MATHEMATICS. metres (D) metres (C)

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1 MATHEMATICS. If is the root of the equation + k = 0, then what is the value of k? 9. Two striaght lines y = 0 and 6y 6 = 0 never intersect intersect at a single point intersect at infinite number of points intersect at more than one point (but finite number of points). If (a, 0), (0, b), (, ) are collinear what is (a + b ab) 0. If A = 0 and B = 0 the following is/are correct? () AB is defined () BA is defined () AB = BA then, which of Select the correct answer using the code given below: Code: only only and only, and only. Using the digits,,, and only once, how many numbers greater than 000 can be formed? 0 6. If an angle is divided into two parts A and B such that A B = and tan A : tan B = :, then what is sin sin (sin ) ( sin ) sin. A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is 60º. The angle of elevation is 0º from a point at a distance y metres from the bank. What is the height of the tree? y metres y metres y y metres metres. If P, Q, R are three non-collinear point, then what is PQ PR Null set {P} {P, Q, R} {Q, R} 9. A, B, C, D and E are coplanar points and three of them lie in a stright line. What is the maimum number of triangles that can be drawn with these points as their vertices? The vector a lies in the plane of vectors b and c. Which one of the following is correct? a.( b c ) 0 a.( b c ) a.( b c ) a.( b c ). Wha t is t he projecti on of t he vector iˆ ˆj kˆ on the vector iˆ ˆj kˆ? 9 9. Which one of the following statement is correct? sin 0º, sin º, sin 60º are in GP cos 0º, cos º, cos 60º are in GP cot 0º, cot º, cot 60º are in AP tan 0º, tan º, tan 60º are in GP. If sum of squares of the roots of the equation + k b = 0 is b, what is k b b 0

2 MATHEMATICS. + k = 0 k 9. y = 0 6y 6 = 0. (a, 0), (0, b), (, ) (a + b ab) 0. A = 0 () AB () BA () AB = BA : B = 0,.,,, A B :, sin sin (sin ) A B = tan A : tan B = ( sin ) sin. y y 60º y 0º y y. P, Q, R PQ PR {P} {P, Q, R} {Q, R} 9. A, B, C, D E a b c a.( b c ) 0 a.( b c ) a.( b c ) a.( b c ). iˆ ˆj kˆ. 9 9 iˆ ˆj kˆ sin 0º, sin º, sin 60º GP cos 0º, cos º, cos 60º GP cot 0º, cot º, cot 60º AP tan 0º, tan º, tan 60º GP. + k b = 0 b, k b b 0

3 . If one root of the equation a + b + c = 0,. If A, B, C are non-empty sets such that a 0 is reciprocal of the other root, then A C =, then what is (A B) (C B) which one of the following is correct? a = c b = c A C A B a = c b = 0. If is the imaginary cube root of unity, B C then what is ( ). If A = {n + n is a natural number} and B = {n n is a natural number}, then what is 6. What is the modulus of 9 i i? (A B) {n + 6n n is a natural number} {n n is a natural number} {60n + 0 n is a natural number} {n 6 n is a natural number}. If the matri. Let M be the set of men and R is a relation "is son of" defined on M. Then R is an equivalence relation a symmetric relation only a transitive relation only None of the above. What is the locus of the point which is at a distance units to the left of y-ais? = y = = y = 9. The number 00 in binary system is represented in decimal system by which one of the following numbers? 0. There are letters and directed envelopes. These letters are randomly inserted into the envelopes. What is the probability that the let te rs a re i nserted into t he corresponding envelopes? None of the above. The average daily income of workers of a factory including that of the owner is ` 0. However, if the income of the owner is ecluded, the average daily income of the remaining 9 workers is ` 6. What is the daily income of the owner? ` 00 ` 6 ` ` 6 A = is such that A = I, then which one of the following is correct? = 0, = or =, = 0 = 0, or 0, = =, 0 or, = 0 0, 0. What is the sum of the focal distances of a point of an ellipse a a b y a? b b 6. What is t he degr ee of t he following differential equation? d y d d y 0 d d. What is the sum of...

4 . a + b + c = 0, a 0. A, B, C A C =, a = c b = c a = c b = 0. ( ) (A B) (C B) A C A B B C. A = {n + n } B = {n n }, (A B) 6. i i 9. M R M. y- R. {n + 6n n } {n n } {60n + 0 n } {n 6 n } A = A = I, = 0, = =, = 0 = 0, 0, = =, 0, = 0 0, 0 = y = = y = y. b a a a b b 6. d y d y 0 d d d. ` 6 ` 0 ` 00 ` 6 ` `

5 6. In a GP of positive terms, any term is equal to one-third of the sum of net two terms. What is the common ratio of the GP?. What does the differential equation y a d (where a is a constant) represent? A set of circles having centre on the y-ais A set of circles having centre on the -ais A set of ellipses A pair of straight lines If A = and B = such that A = B, then what is the value of? 0. What is the value of n, if P(, n ) : P(6, n ) = :? 0. What is the value of the determinant 0? + +. Consider the following statement s in respect of the function f() =, [, ]. f() is increasing in [, ]. f() is has no root in (, ) Which of the statements given above is/are correct? only only Both and Neither nor. The largest value of + for < < occurs when = = = = 0 d. What is 0 sin. If and are the roots of the equation 0 then what is the third root? 9. If ( + tan )( + tan ) =, then what is ( + ) 0º º 60º 90º. If f() is an even function, then what is 0 f (cos ) d 0 0 f (cos ) d f (cos ) d 0 9. What is the value of k for which the system of equations k + y = and + y = has no solution? In how many ways can 6 girls be seated in empty chairs? 0 0. What is the value of 9 log 0 log0 + log0? 0. Which term of the series,,,... 9 th 0 th th th. What is the number of ordered pairs of nonzero positive integers (, y) such that + y <? 6. In the binary syst em of numbers l et a = 00 and 00, then in decimal system what is a b

6 6. GP. y a d GP a ) y A = B = A = B, 0. ( + tan )( + tan ) =, ( + ) 0º º 60º 90º 0. P(, n ) : P(6, n ) = :, n. f() f (cos ) d f() =, [, ]. f(), [, ]. f() (, ). < < + = = = = 0 d. 0 sin k f (cos ) d f (cos ) d 0 k + y = + y = log 0 log0 + log0 0.,,, (, y). + y <? 6 a = 00 b = 00, b a 6

7 . What is the sine of angle between the. If then a, b, c are in b a b c a c vectors iˆ ˆj kˆ and iˆ ˆj kˆ? AP GP HP None of these 6. What is the middle term in the epansion of None of these?. If sinsin cos then what is 0 None of these. What is the sum of the roots of the equation ( ) ( ) ( ) 0?. What is the total number of combinations of n different things taken,,,..., n at a time? n + n + n n 9. One of the roots of the quadratic equation a + b + c = 0, a 0 is positive and the other root is negative. The condition for this to happen is a > 0, b > 0, c > 0 a > 0, b < 0, c > 0 a < 0, b > 0, c < 0 a < 0, c > 0 0. If the solution of the diferential equation d a y f represents a circle, then what is the value of a?. If A, B, C are in AP and b : c = :, then what is the value of sin C?. The poi nts with posit ion vec tors 0iˆ ˆ, j ˆ i ˆ, j aiˆ ˆj are collinear, if the value of a is. What is log( a a ) log a 0 a 6. books are to be chosen from a lot of 0 books. If m is the number of ways of choice when one specified book is always included and n is the number of ways of choice when a specified book is always ecluded, then which one of the following is correct? m > n m = n m = n m = n. Which one of the following is correct in respect of the function f() = +? f() is not continuous at = 0 f() is differentiable at = 0 f() is continuous but not differentiable at = 0 None of the above. What is the condition that one root of the equation a + b + c = 0, a 0 should be double the other? a = 9bc b = 9ac c = 9ab None of the above 9. Consider the following with regard to a relation R on a set of real numbers defined by Ry if and only if + y = :. 0 R. R. R Which of the above are correct? and only and only and only, and

8 .. a, b, c b a b c a c sine 6. AP HP GP. ( ) ( ) (. n,,,..., n ) 0. sinsin cos 0. log( a a ) log a a n + n + n n 9. a + b + c = 0, a 0 m n 0. a > 0, b > 0, c > a > 0, b < 0, c > 0 a < 0, b < 0, c < 0 a < 0, c > 0 d a y f a. A, B, C AP b : c = :, sin C. 0iˆ ˆ, j ˆ i ˆ, j aiˆ ˆj a m > n m = n m = n m = n. f() = + = 0 = 0 = 0 f() f() f(). a + b + c = 0, a 0 9. a = 9bc c = 9ab b = 9ac R, Ry + y =. 0 R. R. R,

9 60. The function 66. What is the angle between the lines whose dire ction cosines a re proport ional to f() = k sin + sin,, and,, respectively? has maimum value at =. What is the value of k? 6. What is sin (cos )d k k k k where k is a constant of integration. 6. If and are the roots of the equation + + = 0, then what is the value of ( )? What is the equation of the line passing through (, ) and parallel to y-ais? y = y = = = 6. What is the set of points (, y) satisfying the equations + y = and + y =? {(, 0), (, 0), (0, )} {(0, ), (0, )} {(0, ), (, 0)} {(, 0), (, 0), (0, ), (0, )} 6. Consider the following statements:. The inverse of a square matri if it eists, is unique.. If A and B are singular matrices of order n, then AB is also a singular matri of order n. Which of the statemens given above is/are correct? only only Both and Neither nor 90º 60º º 0º 6. What is the value of k for which the following function f() is continuous for all? f ( ) ( ) k for for 6. If p, q, r are rational numbers, then the roots of the equation p + p q + qr r = 0 are comple pure imaginary irrational rational 69. If A = {,,, 6} and B = {,, }, then what is (A B) (B A) equal to? {(, ), (, ), (6, ), (, )} {(, ), (, ), (, ), (, )} {(, ), (, )} {(, ), (, ), (, ), (, 6)} 0. What is the differential equation of all parabolas whose aes are parallel to y-ais? d y 0 d d d c d y c d where c is a constant. For the net five () items that follows: The students of a class are offered three languages (Hindi, English and French). students learn all the three languages whereas students do not learn any language. The number of students learning Hindi and English but not French is twice the number of students learning Hindi and French but not English. The number of students learning English and French but not Hindi is thrice the number of students learning Hindi and French but not English. st udents learn only Hindi a nd students learn only English. The total number of.students learning French is 6 and the total number of students learning only French is.. How many students learn precisely two languages? 0 0 9

66.,,,, 60. f() = k sin + sin = k 90º 60º º 0º 6. k f(),? 6. sin (cos )d k k k k k 6. + + = 0 ( 9 ) 9 6. p, q, r p + p q + qr r = 0 69.

10 66.,,,, 60. f() = k sin + sin = k 90º 60º º 0º 6. k f(),? 6. sin (cos )d k k k k k = 0 ( 9 ) 9 6. p, q, r p + p q + qr r = A = {,,, 6} B = {,, }, (A B) (B A) {(, ), (, ), (6, ), (, )} {(, ), (, ), (, ), (, )} {(, ), (, )} {(, ), (, ), (, ), (, 6)} 0. y- d y 0 d d c (, ) y- d c d d y c y = y = = = 6. + y = + y = 6. (, y) {(, 0), (, 0), (0, )} {(0, ), (0, )} {(0, ), (, 0)} {(, 0), (, 0), (0, ), (0, )}.. A B, n AB n ()

11 . How many students learn at least two. What is the cumulative frequency curve of languages? statistical data commonly called? 0 Cartogram Histogram Ogive Pictrogram. If A and B are two mutually eclusive events,. What is the total strength of the class? then what is P(AB) 00 0 P + P P P P P(B A). How many students learn English and. If = sin + cos and y = sin.cos, then French? what is the value of 0 y + y + y +? 0. How many students learn at least one None of these language?. Wha t is lim( a a a 96 None of the above 6. If n In tan d then what is I n + I n 0 n n ( n ) ( n ) ( n ). What is the equation of the line joining the origin with the point of intersection of the lines + y = and + y =? + y = y = y = = y. If the sum of the squares of the distances of the point (, y) from the points (a, 0) and ( a, 0) is b, then which one of the following is correct? + a = b + y + a = b y a = b + y + a = b y 9. If f() =, what is f''() (In) ( ) + (In) (log 0 ) 0. In an eamination, there are multiplechoice questions and each question has choice. If a student randomly selects an answer for all the three questions, what is the probability that the student will not answer all the three questions correctly? What is the geometric mean of the data,,, 6,? 6 0 sin 6. What is d cos c equal to? cos c cos c cos c where c is a constant of integration. Which one of the following is the unit vector perpendicular to the vector iˆ jˆ and iˆ ˆj? iˆ ˆj iˆ ˆj kˆ iˆ ˆj kˆ. Consider t he following stat ements in respect of the vectors u u (,,) (,,) and u u. u is parallel tou. u is parallel tou (,,) (,6,). u is parallel tou Which of the statements given above/is are correct? only only and 9. The line m + ny = passes through the points (, ) and (, ). What is the value of m?

12 .. A B P(AB) 0 0 P + P. P P P P(B A) = sin + cos y = sin.cos n I n tan d I n + I n 0 y + y + y + 0. lim( a a a n n ( n ) ( n ) ( n ). + y = + y = + y = y = y = = y. (a, 0) ( a, 0) (, y) b sin 6. d cos cos c c c cos cos c c. iˆ ˆj iˆ ˆj + a = b + y + a = b y a = b + y + a = b y 9. f() =, f''() (In) ( ) + (In) (log ) 0.. iˆ ˆj iˆ ˆj kˆ iˆ ˆj kˆ ,,, 6, m + ny = (, ) (, ) m

13 90. What is the equation set for the equation 99. Consider the following statements with 6 + = 0? regard to correlation coefficient r between {,,, } {, } random variables and y: {, } {, 0,, } For the net four () items that follow:. r = + or means there is a linear ABC is a triangle right angled at B. The relation between and y. hypotenuse ( AC) is four t imes t he. < r < and r is a measure of the perpendicular (BD) drawn to it from the linear relationship between the opposite verte and AD < DC. variables. 9. What is one of the acute angles of the Which of the statements given above is/are triangle? º 0º correct? º None of these only only 9. What is angle ABD? Both and Neither nor º 0º º None of these 9. What is AD : DC ( ) : ( ) : : None of the above 9. What is tan(a C) 0 None of the above 9. What is the radius of the sphere + y + z y z = 0? 96. An eperiment consists of filpping a coin and then fipping it a second time if head occurs. If a tail occurs on the first flip, then a sifaced die is tossed once. Assuming that the outcomes are equally likely, what is the probability of getting one head and one tail? If, in general, the value of sin A is known, but the value of A is not known, then how many values of tan 9. Consider the following:-. cosec =. sec = 6 Which of the above is/are correct? only only Both and Neither nor 00. If the values of a set are measured in cm, what will be the unit of variance? cm cm cm No unit 0. A bo contains 6 disnict dolls. From this bo, three dolls are randomly selected one by one with replacement. What is the probability of selecting distinct doll? 0 0. For the equation 9 a + by + hy + g + fy + c = 0 where a 0, to represent a circle, the condition will be a = b and c = 0 f = g and h = 0 a = b and h = 0 f = g and c = 0 0. If A and B are events such that P(A B) = 0., P ( B ) 0. and P(A B) = 0., then what is P( A B ) Consider the following relations among the angles,, made by a vector with the coordinate aes:. cos cos cos. sin sin sin Which of the above is/are correct? only only Both and Neither nor

14 = y r {,,, } {, } 9. () ABC B (AC) (BD) AD < DC.. r = + y. < r < r º 9. ABD º 9. AD : DC ( ) : ( ) : : 9. tan(a C) 9. + y + z y z = a + by + hy + g + fy + c = 0 a 0, sin A A 9. A tan. cosec =. sec = 6 a = b c = 0 f = g h = 0 a = b h = 0 f = g c = 0 0. A B P(A B) = 0., P ( B ) 0. P(A B) = 0., P( A B) ,,. cos cos cos. sin sin sin

15 0. Which one of the following points lies on the. Class Interval plane + y 6z =? Frequency (,, ) (,, ) Consider the following statements in (,, ) (,, ) respect of the above frequency distribution: 06. What is the acute angle between the planes. The median is contained in the modal + y + z = and + y z =? class.. The distribution is bell-shaped. Which of the above statements is/are correct? 6 0. What is the area bounded by the curves y = e, y = e and the straight line =? e square units e e square units e e square units e e square units e 0. What are the points of intersection of the curve 9y = with its conjugate ais?, 0 and, 0 (0, ) and (0, ) (0, ) and (0, ) No such points eist 09. What is the locus of a point which moves quidistant from the coordinate aes? + y = 0 + y = 0 + y = 0 None of the above 0. What is e d e + c ( ) c e e ( ) c e + c where c is a constant of integration.. Let p, q, r, s be respectively the magnitudes of the vectors iˆ ˆ, j ˆ i ˆj kˆ, iˆ ˆj kˆ, iˆ ˆj kˆ. Which of t he following is correct? r > s > q > p r > s > p > q s > r > p > q s > r > q > p. In a triangle ABC, if c =, A = 0º, a = 6, then what is C 0º º 60º º only only Both and Neither nor For the net two () items that follow: The following table gives the continuous frequency distribution of a continuous varible X:. What is the median of the above frequency distribution? 6. What is the mean of the above frequency distribution? 6 6. If the ma tri A = 0 is signular, then what is the solution set S? S = {0,, } S = {,, } S = {,, } S = {, }. What is the range of f ( ) cos sin? [, ] [, ],,. What is the solution of the differential equation d y 0? sin y + sin = c sin y sin = c sin y + sin = c sin y sin = c where c is a constant. 9. If z = + cos + i sin, then what is z cos sin cos sin If iˆ yj ˆ zkˆ is a unit vector and : y : z = : :, then what is the value of z? 6

16 0. + y. ABC, c =, A = 0º, a = 6, C 6z = (,, ) (,, ) 0º º (,, ) (,, ) 60º º y + z = + y z = 6 0. y = e, y = e =.. e e X e e. e e e e 0. 9y = 09., 0 (0, ) (0, ) (0, ) (0, ), 0 + y = 0 + y = 0 + y = 0 0. e d e + c e ( ) c A = 0 S S = {0,, } S = {,, } S = {,, } S = {, }. f ( ) cos sin [, ] [, ]., d y 0 sin y + sin = c sin y sin = c sin y + sin = c sin = c c 9. z = + cos + i sin, z cos sin e ( ) c e + c c. iˆ ˆ, j ˆ i ˆj kˆ, iˆ ˆj kˆ, iˆ ˆj kˆ p, q, r, s cos 0 0. iˆ yjˆ zkˆ = : :, z 6 sin 0 : y : z r > s > q > p r > s > p > q s > r > p > q s > r > q > p 6

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DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO T.B.C. : P-AQNA-L-ZNGU Serial No.- TEST BOOKLET MATHEMATICS Test Booklet Series Time Allowed : Two Hours and Thirty Minutes Maximum Marks : 00