus space 4 x y space minus space 5 y squared equals space 0$

(D) $5 x squared space plus space 4 x y space plus 3 y squared equals space 0$

Q.8. If acute angle between lines $a x squared space plus space 2 h x y space plus b y squared equals space 0$ is $straight pi over 4 comma$ then $4 h squared$ =__________.

(A) $a squared space space plus space 4 a b space plus space b squared$

(B) $a squared space plus space 6 a b space plus space b squared$

(C) $open parentheses a space plus space 2 b close parentheses open parentheses a space plus space 3 b close parentheses$

(D) $open parentheses a space minus space 2 b close parentheses open parentheses 2 a space plus space b close parentheses$

Q.9. If $h to the power of 2 space end exponent equals space a b comma$ then the slop of lines $a x squared space plus space 2 h x y space plus space b y squared space equals space 0$ are in the ratio _______.

(A) 1 : 2

(B) 2 : 1

(D) 1 :1

Q.10. If the slope of one of the lines given by $a x squared space plus space 2 h x y space plus space b y squared space equals space 0$ is two times the other then_______.

(A) $8 h squared space equals space 9 a b$

(B) $8 h squared space equals space 9 a b squared$

(D) $8 h space equals space 9 a b squared$

Q.11. Auxiliary equation of $2 x squared space plus space 3 x y space minus space 9 y squared space equals$ 0 is _________.

(A) $2 m squared space plus space 3 m space minus space 9 space equals space 0$

(B) $9 m squared space minus space 3 m space minus space 2 space equals space 0$

(D) $negative 9 m squared space minus space 3 m space plus space 2 space equals space 0$

Q.12.The difference between the slopes of the lines represented by $3 x squared space minus space 4 x y space plus y squared space equals 0$ is ________.

(A) 2

(B) 1

(D)4

Q.13. If the two lines $a x squared space plus space 2 h x y space plus space b y squared space equals space 0$ make angles $alpha space a n d space beta$ with X-axis, then tan $open parentheses alpha space plus space beta close parentheses space equals$ _________.

(A) $fraction numerator h over denominator a plus b end fraction$

(B) $fraction numerator h over denominator a minus b end fraction$

(D) $fraction numerator 2 h over denominator a minus b end fraction$

Q.14. If the equation $3 x squared space minus space 8 x y space plus space q y squared space plus space 2 x space plus 14 y space plus space p space equals space 1$ represents a pair of perpendicular lines then the values of p and q are respectively________.

(A) -3 and -7

(B) -7 and -3

(D) -7 and 3

Q.15. The area of triangle formed by the lines $x squared space plus space 4 x y space plus space y squared space equals space 0$ and x - y - 4 = 0 is________.

(A) $fraction numerator 4 over denominator square root of 3 end fraction S q. u n i t s$

(B) $fraction numerator 8 over denominator square root of 3 end fraction space S q. u n i t s$

(D) $fraction numerator 15 over denominator square root of 3 end fraction S q. u n i t s$

Q.16. If the equation $4 x to the power of 2 space end exponent plus space h x y space plus space y squared space equals space 0$ represents two coincident lines, then h = _______.

(A) $plus-or-minus 2$

(B) $plus-or-minus 3$

(C) $plus-or-minus 4$

(D) $plus-or-minus 5$

Q.17. If slope of one of the lines $a x squared space plus space 2 h x y space plus space b y squared equals space 0$ is 5 time the slope of the other, then $5 h squared equals$ _______.

(A) ab

(B) 2 ab

(D) 9 ab

Q.18. The point of intersection of lines represented by $x squared space minus space y squared space plus space x space plus 3 y space minus space 2 space equals 0$ is _______.

(A) (1, 0)

(B) (0, 2)

(C) $open parentheses negative 1 half comma 3 over 2 close parentheses$

(D) $open parentheses 1 half comma 1 half close parentheses$

Q.19. If distance between lines $open parentheses x space minus space 2 y close parentheses squared space plus space k open parentheses x space minus space 2 y close parentheses space equals space 0$ is 3 units, then k =

(A) $plus-or-minus 3$

(B) $plus-or-minus 5 square root of 5$

(D) $plus-or-minus 3 square root of 5$

Q.20. The slopes of the lines given by $12 x squared space plus space b x y space minus space y squared equals space$ 0 diffter by 7. Then the value of b is:

(A) 2

(B) $plus-or-minus 2$

(C) $plus-or-minus 1$

(D) 1

Q.21. If the sum of the slopes of the lines represented by $x squared space plus space k x y space minus space 3 y squared equals space 0$ is twice their product, then the value of $apostrophe k apostrophe$ is _______.

(A) 2

(B) 1

(D) -2

Q.22. The measure of the angle between lines $open parentheses sin squared space theta space minus space 1 close parentheses space x squared space minus space 2 x y cos squared space theta space plus space cos squared theta y squared space equals space 0$ is _______.

(A) $straight pi over 2$

(B) $straight pi over 6$

(D) $straight pi over 3$

Q.23. The measure of the acute angle between the lines given by the equation $3 x squared minus 4 square root of 3 space x y plus 3 y squared equals 0$ is

(A) $60 to the power of ring operator$

(B) $70 to the power of ring operator$

(C) $30 to the power of ring operator$

(D) $45 to the power of ring operator$

IIT JEE & NEET Question Bank with Solution

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Wednesday, September 8, 2021

HSC Pair of Straight Lines Solved MCQ : Maharashtra Board