Math Chapter Wise

EnglishEMRS PGT-2023

Q01.A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is:

A(2, –4) B9 9, 8 2 − C9 9, 8 2 D(2, 4)

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EnglishEMRS PGT-2023

Q02.A triangle PQR is inscribed in the circle x2 +y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, that ∠ ∠ ∠QPR is equal to:

A3/π B4/π C6/π D2/π

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EnglishEMRS PGT-2023

Q03.The number of circles that can be drawn touching all the lines x = y + 2, y = x + 3 and 2x + 3y = 4 is:

A2 B3 C4 D1

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EnglishEMRS PGT-2023

Q04.The distance between the foci of a hyperbola is 16 and its eccentricity is 2. The equation of the hyperbola is:

A2 2 x y 1 4 9 − = B2 2 2x 3y 7 − = C2 2 x y 1 9 4 − = D2 2 x y 32 − =

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EnglishEMRS PGT-2023

Q05.If the parabola y2 = 4ax passes through the point (3, 2), then the length of its latus rectum is:

A4/3 B1/3 C4 D2/3

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EnglishEMRS PGT-2023

Q06.() 3, 0 is a vertex of the hyperbola 2 2 x y - = 1 a b and a: b = 3: 4. Then its foci are:

A() 0, ± 5 B() 5, 0 ± C() 10, 0 ± D() 5, 0 ±

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EnglishBihar (TRE 2.0)-2023

Q07.The area of the ellipse 2 2 x y + = 1 a b is

Aπ 2 a b Bπab Cπ 1 1 a b + DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q08.The equation of hyperbola with foci on the x- axis and centre (0, 0) is

A2 2 x y 1 a b + = B2 2 x y 1 a b − = C2 2 x y 1 a b + = + DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q09.The centre of the circle x2 + y2 - 4x - 10y + 4 = 0 is

A(2, 5) B(-2, - 5) C(5, 2) DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q10.The equation of the parabola with vertex at the origin and directrix x - 2 = 0 is

Ay2 = -4x By2 = -8x Cy2 = 4x DMore than one of the above ENone of the above

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EnglishEMRS TGT-2023

Q11.The area of a sector of a circle of radius 16 cm cut off by an arc of length 18.5 cm, is:

A148 cm2 B154 cm2 C176 cm2 D168 cm2

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EnglishKVS PGT 2023

Q12.Equation of the circle with centre on y-axis and passing through the origin and the point (2, 3) is

A3x2 +3y2 - 13y = 0 B3x2 +3y2 + 13y = 0 C6x2 +6y2 - 13y = 0 D6x2 +6y2 + 13y = 0

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EnglishKVS PGT 2023

Q13.The circles x2 + y2 + 6x + 2y + 8 = 0 and x2 + y2 − −8x − − − 4y + 4 = 0:

Atouch internally Btouch externally Cintersect each other Ddo not intersect

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EnglishKVS PGT 2023

Q14.The number of common tangent to the circles x2 + y2 = 4 and x2 + y2 − − 8x + 12 = 0 is:

A1 B2 C3 D4

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EnglishKVS PGT 2023

Q15.The maximum distance of the point (10, 7) from the circle x2 + y2 − −4x − − −2y − − − 20 = 0 is:

A10 B15 C12 D20

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EnglishKVS PGT 2023

Q16.The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y − − − 3 = 0

A(3, −4) B(−3, 4) C(−3, −4) D(3, 4)

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EnglishNVS PGT 2022 PGT 2011

Q17.The number of common tangents to the circles x2 + y2 − x = 0 and x2 + y2 + x = 0 is:

A2 B1 C4 D3

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EnglishNVS PGT 2022

Q18.The conic x2 + xy + 2y2 + x + y = 1 is:

Aan ellipse Ba hyperbola Ca parabola Da pair of straight lines

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EnglishNVS PGT 2022

Q19.The equation of the hyperbola where foci are (0, ± 12) and the length of the latus rectum is 36 is:

Ax2 − 3y2 = 108 Bx2 − y2 = 54 Cy2 − x2 = 54 D3y2 − x2 = 108

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EnglishKVS PGT 2022

Q20.The vertex of a parabola is at (−3, 0) and the directrix is the line x+5=0, then its equation is:

Ay2 =8(x+3) By2 =−8(x+3) Cx2 =8(y+3) Dy2 =8(x+5)

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