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Student ID:, , , , , , , , WINNING STAR INSTITUTE, “Centre for educational excellence”, , (School Tuitions, College Tuitions, NIOS, NEET, ItF-JEE), NO 77/29 MS Naidu street, Old Washermanpet, Chennai 21, Contact : 72000 37940, 044 4862 6933, winningstar.in, , One mark test-Maths, , Std : 12* Science Date : 28.11.2021, Duration : 50 minutes Max :50, , PART-1 (1 x 50=50), Note:, , 10,, , ll., , (i) Answer all the questions., (ii) Choose the most appropriate answer from the given four alternatives, and write the option code and the corresponding answer, If Ais a 3 « 3 non-singular matrix such that AAT=ATAand=A-I1AT,, , thenBB T=, , 1A 2)B 3)I 4) BT, A= [2 3 Joe such that 24-1 =A, then Ais, , 117 2) 14 3) 19 4) 21, , If ATA -t is symmetric, then A? =, , WA Q\(AT ) 2 3)AT 4) (At)?, If |z-3/ z | = 2, then the least value of |z| is, , 1)1 2)2 3)3 4)5, , If z is a non zero complex number, such that 2iz? = z then |z2| is, , 1/2 2)1 3)2 43, , The area of the triangle formed by the complex numbers z, iz, and 2tiz in the, Argand’s diagram i, , 1j1/2 Tat 2 2)|z| 2 33 /2 |z|? 4) 2|z|?, If z-1/ z+1 is purely imaginary, then |z| is, y1s2 2)1 3)2 4)3, If |z| = 1, then the value of 1+z /1+z is, , ljz az 31/2 4)1, If z is a complex number such that z € C\R and z+ 1/ z€ R, then |z| is, 10 2)1 3)2 43, A zero of x3 + 64 is, 1)0 24 3) 4 4)4, A polynomial equation in x of degree n always has, 1) n distinct root 2) n real roots, , 3) Exactly n roots 4)Atmost one root, , Scanned by TapScanner
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Page 2 of 5, , 12., , 13., , 14,, , 15., , 16., , 17., , 18,, , 19, , 21,, , 22,, , 23., , The polynomial x ++ 2x + 3 has, 1) one negative and two real roots, 2) one positive and two imaginary roots, 3) three real roots, 4) no solution, , If f and g are polynomials of degrees m and n respectively, and if h(x|=(f*g}(x}, then, the degree of his, 1) mn Amen 3) m= 4)n=, , The number of positive roots of the polynomial ¥ nCr n j=0 (-1) rx ris, , 0 2)n 3) <n 4jr, sin- (cos x| = (m/ 2) - x is valid for, lj-wsx<0 2)0sxs, 3)-w#2<sxen2 4)-a4sx<e3n, , sin- (2cos?x - 1) + cos-* (1 — 2sin?x) =, , 1jx/2 2n/3 3)a/4 4), The equation tan-1x - cot-1x = tan-1( 1 V3) has, 1) no solution 2) unique solution, 3) two solution 4) infinite number of solution, If sin-1x - cot-1(1/ 2) - #/ 2, then x is equal to, H1s2 21/5 3) 2// V5 4) V3/ 2, , If | adj(adj A)| = |A| ? , then the order of the square matrix A is, 1)3 24 3)2 45, , Which of the following is/are correct? (i) Adjoint of a symmetric matrix is also a, symmetric matrix. (ii) Adjoint of a diagonal matrix is also a diagonal matrix. {iii] If A, is a square matrix of order n and A is a scalar, then adj(AA} = A *adj(A). (iv) Aladj A) >, (adj AJA = |A|i, , 1) only (i) 2) {ii) and (iii), 3) (iii) and (iv) 4) (i), (ii) and (iv), , The circle x2 + y? = 4x + 8y + 5 intersects the line 3x - 4y = m at two distinct points, if, , 1) 15<m<65 2)35<m< 85, 3)-85 < m< -35 4)-25<m<15, , The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal, to half the distance between the foci is, , 14/3 2) 4/ 3 3) 2/V3 4)3/ 2, The radius of the circle 3x2 + by? + 4bx - 6by + b2 = Ois, , Scanned by TapScanner
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Page 3 of 5, , 24., , 25., , 27., , 28., , 31., , 32., , 33., , 35, , yl 23 3) V10 4)v11, If x + y = k is a normal to the parabola y ? = 12x, then the value of k is, Ys 2)-1 3)1 4)9, , The equation of the circle passing through the foci of the ellipse x2 16+ y29=1, having centre at (0,3) is, , 1) x? + y2- 6y -7=0 2) x2 + y2-6y+7=0, 3) x2 +92 -6y-5=0 4)x2 + y2-6y+5=0, , The circle passing through (1,-2) and touching the axis of x at (3,0) passing through, the point, , 1) (-5,2) 2) (2, -5) 3) (5, ~2) 4) (-2,5), , If the two tangents drawn from a point P to the parabola y 2 = 4x are at right angles, then the locus of P is, , 1) 2x+1=0 2)x=-1 32x-1=0 4jx=1, If a* and b” are parallel vectors, then [a” , ¢” , b” ] is equal to, 1)2 2) -1 31 4)0, , a’, b*, ¢ are three unit vectors such that a” is perpendicular to b* , and is parallel, to ¢ then a” * (Bb * ¢”) is equal to, , lja 2)6 3)c 40°, Ifa" = & f+ K, = & f, @ = Cand (a * b”) * ¢ =Aa” + wb”, then the value of A + wis, 1)0 2)1 3)6 4)3, , If the volume of the parallelepiped with a” * b , b * c , c * a” as coterminous edges is, 8 cubic units, then the volume of the parallelepiped with (a” * b}) *(b * c),(b * c) *(¢, * a” | and (c x a”) x (a” * b jas coterminous edges is,, , 1) 8 cubic units 2) 512 cubic units, , 3) 64 cubic units 4) 24 cubic units, , The angle between the line r° = (& 2f- 3K) + (20+ f- 2K) and the planer”. (# f)+4=, Ois, 1) 0° 2) 30° 3) 45° 4) 90°, , The system of linear equations x + y + z= 2, 2x +y -z=3, 3x + 2y +kz=hasa, unique solution if, (kso (2)-1<k<1 (3) -2<k<2 (4) k=O, , Every homogeneous system, (1) Is always consistent, , (2) Has only trivial solution, (3) Has infinitely many solution, (4) Need not be consistent, , , , If z=x+iy is a complex number such that |z+2|=|2-2|, then the locus of z is, (1) real axis (2) imaginary axis (3) ellipse (4) circle, , Scanned by TapScanner
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Page 4 of 5, , 36, , 37, , 38, , 39, , 40, , 41., , 42., , 43, , 45, , 46, , 47, , 48, , 49, , The points represented by 3 - 3i, 4 - 2i, 3 - i and 2 - 2i form in the argand, plane., , (1) collinear points (2) Vertices of a parallelogram, , (3) Vertices of a rectangle (4) Vertices of a square, , If f and g are polynomials of degrees m and n respectively, and if h(x) ~(f 0 g)(x),, then the degree of \h is, , (1) mn (2) men (3) m= {4)n™, Let a> 0, b> 0, ¢ > 0, hn both th root of th quatlon ax +bt+C= 0 are, (1) real and negative (2) real and positive, , (3) rational number (4) none, , If p(x) = ax + bx + c and Q(x} = -ax + dx + c where ac # 0 then p(x}. Q(x) = 0 has at, least _____ real roots., , (1) no (2) 1 (3) 2 (4) infinite, The principle argument of a complex number., , (1) O-a (2) 0--a (3)nf/2-a (4)0-aen, The rank of any 3 x 4 matrix is, , (1) May be 1 (2) May be 2 (3) May be 3 (4) Maybe 4, If A is symmetric then, , (IJA-A (2) adj A is symmetric, , (3} adj (A )> (adj A) (4) Ais orthogonal, , If Ais a non-singular matrix of odd order them, 1) Order of A is 2m + 1 (2) Order of A is 2m + 2, , (3) | adj Al is positive (4) IAL 40, , If A is a orthogonal matrix, then, , (1) AAT=ATA=I (2) Ais non-singular, (3) IAI- 0 (4) AAT, , A matrix which is obtained from an identity matrix by applying only one elementary, transformation is, , (1) Identity matrix (2) Elementary matrix, (3) Square matrix (4) Equivalent to identify matrix, , i=, , (afi (2)i ()-i (4) 1/ i?, , When z =xtiy, then iz is, , (1) x-iy (2) ifx+iy), , (3) -y+ix (4) Rotation ofz by 90° in the counter clockwise direction, (1+33) (1-33), , 1) (1p - (31)? (2)1+9 {3) 10 (4) -8, , If z=x+iy, then zz =, (1) betiy) (e-iy) (2) Jz]? (3) x + y2 (4) lz], , Scanned by TapScanner
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Page 5 of 5, , 50 = Application of De Moivre's theorem., (1) [sin 8 + i cos 6)> = sin n® + i cos nO, (2) [cos 6 + i sin6|* = cos n6 + i sin nO, (3) (cos 8 + i sin 8)> = cos n6 -i sin nO, (4) [cos 6 -i sin 6)" = cos nO +i sin nd, , ***Don’t stop until you’re proud***, , Scanned by TapScanner
