DAV PUBLIC SCHOOL , GEVRA PROJECT Class : XII Question .

DAV PUBLIC SCHOOL , GEVRA PROJECTClass : XIIQuestion Bank 2019-20MATHEMATICS Q.1 If tan-1x tan-1y 4(i)then cot-1x cot-1y equals(ii) )(iii) )(iv)Q.2 The value of c in Rolle’s theorem for the function f(x) x3-3x in the interval [0,3] is(i) 1 (ii) -1 (iii) 3/2 (iv) 1/3Q.3 Which of the term is not used in a linear programming problem ?(i) Optional solution (ii) Feasible solution (iii) Concave region (iv) Objective functionQ.4 If A is a matrix of order 3 such that A(adjA) 10 I.Then the value of I adjA I is ---------Q.5 If f’(x) changes sign from positive to negative as x increases through c, then c is called point of .Q.6 If two lines do not meet andnot parallel, then they are known as .Q.7 Evaluate :Q.8 If A’ and B , then find the value ofQ.9 Write the equation of the liner (2 ) (A 2B)’.- 4 ).Q.10 If A and B are events such that P(A) 0.4, P(B) 0.3 and P(AUB) 0.5, then P(B’ A) (i) 2/3 (ii)Q.111/2 (iii) 3/10 (iv) 1/5 (i)(ii)(iii)(iv)Q.12 The equation of the normal to the curve y sin x at (0,0) is(i) x 0 (ii) y 0 (iii) x y 0Q.13(iv) x-y 0is equal to(i) 1/2 log( 2/3) (ii) 1/2log(3/2) (iii) 2/3 log (3/2) (iv) 1/3 log(2/3)Q.14 If f(x) cos-1(sin x), then f ‘(x) ---(i) 0 (ii) 1 (iii) -1 (iv) noneQ.15 If A and B are symmetric matrices, then AB-BA is .

Q.16 Solution obtained by giving particular values to the arbitrary constants in thesolutions of a differential equation is called .generalQ.17 Evaluate :Q.18 The differential equation of all non-vertical lines in a plane is(i)(ii)(iii) 0 (iv) 0Q.19 A function f(x) is said to be a .function on (a,b), if x1 x2 implies f(x1)x1,x2Q.20f(x2) for allIf A and B are two mutually exclusive events, then P(A and B) .Q.21 A corner point of a feasible region is a point in the region which is the of two boundarylines.Q.22 The normal at the point (1,1) on the curve 2y x2 3 is(i) x y 0 (ii) x-y 0 (iii) x y 1 0 (iv) x-y 1 0Q.23 If P(A) ½, P(B) 0,then Pis(i) 0 (ii) 1/2 (iii) not defined (iv) 1Q.24 The interval in which y x2e- x is increasing with respect to x is(i) (-) (ii) (-2,0) (iii) (2,(0,2)Q.25 Find the minimum value of the function h(x) sin(2x) 5 .Q.26 An integrating factor of thew differential equation (1 x2) (i)(ii)(iii) 1/2log(1 xy x is) (iv) 5xQ.27 The matrix obtained by interchanging the rows and columns of a given matrixcalled .Q.28 Findsuch that the line A, isis parallel to the plane 3x-y-2z 7.(OR)Find the vector equation of the straight line passing through (1,2,3) and perpendicular tothe planer.(-5 ) 9 0Q.29 Find an anglewhich increases twice as fast as its sine.Q.30 The probability of obtaining an even prime number on each die when a pair of dice is rolled is(i) 0 (ii) 1/18 (iii) 1/12 (iv) 1/36

Q.31 The total revenue in Rs. received from the sale of x units of a product is given by R(x) 3x2 36x 5. The marginal revenue when x 15 is (i) 116 (ii) 96 (iii) 90 (iii) 126Q.32 The range of cos- 1x is [0, ](True/False)Q.33 If A and B are matrices of order 3 and 5, 3,then findQ.34 If 2P(A) P(B) 5/13 and P(A/B) 2/5, Then P(AUB) (i) 11/26 (ii)13/25 (iii) 11/24 (iv) 11/21Q.35 If a matrix A is both symmetric and skew-symmetric matrix, then A is .(OR)IfA is a non-singular square matrix of order n, then .Q.36 Any three numbers which are proportional to the direction cosines of a line ,arecalled Q.37 If E1 and E2 are two independent events such that P(E1) 0.35 and P(E1UE2) 0.60, Then P(E2) is(i) 4/13 (ii) 3/13 (iii) 5/13 (iv) 8/13Q.38 Find the projection of the vector 7 -4on 2 6 3 .Q.39 If 4cos- 1x sin- 1x (i) 3/2 (ii) 1/(iii)/2 (iV) 2/Q.40 What are the direction cosines of a line which makes equal angles with the coordinate axes?Q.41 A problem in Mathematics is given to three students A,B and C and their respective probabilityofSolving the problem is 1/2 ,1/3 and ¼ .Probability that the problem is solved is(i)3/4 (ii) 1/2 (iii) 2/3 (iv) 1/3Q.42 The integrating factor of differential equation cos x y sinx 1 is(i) cosx (ii) sinx (iii) secx (iv) tanx.Q.43 A diagonal matrix in which all diagonal element are equal and non-zero is called matrix.(OR)The sum of products of elements of any row with the cofactors of corresponding elements isequal to .Q.44 The angle of intersection between two curves is the angle between the .to the curves atthe point of intersections.

Q.45 For what value of k, the matrixis not invertible ********************************DAV ACC JamulSUBJECT- MATHS CLASS (XII)1 MARKS QUESTIONS1. Is f: R R, given by f(x) x – 1 is one-one? Give reason?2. If f : {1, 3} {1, 2, 5} and g : {1, 2, 5} {1, 2, 3, 4} be given byf {(1, 2), (3, 5)}, g {(1, 3), (2, 3), (5, 1)}Write down gof3. If f: R A, given byf(x) x2 – 2x 2 is onto function, find set A.4. Evaluate: sin [2cos‒1(‒3/5)].5. What is the principal value of tan‒1 [tan 2π/3]?6. Write the value of tan‒1 (a/b) ‒ tan‒1[(a ‒ b)/(a b)].7. If sin-1 x sin-1 y 2π/3, then the value of cos-1 x cos-1 y is8. Suppose P and Q are two different matrices of order 3 n andthe matrix P Q is?n p, then the order of9. A and B are square matrices of order 3 each, A 2 and B 3. Find 3AB 10. Find the vector equation of a plane which is at a distance of 5 units from the origin andits normal vector is 211. If A is a square matrix of order 3 such that adj A 64, find A .12. If A is any square matrix of order 3 3 such that A 3, then the value of adj A is?13. If (2 i 6 j 27 k) x (i p j q k) 0, then the values of q and q are?14. If A and B are two events such that P (A) 0.2, P (B) 0.4 and P (A U B) 0.5, thenvalue of P (A/B) is?15. An urn contains 6 balls of which two are red and four are black. Two balls are drawn atrandom. Probability that they are of the different colours.16. For what value of x, f(x) 2x – 7 is not derivable.17. Write derivative of sin x w.r.t. cos x18. If f(x) x2g(x) and g(1) 6, g ́(1) 3 find value of f (́ 1).19. Write the number of points of discontinuity of f(x) [x] in [3, 7].

20. What is derivative of x – 3 at x – 1.21. The side of a square is increasing at the rate of 0.2 cm/sec. Findthe rate of increase of perimeter of the square.22. Without using derivatives, find the maximum and minimum value of y 3 sin x 1 .23. Write the interval for which the function f(x) cos x, 0 x 2π is decreasing24. Find the value of a for which the function f(x) x2 – 2ax 6, x 0 is strictlyincreasing25. If f (x) ax cos x is strictly increasing on R, find a.26. Find the point on the curve y 3x2 – 12x 9 at which the tangent isparallel to x-axis.27. If a manufacturer’s total cost function is C(x) 1000 40x x2, wherex is the output, find the marginal cost for producing 20 units28. Write the interval in which the function f(x) x9 3x7 64 is increasing29. Evaluate. e log x logsin x dx30. Find the area enclosed by circle x2 y2 a231. Write a unit vector in xy-plane, making an angle of 30 with the vedirection of x–axis.32.What is the perpendicular distance of plane 2x – y 3z 10 from origin?33.What is the angle between the lines 2x 3y – z and 6x – y – 4z?34.What is the distance between the planes 2x 2y – z 2 0 and4x 4y – 2z 5 0.35. What is the equation of the plane through the point (1, 4, – 2) and parallel to theplane –2x y – 3z 7?36. What is equation of the plane if the foot of perpendicular from origin tothis plane is (2, 3, 4)?37. If O is origin OP 3 with direction ratios proportional to –1, 2, – 2 thenwhat are the coordinates of P?

38. Are the planes x y – 2z 4 0 and 3x 3y – 6z 5 0 intersecting?39. Write equation of a line passing through (0, 1, 2) and equally inclined toco-ordinate axes.40. Find the angle between the planes 2x – 3y 6z 9 and xy – plane.41. What is the equation of the plane which cuts off equal intercepts of unitlength on the coordinate axes.42. Find P(A B) if A and B are two events such that P(A) 0.5, P(B) 0.6and P(A B) 0.843. A soldier fires three bullets on enemy. The probability that the enemy will bekilledby onebullet is 0.7. What is the probability that the enemy is still alive?DAV PS, ChhalMathematics (041)Q1. Let R be the relation in the set N given by R {(a,b):a b-2,b 6}. Choose the correct answer.(a) (2,4) R(b) (3,8) R(c) (6,8) R(d) (8,7) RQ2. Ifbe given by(a)then(b)is equal toQ3.is(c)(d)(a)(b)(c)(d)Q4. if A, B are symmetric matrices of same order, then AB - BA is a(a) Skew symmetric matrix(b) Symmetric Matrix(c) Zero matrix(d) Identity matrixQ5. If then x is equal to(a)6(b) 6(c) -6(d) 0Q6. Which of the following is correct.(a) Determinant is a square matrix.(b) Determinant is a number associated to amatrix.(c) Determinant is a number associated to a square matrix(d) None of theseQ7. Derivative ofw.r.t. x is,(a)(a)Q8. The slope of the normal to the curve(a)3(b)Q9.Q10.equals(a) tan x cot x c(c) tan x. cot x cequals(a)(a)is(c) -3(b) tan x –cot x c(d) tan x – cot 2x c(d)

(a)(b)(c)(d)Q11. The point on the curvefor which the abscisa and ordinate change at the same rate.(a) (2,4)(b) (1,2)(c) (2,1)(d) (5,2)Q12. The total revenue received from the sale of x units of a product is given by. The marginal revenue whenis(a) 205(b) 201(c) 102(d)208Q13. The slope of the tangent to the curvewhen x 0 is(a) 2(b) 3(c) 5(d) 1Q14. The value of c in Rolle’s therom whenis(a) 2(b) –(c) -2(d)Q15. The angle of intersection of parabola(a)(b)(c)and(d)at the origin isQ16. Find the equation of the tangent to the curveat.Q17. Find the interval in whichis decreasing.Q18. At what point the slope of the tangent to the curveis zero.Q19. Show that the function, is strictly increasing on R.Q20. If, then findwhen.Q.21 Area bounded by the curve y is(a) -9(b), the x-axis and the ordinates x -2 and x 1-15/4(c)15/4(d)Q.22 If17/4ofis(a) 1(b) 3(c)-3/2(d)none of these.Q.23 In a college, 30% students fail in physics, 25% fail in mathematics and 10% Fail inboth. One student is chosen at random. The probability that she fails in physics Ifshe has failed in mathematics is(a) 1/10(b) 2/5(c) 9/20(d) 1/3Q.24 The plane 2x-3y 6z-11 0 makes an angleof α is(a) 3/2(b) 2/3(c) 2/7Q.25 The reflection of the point (with x- axis.Then The value(d)3/7in the xy-plane is(a) (Q.26 If(a) 64(b) 46Q.27 If z is(c) 100(d) 62 3i-yj k are two equal vectors,then the value of x y(a) 0(b) 1(c) -2Q.28 Write the equation of line passing through the point (z-axis.(d) -1and parallel ToQ.29 If the fessible region for a LPP is , then the optimal value of theObjective function Z ax by may or may not exist.Q30. If P(E) 7/13, P(F) 9/13 and P(EUF) 8/13 then the value of P(F/E) is .

Q31.is equal to(a)(b)(c)Q32. Matrices A and B will be inverse of each other only if,(a) AB BA (b) AB BA 0(c) AB 0,BA IQ33.(d)(d) AB BA Iis equal to(a)Q34.is equal to(a)(c) 0Q35. If the matrix A is both symmetric and skewsymmetric then,(a) A is a diagonal matrix(b) A is zero matrix(c) A is a square matrix(d) None of theseQ36.(d) 2dx is equal to(a)Q37. If the curveandcut orthogonaly at (1,1) then the value of a is(a) 1(b)0(c) -6(d)6Q38. Which of the following function is decreasing on(a) sin 2x(b) tan x(c) cos x(d) cos 3xQ39. The equation of normal to the curveat (0,0) isQ40. If the, then the value of a is(a) 3(b) 1(c) 8(d) 2Monnet DAV PS Raigarh-1QUESTION BANKMATHEMATICSSection –A1. Zeroes of P(Z) Z2 -27 are(A) 3 3(B) - 3 3(C) None of these(D) 3 32. The ratio between the LCM and HCF of 5,15,20 is:(A)9:11(B) 4:3(C) 11:1(D) 12:13. If the P(x) ax2 bx2 c , then–b/a is equal to(A) 0(B) 1(C) product of zeros(D) sum of zeros4. The pair of equations ax by 7 and 3x 3y 16 represented parallel lines if(A) a bCLASS-X