GuruAanklan Foundation / MHT-CET / Examination

GuruAanklan Foundation / MHT-CET / Examination / Set-A / Mathematics / QPGuruAanklan Foundation / MHT-CET / ExaminationMathematicsSet - [A]MATHEMATICSGeneral Instructions :(i)The test is of 1½ hours duration. This Question Paper is of total Pages(ii)This paper consists of 50 questions. The maximum marks are 100.(iii)There is ONE part in the question paper.The distribution of marks is as under for each correct response.Q. No.1 - 50(iv)–MATHEMATICS( 2, 0)(100 marks) – 50 questionsEach question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Candidateswill be awarded TWO marks each for indicating correct response of each question & there is nonegative marking.MATHEMATICS[Single Answer Choice Type]This Section contains 50 Single choice questions. Each question has 4 choices (A), (B), (C)and (D) out of which ONLY ONE is correct. 1.If P is a point on an ellipse 5x 2 4y 2 80 whose foci are S and S' . Thus PS PS' (A) 4 52.(B) 4(D) 10 1 x 2 sin 1 x 1 x dx isThe value of e 1 x 2 x 1(A) e sin x c3.(C) 8Ifx 1(B) e sin x c(C)ex1 x2 c(D) e x1 x21 xf x dx 2 f x c then f x is(A) ex(B) e x(C) log x1x(D) e2 c

GuruAanklan Foundation / MHT-CET / Examination / Set-A / Mathematics / QP4.The value of(A)1log33 tan x c3 tan x(B)(C)1log33 tan x c3 tan x(D)2 5.sin x sin 3x dx is e0(A)x2 312 3log3 tan x c3 tan xlog3 tan x c3 tan x x dx 2 4 2(B) 2 2 5 1 1 (C) e 2 4 2 2 46.1 5 1 1 (D) e 2 4 2 2 4The equation of line passing through the point (–5, 4) and making the intercept of length2between5the lines x 2y 1 0 and x 2y 1 0 is.(A) 2x y 4 0(B) 2x y 14 0(C) 2x y 14 0(D) None of theseb7.If f a b x f x then x f x dx abb(A)8.32sq.units3(B)bba bf x dx2 a(C)b af x dx2 a(D)b af b x dx2 a16sq.units3(C)8sq.units3(D)4sq.units3 dy Particular solution for the differential equation, cos a , R, y 0 2 is dx y 2 (A) sin a x 10.(B)Area of the region bounded by the parabola y x 2 and the line y 4x is(A)9.a bf b x dx2 a y 2 (C) cos a x y 2 (B) sin a x The solution of the differential equation y 2 (D) cos a x dy2 4x y 1 isdx3(A) 4x y 1 2 tan 2x k (B) 4x y 1 3 tan 2x k 2(D) 4x y 1 3tan 2x k (C) 4x y 1 2 tan 2x k 2

GuruAanklan Foundation / MHT-CET / Examination / Set-A / Mathematics / QP11.12.13.If for the triangle perimeter is 37 cms and length of sides are in G.P. also the length of the smallest sideis 9 cms, then length of remaining two sides are and(A) 12, 16(B) 14, 14(C) 10, 18(D) 15, 13The bacteria culture grows at a rate proportional to its size. After 2 hours there are 600 bacteria andafter 8 hours the count is 75000, then its initial population is(A) 102(B) 120(C) 124(D) 142A random variable X has the following probability distributionX x 2 1 012 3P X x 0.1 k 0.2 2k 0.3 k14.then the expected value is(A) 0.6(B) 0.5(C) 0.7(D) 0.8The probability distribution of X, the number of defects per 10 meter of a fabric asX x01234P X x 0.45 0.35 0.15 0.03 0.02 then variance (x) is(A) 0.532615.n k p k 1 q(D) 0.8676(B)n k 1 p kq(C)P X k isP X k 1 n 1 p k q(D)2 5x 77(B) y 23x 15 77(C) y 315x 77(D) y 2(B) r p q (C) r p q (D) p q r 18.The disjunction pv q is false only when(A) both p and q are false(B) p is true and q is false(C) p is false and q is true(D) both p and q are true19.The simple logical expression of p q p q p q is(A) p q(B) p q(C) p q(D) p qnIf a nilpotent matrix of order 2 then A 1 A is equal to(A) A21.3x 15 77The contrapositive of the statement pattern p q r is(A) r p q 20.n 1 p k 1 qA common tangent to 9x 2 16y 2 144 and x 2 y 2 9 is(A) y 317.(C) 1.54If X has binomial distribution with mean ‘np’ and variance ‘npq’ then(A)16.(B) 0.82(C) A 2(B) 0(D) A 1If the line x 1 0 is the directrix of the parabola y 2 kx 8 0 then one of the value of k is(A) 4(B)18(C)314(D) 8

GuruAanklan Foundation / MHT-CET / Examination / Set-A / Mathematics / QP22. 0 0 1 0 0 Let A 2 1 0 , if u 2 and u 3 are column matrices such that Au 2 1 , Au 3 0 then, 0 1 3 2 1 u1 u 2 0 (A) 1 1 23. 1 (B) 1 1 In ABC if cos A In ABC,(A) 25.(B) scalene(C) an equilateral(D) right angledc b cos A b c cos Acos Bcos C(B)cos Ccos B(C)cos Bcos C(D) (C)17(D)cos Ccos B 1 1 tan tan 1 tan 1 is 2 3 (A)26. 1 (D) 1 0 sin B, then is2sin C(A) an isosceles24. 0 (C) 1 1 13(B)1519The number of integral value of m for which x 2 y2 1 m x my 5 0 is the equation of a circlewhose radius cannot exceed 5, is(A) 20(B) 18(C) 16(D) 24227.e x cos xIf f(x) is continuous at x 0, where f x ,for x 0, then f 0 isx2(A) 128.If x K yT x y (A)29.xy(B)K Tthen2332(D)(C)yx(D) dyisdx(B) xyIf y logx logx logx . then(A) xy52(C)(B)yxdy dx1x 2y 1 (C) –xy4(D) 12xy

GuruAanklan Foundation / MHT-CET / Examination / Set-A / Mathematics / QP30. x 2 y2 d2yIf cos 2 a then 2 is2 dx x y 1(A)31.xy(D) 2y(C) 0.9 (B) 2 55(D) 0.9The function f x 2x 3 15x 2 144x 7 is decreasing for(A) 3 x 833.(C) 0In a box containing 100 bulbs, 10 bulbs are defective. The probability that out of a sample of 5 bulbs,none is defective is(A) 10 532.(B) 2x(B) 3 x 8(C) –3 x 8(D) 3 x 8If displacement of particle is given by x 160t 16t 2 , then at t 1 and t 9, velocities are(A) equal(B) equal and opposite(C) zero(D) in the ratio 2 : 134.If the equation 3x 2 10xy 3y 2 16y k 0 represents a pair of lines, then k is35.(A) 16(B) –12(C) –16(D) 12The combined equation of the lines passing through the origin and which are at a distance of 9 unitsfrom the y-axis, is(A) x 2 81 0(C) y 2 81 0(B) x 2 81 0(D) y 2 81 036.In a certain town 30% families own a scooter and 40% on a car 50% own neither a scooter nor a car200 families ow both a scooter and car consider the following statements in this regard(1) 20% families own both scooter and car(2) 35% families own either a car or a scooter(3) 10000 families live in townWhich of the above statements are correct?(A) 2 and 3(B) 1, 2 and 3(C) 1 and 2(D) 1 and 337.If the slope of one of the lines given by kx 2 4xy y 2 0 exceeds the slope of the other by 8, then38.39.value of k is(A) 8(B) 16(C) 4(D) 12The volume of tetrahedron whose vertices are P (–1, 2, 3), Q (3, –2, 1), R (2, 1, 3), S (–1, 2, 4) isp b c,q a b c is(A) 040.c aa b,r , a b c are non-coplanar vectors then a b c p q r a b c a b c (B) 2(C) 3(D) –1Let the vectors a and b represents adjacent sides AB and BC respectively of regular hexagon ABCDEF.Then the vector representing side CD is(A) b a(C) a b(B) b a5(D) 2a b

GuruAanklan Foundation / MHT-CET / Examination / Set-A / Mathematics / QP41.42.43.44.x 5 If f x sin 2 x sin 2 x cos x cos x and g 1 then gof(x) .3 3 4 (A) 1(B) 2(C) -2(D) -1The line joining the points (–2, 1, –8) and (a, b, c) is parallel to the line whose direction ratio are 6, 2,3 then(A) a 0, b 5, c 5 (B) a 4, b 3, c –5 (C) a 3, b 5, c 11 (D) a 1, b 2, c –6If a straight line in space is equally inclined to the co-ordinate axis, then the cosine of its angle ofinclination to any one of the axes is1111(A)(B)(C)(D)2323 r 4i j i 2j 3k andTheshortestdistancebetweent helines r i j 2k i 4 j 5k , is113(C)(D)2 332If the points 5,5, , 1,3, 2 and 4, 2, 2 are collinear then (A) –6(B) 5(C) 6(D) 10x 1 y 1 z 2If is acute angle between the lineand the plane 2x y z 4 0 such that 122(A)45.46.23(B) 8 cos 1 then 3 43(A)(B)3447.48.49.(C) 35(D)53 1 2 4 If the plane meets the co-ordinates axes at A, B, C such that the centroid of triangle ABC is , , 3 3 3 then equation of plane is(A) x 2y 4z 4(B) 4x 2y z 4(C) x y z 4(D) x 2y 3z 8The distance between the planes 2x – y 2z 3 0 and 4x – 2y 4z 5 0 is2111(A)(B)(C)(D)3356The feasible region is represented byB(0,20)D(0,16)50.E(20/3, 40/3)C(40,0)x0A(20,0)(A) 2x 5y 80, x y 20, x 0, y 0(B) 2x 5y 80, x y 20, x 0, y 0(C) 2x 5y 80, x y 20, x 0, y 0(D) 2x 5y 80, x y 20, x 0, y 0If A is the set of even natural numbers less then 8 and b is the set of prime numbers less than 7, then thenumber of relations from A to B is(A) 29(B) 92(C) 32(D) 29 16

GuruAanklan Foundation / MHT-CET / Examination / Set-A / Mathematics / QP 1 MATHEMATICS General Instructions : (i) The test is of 1½ hours duration. This Question Paper is of total _ Pages (ii) This paper consists of 50 questions. The maximum marks are 100. (iii) There is ONE part in the question paper. The dis