Regd. Office : Aakash Tower, Plot No.-4, Sec-11, MLU, Dwarka, New Delhi Ph.: Fax :

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1 Regd. Office : akash Tower, Plot No.-, Sec-, MLU, Dwarka, New Delhi-007 Ph.: Fax : dmission-cum-scholarship Test (Sample Paper) First Step Course for JEE (Main & dvanced) 0-07 (Syllabus of the Test : Mathematics of Class IX & X) Roll No.: Test Booklet Code : Time : ½ Hrs. Max.Marks : 00 INSTRUCTIONS TO THE CNDIDTES. The initial 0 minutes are earmarked for the candidates to carefully read the instructions. (Note : The candidates are not allowed to either look inside the question booklet or start answering during these initial 0 minutes.). The question booklet and answer sheet are issued separately at the start of the examination.. This question booklet contains 0 questions.. Read each question carefully.. Determine the correct answer, one out of the four available choices given under each question. 6. It is mandatory to use Ball Point Pen to darken to appropriate circle in the answer sheet. 7. For each correct answer, four marks will be awarded. There is no negative marking. For Example Q. : In the Question Booklet is: Which one of the following is linear in Geometry? (nswer Sheet) () SO Q.. () CO () NO () KO Thus as the correct answer is choice, the candidate should darken completely (with a blue/black Ball point pen only) the circle corresponding to choice against Question No. on the nswer Sheet. If more than one circle is darkened for a given question such answer will be rejected. 8. Do not use white-fluid or any other rubbing material on answer sheet. No change in the answer once marked is allowed. Before handing over the answer sheet to the invigilator, candidate should check that Roll No. and Test-Booklet code have been filled and marked correctly. 9. Rough work should be done only on the space provided in the question booklet. 0. Immediately after the prescribed examination time is over, the nswer sheet and Question booklet are to be returned to the invigilator. If the candidate wants to leave the examination hall before time, he/she should hand over the question paper and answer sheet to the invigilator. However, no student can leave the examination hall before half time.

2 First Step Course for JEE (Main & dvanced) 0-07 Sample Paper MTHEMTICS Choose the correct answer :. x is always divisible by 8, if x is a/an () Integer () Natural number () Odd integer () Even integer. If the zeroes of the quadratic polynomial px + qx + r, r 0 are equal, then () r and p have opposite signs () r and q have opposite signs () r and p have the same sign () r and q have the same sign. The value of 0 is () 9980 () 9980 () 9980 () The value of p for which the lines x = y 8 and 6x + my + 6 = 0 coincide is () () () (). The condition for m for which the expression mx + x cannot be factorized into two linear factors is () () m () m () m m 6. The length of the longest pole that can be put in a room of dimensions 0 m m m is () m () 9 m () 7 m () 8 m 7. In a given P, if the a th term is b and the b th term is a, then its n th term is () a + b n () a + b + n () a b + n () a b n 8. If the edges of a triangular board are cm, 6 cm and 9 cm, then the cost of painting its one of the faces at the rate of paise per cm is () ` () `. () ` 0 () `.6 9. In ΔPQR, if PS is the median, then PQ + PR is equal to ( PS QS ) () PS + QS () () (PS + QS ) () PS + QS 0. In the given figure, if QOP is a diameter of the circle and PMR RNQ, then the measure of ROQ is R M P O N () 08 () 7 Q () 6 (). If two dice are thrown simultaneously, then the probability of getting a doublet or a total of 6 is () () 7 8 () () 8 6. If cos 8α = sin α and 8α < 90, then the value of tan 6α is () 0 () () () Not defined - -

3 Sample Paper First Step Course for JEE (Main & dvanced) The perpendicular distance of the point (, ) from the y-axis is () units () units () units () units. The figure obtained by joining the mid-points of the adjacent sides of a rhombus, taken in order, is always a () Rhombus () Rectangle () Square () Kite. In the given figure, if PQ and RS are two equal chords of a circle with centre O, then the measure of PB is P R Q 60 O () 70 () 0 () 80 () Which of the following is not a linear equation in two variables? () x + 7y = 0 () x = () y = () 0.x +.y 7. The value of (n ) is n () 69 () 96 () () 8. If α, β, γ are the zeroes of the polynomial x + x 7x, then the value of αβγ is () () 7 () () B 7 9. Which term of the P, 8,,..., is the first negative term? () 0 th () nd () nd () 6 th S 0. To construct a triangle similar to a given ΔBC with its sides of the corresponding sides of ΔBC, draw a ray BX such that CBX is an acute angle and X is on the opposite side of with respect to BC. The minimum number of points to be located at equal distances on ray BX is () () () 7 () 6. Which constant must be added and subtracted to solve the quadratic equation y y 0 by the method of completing the square? () () 9 6. bag contains 6 black balls and some green balls. If the probability of drawing a green ball from the bag is times that of a black ball, then the number of green balls in the bag is () 8 () 0 () 6 (). The average of all the prime and composite numbers upto 99 is () () 9. () 0. (). If a largest possible cone is cut out from a cube of volume 78 dm, then the surface area of the cone (in m ) is ().6 π (). π ().07 π () 0.9 π. The value of () () 9 sin6sin cos6cos is () () () () - -

4 First Step Course for JEE (Main & dvanced) 0-07 Sample Paper 6. If pq + qr + rp = and p + q + r =, then the value of p + q + r is () 6 () 0 () () 7. If from a point X in the interior of ΔDEF, perpendiculars X, XB and XC are drawn to the sides EF, FD and DE respectively, then which of the following is always true? () DC + E + FB = DB + F + EC () DE + EF = DF () DC + E + FB = (DB + F + EC ) () DC E FB = DB F EC 8. The points (, ), (, ) and (, 7) form a/an () Right angled triangle () Equilateral triangle () Isosceles triangle () Straight line 9. In the given circle with centre O and radius r, if OB = 0, then the sum of the areas of quadrilaterals OBX and OCYD is X M O N D Y. If the diagonals KT and EI of a parallelogram KITE intersect at O and P, Q, R and S are the midpoints of KO, EO, TO and IO respectively, then the ratio of (PQ + QR + RS + SP) to (KE + ET + TI + IK)is () : () : () : () :. If the ratio of the angle bisectors of two similar triangles is :, then the ratio of their corresponding areas is () : () : 8 () : () :. Which of the following is equal to (cosec θ sin θ) (sec θ cos θ)? () sec θ + tan θ () tancot () tan θ + cot θ () sec θ tan θ. If a m high vertical pole casts a shadow m long on the level ground, then the sun's elevation at that instant is () 60 () 0 () () 90. In the given figure, if the perimeter of ΔBC is 08 cm, then the value of Q + BC is B C () r () r Q R () r () r 0. If the zeroes of the polynomial px + qx + r are of the form (p + q + r) is and, then the value of () q pr () q pr () q pr () q pr B P C () 7 cm () cm () 6 cm () cm 6. The value of k for which the quadratic equation (k )x + (k )x + = 0 has equal roots is () () 7 () () - -

5 Sample Paper First Step Course for JEE (Main & dvanced) If a hexagon PQRSTE circumscribes a circle, then PQ + RS + TE is equal to () QR + ST + EP () QR ST EP () QR ST + EP () QR + ST EP 8. Which amongst the following lies on the vertex of a triangle? () Orthocentre of an obtuse triangle () Circumcentre of a right triangle () Circumcentre of an obtuse triangle () Orthocentre of a right angled triangle 9. How many cubes of side cm can be cut from a cube of side 00 m? () 0 7 () () 8 0 () n arithmetic progression has terms. Its 8 th term is 8. If S is the sum of its terms, then which of the following is true? () S > 00 () S = 00 () S < 00 () S 00. Three fair dice are rolled simultaneously. The probability that the first die shows a composite number, second die shows an odd number and third die shows an odd prime number is () () 6 () () 7 8. If LCM (p, q, r) = 0, HCF (p, q, r) =, HCF (p, q) =, HCF (q, r) = and HCF (p, r) =, then the product of p, q and r is () 60 () 600 () 0 () 600. In a right angled ΔBC, B is the right angle and C = cm. If B BC = cm, then cos is equivalent to () sin () sin C () cos C () cos C. If tan () () 7 cos, then the value of sin is. If the length of sides of a triangle are 8 cm, cm and 6 cm, then the length of altitude corresponding to the longest side is () () 7 () () cm () cm () 9 7 cm cm 6. When f(x) = x 8x x + 68x is divided by g(x) = (x ), then the remainder is () () () () 7 7. In the given figure, the value of y is x () 0 () () 0 () y x - -

6 First Step Course for JEE (Main & dvanced) 0-07 Sample Paper 8. In the given figure, D is a point on BC such that BD : DC = :. If O is the midpoint of D, then the ratio of areas of ΔOB and ΔBC will be 9. The volume of a hollow cylinder is 88 cm. If the height of the cylinder is 8 cm and the outer radius is cm, then the inner radius is () 8 cm () 0 cm () 7 cm () 9 cm O B D C () : 8 () : () : () : 6 0. The area enclosed by the points (, ), (, ), (, ) and (, ) is () 6 sq. units () sq. units () 0 sq. units () sq. units - -

7 Test Booklet Code : Regd. Office : akash Tower, Plot No.-, Sec-, MLU, Dwarka, New Delhi-007 Ph.: Fax : dmission-cum-scholarship Test (Sample Paper) First Step Course for JEE (Main & dvanced) 0-07 nswers. (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). (). () 6. () 6. () 6. () 6. () 6. () 7. () 7. () 7. () 7. () 7. () 8. () 8. () 8. () 8. () 8. () 9. () 9. () 9. () 9. () 9. () 0. () 0. () 0. () 0. () 0. ()