Complete Syllabus of Class XI & XII

Transcription

1 Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-0005 Ph.: Fa : MM : 0 Sample Paper : Campus Recruitment Test Time : ½ Hr. Mathematics (Engineering) Complete Syllabus of Class XI & XII Instructions: (i) Use ball point pen only to darken the appropriate circle. (ii) Mark should be dark and should completely fill the circle. (iii) Dark only one circle for each entry. (iv) Dark the circle in the space provided only. (v) Rough work must not be done on the Answer sheet and do not use white-fluid or any other rubbing material on Answer sheet. (vi) Each question carries marks. For every wrong response mark shall be deducted from the total score. Choose the correct answer :. Let f : R A defined by f() = [ ] + [6 ], [.] denotes the greatest integer function. Then f many one and even function () f onto if A = I (set of integers) f many one and odd function. If the sine of angles of a triangle ABC satfy the equation c c (a + b + c) + λ + μ = 0 (where a, b, c are the sides of a triangle ABC), then the triangle ABC Always right angled for any real value of λ, μ () Right angled only when λ = c(ab + bc + ca), μ = abc () f one-one and odd function. If for a function f(), f =, f = 5, then ([.] denotes the greatest integer function) Is equal to () Is equal to Is equal to 5 lim [ f( )], Right angled only when abc μ= 8 () Never right angled cab ( + bc+ ca) λ=, 5. If α and β are non-real, then the condition for + α + β = 0 to have a real root () Does not et. Let a, a,..., a 0 be 0 non-negative real number such that a + a a 0 = and S = a a + a a + a a a 9 a 0. Then S 6 () S > S < 8 () S > 7 () () ( α α) ( β β ) = ( αβ αβ) ( α α) ( αβ αβ ) = ( β β) ( β β) ( αβ αβ ) = ( α α) ( α α)( β β ) = ( αβ+αβ)

2 k+ k 6. If f( ) =, f ( ) = f( f( )), f ( ) = f( f ( )) + k =,,,..., and gd ( ) equal to e 0 () e () 9 g ( ) = f ( ), then 7. If ( + + ) n = a 0 + a + a a n n ; n, then the value of the determinant n n n+ n 6 n n+ n n 7 n+ 7 Is always positive () Is always negative Is zero () Can't be predicted 8. Let P n denotes the product of all the coefficients of ( + ) n and 0! P n + = n.p n, then n equal to 9. If 9 () 0 () k r = 0 k r = 0 r r a polynomial in ; p and q are any two values of k, then the roots of the equation + p + 5q = 0 cannot be Real () Imaginary Rational () Irrational 0. Let z be a non-zero comple number. If z i = z sin argz, then the locus of z A pair of straight lines () Circle Parabola () Ellipse. Let N be any five digit number say 5. N Then the maimum value of equal to 0000 () (). Let ˆ ˆ ˆ a = i + j + k, b = ˆ ˆ ˆ i + j + k, where,, {,,, 0,, }. Number of possible vector b such that a and b are mutually perpendicular, () 5 () 0. For the series,,,..., k, k, the A.M. and G.M. of the first and the last number ets in the given series. If k a three digit number, the number of possible values of k 5 () 6 (). The number of solutions of the equation n cos cos ( ) m + =, where m > 0, n 0, 0 () () 5. Let f() = sin + [] ([.] denotes the greatest integer function). Then the number of points in [0, 0] at which f() assumes its local maimum value 0 () 0 9 () 0 6. Five different digits from the set of numbers {,,,, 5, 6, 7} are written in random order. The probability that 5 digit number thus formed divible by 9, 8 () () 0 7. The reflection of the point (t +, t) in a line (t, t + ). Then the equation of the line can be = y + () = y = y + () = y 8. The area bounded between the tangents, drawn to the circle + y = at its points of intersection with the curve y = A B C sq. units. Then the value of (A + C B) equal to 9 () 6 7 () 8 ()

3 9. Suppose the number of elements in set A p, the number of elements in set B q, and the number of elements in set (A B). Then p + q equal to 70 () 0 0 () 0 0. For each of two data sets, each of size, the variance are given to be and and corresponding means are given to be and respectively. The variance of the combined data equal to () 5 (). If cosec cos + sec sin = 0 and (0, ), then the number of integral values of () 5 6 () 7. The minimum value of y = sec + cosec in (0, ] 5 () (). The product of roots of the equation ( ) ( ) log log + = 0 () 8 (). Let z = z +, where z a comple number then argument of z may be 6 5. Let f( ) = ( ) a real valued function and [ ] and { } represents greatest integer function and fractional function respectively then the number of integers in the domain of f([ ] + { } + 6) () () 5 () 0 () 6. Consider A, B, C, D are four collinear points on a horizontal plane. The angle of elevation of a tower situated at point D from A, B, C α β, α + β and α respectively. If AB = BC = CD =, then the height of the tower () () 7. The number of five digit numbers using,,, 5 only such that the sum of digits, 5 () 5 0 () 0 8. If C0, C, C, C,... C n are the binomial coefficients in the epansion of ( + ) n then the value of n C+ (. ) C + (. ) C + (. ) C ( n.( ) C n ).5 n n () n n. n () n. n 9. Two harmonic means H, H are inserted between two numbers whose arithmetic mean A and geometric mean G. If the arithematic mean of H, H h and geometric mean g then the value of hg g A () () 0. The point (α, α) lies inside the triangle formed by the lines = 0, y = 0, + y = then the number of integral values of α () () 0. The tangents from origin to the circle + y y + = 0 meet the circle at A and B. The radius of the circle passing through A, B and (, 0) 7 () () 5. Tangents PA, PB are drawn to parabola y y + 5 = 0 from P(0, ). The locus of centre of the ellipse whose major and minor aes are of constant length and which touches the tangents PA and PB, Circle () Parabola Straight line () Hyperbola

4 . The number of solution(s) of the equations + y + z =...(i) 7. The area bounded by -a in [0, ] f( ) = ma{, sin } and y + z =...(ii) + y z =...(iii) () 0 () () Infinite. Let f : R R and f( + ) + f( ) = f( + ) and g f f ( ) = ( ) ( + 6) , where R then g ( ) continuous only for some values of () g ( ) differentiable only for some values of g ( ) continuous but not differentiable () g ( ) continuous and differentiable for all R 5. The sum of and y coordinates of all the points on the curve y = + + where tangent equally inclined to the co-ordinate aes 6. Let () () e ((sin cos ) + (cos sin )) d = ef( ) + c then the range of f( ) 0, () [0, ] [0, ] () [0, ] + () + 8. The solution of differential equation dy + (sec )( y ) + tan = 0 ( ) ( ), d y = + c f where c the arbitrary constant then the value of f(0) 0 () () 9. Four students A, B, C, D apply for admsion in four centres of Aakash Institute named C, C, C, C. The probability that A, B, C, D never get the admsion in C, C, C, C respectively such that no two gets admsion at the same centre and all gets admsion, p then the value of (56 p) 9 () 8 7 () 5 0. Let a, b, c are vectors having magntidues, and respectively and ( a. b) a+ b = c then the angle between a and b () () 6 ()

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