Public – 2007 One Mark Questions One Mark Questions PREPARED BY: R.RAJENDRAN. M.A., M. Sc., M. Ed., K.C.SANKARALINGA NADAR HR. SEC. SCHOOL, CHENNAI-21

Choose the Correct Answer The degree of the differential equation (a) 1 (b) 2 (c) 3 (d) 6 The particular integral (P.I) of (3D2 + D – 14) y = 13 e 2x is (a) 26x e 2x (b) 13x e 2x (c) x e 2x (d) x2/2 e 2x

Choose the Correct Answer. p  q is equivalent to (a) p  q (b) q  p (c) (p  q)  (q  p) (d) (p  q)  ( q  p) The order of [7] in (Z9, + 9) is (a) 9 (b) 6 (c) 3 (d) 1

Choose the Correct Answer. In the set of integers under the operation * defined by a * b = a + b – 1, the identity element is (a) 0 (b) 1 (c) a (d) b is (a)  (b) 0 (c) log (d)

Choose the Correct Answer. The stationary point of f(x) = x 3/5 (4 – x) occurs at x = ----------- (a) (b) (c) 0 (d) 4 If u = log then is (a) 0 (b) u (c) 2u (d) u–1

Choose the Correct Answer. The curve a2y2 = x2 (a2 – x2) a > 0is symmetrical about (a) x – axis only (b) y – axis only (c) y = x (d) both the axes and about origin The value of is (a) (b) (c) 0 (d)

Choose the Correct Answer. If (m – 5) + i(n + 4) is the complex conjugate of (2m + 3) + i(3n – 2) then (n, m) are (a) (b) (c) (d) The polar form of the complex number (i25) 3 is (a) cos + i sin (b) cos + i sin (c) cos – i sin (d) cos – i sin

Choose the Correct Answer. The equation having 4 – 3i and 4 + 3i as roots is (a) x2 + 8x + 25 = 0 (b) x2 + 8x – 25 = 0 (c) x2 – 8x + 25 = 0 (d) x2 – 8x – 25 = 0 The value of ei – e–i is ----------- (a) sin  (b) 2sin (c) i sin (d) 2isin

Choose the Correct Answer. The length of the latus rectum of the parabola y2 – 4x + 4y + 8 = 0 is (a) 8 (b) 6 (c) 4 (d) 2 If A = , then (adjA) A = (a) (b) (c) (d)

Choose the Correct Answer. If A and B are any two matrices such that AB = 0 and A is non-singular, then (a) B = 0 (b) B is singular (c) B is non-singular (d) B = A The system of equations ax + y + z = 0; x + by + z = 0; x + y + cz = 0 has a non-trivial solution then = (a) 1 (b) 2 (c) – 1 (d) 0

Choose the Correct Answer. If (A)  (A,B), then the system is ----------- (a) consistent and has infinitely many solutions (b) consistent and has a unique solution (c) consistent (d) inconsistent If is a non- zero vector and m is a non-zero scalar then m is a unit vector if (a) m = 1 (b) a = m (c) a = 1/m (d) a = 1

Choose the Correct Answer. Let p be ‘Kamala is going to school’ and q be ‘there are twenty students in the class’. ‘Kamala is not going to school or there are twenty students in the class’ stands for ………. (a) pq (b) pq (c) p (d) pq If f (x) = , –  < x <  is a p.d.f of a continuous random variable X, then the value of A is (a) 16 (b) 8 (c) 4 (d) 1

Choose the Correct Answer. If in a Poisson distribution P(X = 0) = k then the variance is (a) log (b) log k (c) e (d) In a binomial distribution if n = 5, P(X = 3) = P(X = 2), then -------------- (a) p = 2q (b) 2p = q (c) p = q (d) 3p = 2q

Choose the Correct Answer. If f (x) is a p.d.f of a normal distribution with mean  then is (a) 1 (b) 0.5 (c) 0 (d) 0.25 The area between the ellipse and its auxiliary circle is (a) b (a – b) (b) 2a (a – b) (c) a (a – b) (d) 2b (a – b)

Choose the Correct Answer. The volume of the solid obtained by revolving about the minor axis is (a) 48 (b) 64 (c) 32 (d) 128 The surface area of the solid of revolution of the region bounded by y = 2x, x = 0 and x = 2 about x – axis is (a) 85 (b) 25 (c) 5 (d) 45

Choose the Correct Answer. The integrating factor of is (a) ex (b) log x (c) 1/x (d) e–x In finding the differential equation corresponding to y = emx where m is the arbitrary constant, then m is (a) (b) (c) y’ (d) y

Choose the Correct Answer. The eccentricity of the conic 9x2 + 5y2 – 54x – 40y + 116 = 0 is (a) (b) (c) (d) The co-ordinate of the vertices of the rectangular hyperbola xy = 16 are (a) (4, 4), (– 4, – 4) (b) (2, 8), (– 2, – 8) (c) (4, 0), (– 4, 0) (d) (8, 0), (– 8, 0)

Choose the Correct Answer. The difference between the focal distances of any point on the hyperbola is 24 and the eccentricity is 2. Then the equation of the hyperbola is (a) (b) (c) (d) The slope of the tangent to the curve y = 3x2 + 3sin x at x = 0 is (a) 3 (b) 2 (c) 1 (d) – 1

Choose the Correct Answer. If s = t3 – 4t2 + 7, the velocity when the acceleration is zero is (a) 32/3 m/ sec (b) – 16/3 m / sec (c) 16/3 m / sec (d) – 32/3 m / sec If then (a) is a unit vector (b) (c) (d)

Choose the Correct Answer. If  +  =  –  then (a) is parallel to (b) is perpendicular to (c)   =   (d) and are unit vectors

Choose the Correct Answer. The non – parametric vector equation of a plane passing through three points, whose position vectors are , and is (a) (b) (c) (d)

Choose the Correct Answer. The shortest distance of the point (2, 10, 1) from the plane is (a) (b) (c) 2 (d)

Choose the Correct Answer. The point of intersection of the line and the plane is (a) (8, 6, 22) (b) (–8, –6, –22) (c) (4, 3, 11) (d) (–4, –3, –11)

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