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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. ()

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