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  • Question 1
    If the H.C.F. of (x, y) = 1, then the H.C.F. of (x – y; x + y) =

    (A) 1 or 2

    (B) x or y

    (C) x + y or x – y

    (D) 4 VIEW SOLUTION
  • Question 2
    In Euclid’s division Lemma for positive integers a and b, the unique integers q and r are obtained such that a = bq + r is

    (A) 0 < r < b

    (B) 0 ≤ r ≤ b

    (C) 0 < r ≤ b

    (D) 0 ≤ r < b VIEW SOLUTION
  • Question 3
    The cubic polynomial p(a) = a3 – a has _____ zeros.

    (A) 0

    (B) 1

    (C) 2

    (D) 3 VIEW SOLUTION
  • Question 4
    If one root of equation x2 + ax – 8 = 0 is 4, then a =

    (A) 2

    (B) 4

    (C) −2

    (D) −4 VIEW SOLUTION
  • Question 5
    The product of the zeroes of the cubic polynomial p(x) is _____

    (A) Coefficient of -x2Coefficient of x3 

    (B) Coefficient of xCoefficient of x3

    (C) -The constant TermCoefficient of x2

    (D) None of these. VIEW SOLUTION
  • Question 6
    The diagram below shows two sticks – one BLACK and the other WHITE. Based on the measurements shown, what is the length of the white stick?

    (A) 5 cm

    (B) 8.5 cm

    (C) 13.5 cm

    (D) 17 cm VIEW SOLUTION
  • Question 7
    x = ___________ is identified as a GOLDEN NUMBER

    (A) 1+52

    (B) 0

    (C) 1+22

    (D) 1 VIEW SOLUTION
  • Question 8
    The Discriminant value of equation 5x2 – 6x + 1= 0 is………

    (A) 16

    (B) 56

    (C) 4

    (D) 56 VIEW SOLUTION
  • Question 9
    If ___________, then the quadratic equation does not have real solution.

    (A) D = 0

    (B) D > 0

    (C) D < 0

    (D) D ≥ 0 VIEW SOLUTION
  • Question 10
    Given below is a graph showing two lines.

    Which of the following statements is true about the solution(s) of the pair of equations represented by these lines?

    (A) They have a unique solution.

    (B) They do not have any solution.

    (C) They have infinite solutions.

    (D) We cannot predict the number of solutions without knowing the algebraic form of these equations. VIEW SOLUTION
  • Question 11
    2 years ago, the addition of ages of father – mother and their two daughters was 40 years. After 3 years the addition of their ages will be………

    (A) 40

    (B) 46

    (C) 50

    (D) 60 VIEW SOLUTION
  • Question 12
    In a two digit number, the digit at the ten’s place is 4 and the product of the two two digits is 4 times greater than the value of the digit in the ten’s place. What is the two digit number?

    (A) 42

    (B) 48

    (C) 44

    (D) 84 VIEW SOLUTION
  • Question 13
    As per the given figure, the graph of y = p(x) has _________ real zeros.



    (A) 0

    (B) 1

    (C) 2

    (D) 3 VIEW SOLUTION
  • Question 14
    If 2k + 1, 13, and 5k – 3 are three consecutive terms in an A.P., then k =
    (A) 17
    (B) 13
    (C) 4
    (D) 9 VIEW SOLUTION
  • Question 15
    The sequence 1, 1, 2, 3, 5, 8, 13, 21, 34,………., is said to be in _______________.

    (A) Arithmetic Progression.

    (B) Finite Sequence.

    (C) Fibonacci Sequence.

    (D) None of the above. VIEW SOLUTION
  • Question 16
    Sn = 2n2 + 3n; then d =_______________.

    (A) 13

    (B) 4

    (C) 9

    (D) −2 VIEW SOLUTION
  • Question 17
    In ΔABC, the bisector of ∠A intersects BC at a point D. Then

    (A) BD × AC = BC × AB

    (B) BD × AB = DC × AC

    (C) AC × AB = DC × BC

    (D) BD × AC = DC × AB VIEW SOLUTION
  • Question 18
    In ΔABC, the measures of BC, CA and AB are in the ratio 3 : 4 : 5. Correspondence ABC ↔ PQR is congruence. If PR = 12, then the perimeter of ΔPQR is ____________

    (A) 12

    (B) 24

    (C) 27

    (D) 36 VIEW SOLUTION
  • Question 19
    Out of following triplets _________ is not a Pythagorean triplet.

    (A) 7, 24, 25

    (B) 20, 21, 29

    (C) 11, 60, 61

    (D) 13, 35, 37 VIEW SOLUTION
  • Question 20
    In ΔABC, AD is a median, hence according to the Apollonius theorem, _____________ is true.

    (A) AB2 + AC2 = 2 (AD2 + BC2)

    (B) AB2 + AC2 = 2 (BD2 + DC2)

    (C) AB2 + AC2 = 2 (AD2 + DC2)

    (D) AB2 + AC2 = 2 (BD2 + BC2) VIEW SOLUTION
  • Question 21
    In Mathematics Exam, the probability of Aayushi scoring 100 out of 100 is

    (A) 1

    (B) 0

    (C) 1100

    (D) 1101 VIEW SOLUTION
  • Question 22
    The probability in an event k is

    (A) 0 ≥ P (k) ≥ 1

    (B) 0 ≤ P (k) ≤ 1

    (C) 0 > P (k) > 1

    (D) 0 < P (k) < 1 VIEW SOLUTION
  • Question 23
    If a dice is tossed once, then the probability of getting a prime number is

    (A) 13

    (B) 16

    (C) 12

    (D) 1 VIEW SOLUTION
  • Question 24
    x-Z=3, x+Z=45, then M =

    (A) 22

    (B) 23

    (C) 24

    (D) 26 VIEW SOLUTION
  • Question 25
    Rachna had an average score of 45 from 6 tests. Her teacher dropped her lowest score, which is 30 and calculated the average of the remaining scores to decide her grade. Which of the following gives her new average score?

    (A) 45×5-305

    (B) 45×5-306

    (C) 45×6-305

    (D) 45×6-306 VIEW SOLUTION
  • Question 26
    In a Math test taken by 35 students, the average score of 15 girls is 10 and that of 20 boys is also 10. Which of the following can be calculated based on the above data?

    (A) The highest score in the class.

    (B) The lowest score among the boys in the class.

    (C) The sum of the scores of the 35 students of the whole class.

    (D) All of the above. VIEW SOLUTION
  • Question 27
    tan2θ = sin2θ + cos2θ, then θ =……………

    (A) 30

    (B) 45

    (C) 60

    (D) 90 VIEW SOLUTION
  • Question 28
    Which of the following pair is a correct trigonometric inter-relationship?
     
    (1) cos θ (a) cos θsin θ
    (2) tan θ (b) 1cosec θ
    (3) cot θ (c) 1sec θ
    (4) sin θ (d) 1cot θ
      (e) sin θ . cos θ

    (A) 1-d, 2-e, 3-b, 4-a

    (B) 1-b, 2-a, 3-e, 4-d

    (C) 1-c, 2-d, 3-a, 4-b

    (D) 1-e, 2-b, 3-c, 4-d VIEW SOLUTION
  • Question 29
    tan7θ . tan3θ = 1, ∴ θ =

    (A) 0°

    (B) 9°

    (C) 10°

    (D) 18° VIEW SOLUTION
  • Question 30
    When observed from top of a tower, the angle of depression of two houses A and B in the eastern and western directions is 30° and 60° respectively, then

    (A) House A is nearer to the tower than house B.

    (B) House B is nearer to the tower than house A.

    (C) House A and B are equidistant from the tower.

    (D) None of the above. VIEW SOLUTION
  • Question 31
    On walking x meters, making an angle of 30° with the ground, to find a ball fallen in a valley, one can reach a depth of ‘y’ meters below the ground, then

    (A) x = y

    (B) x = 2y

    (C) 2x=3y

    (D) 2x = y VIEW SOLUTION
  • Question 32
    If the length of a minor arc AB of a circle is 14 of its circumference, then the angle subtended by the minor arc AB at the center will be

    (A) 30

    (B) 45

    (C) 90

    (D) 60 VIEW SOLUTION
  • Question 33
    The length of the minute hand of a clock is 14 cm. If minute hand moves from 1 to 10 on the dial, then an area of ______ cm2 will be covered.

    (A) 462

    (B) 154

    (C) 308

    (D) 616 VIEW SOLUTION
  • Question 34
    If the radius of a circle is increased by 10%, then the corresponding area of the new circle will be _________. (π = 3.14)

    (A) 121 πr2

    (B) 12.1 πr2

    (C) 1.21 π2

    (D) None of the given three. VIEW SOLUTION
  • Question 35
    The maximum area of a triangle inscribed in a semi-circle having radius 10 cm is _________ cm2.

    (A) 10

    (B) 50

    (C) 100

    (D) 200 VIEW SOLUTION
  • Question 36
    If the area of a circle is 38.5 m2, then its circumference will be

    (A) 22

    (B) 2.2

    (C) 38.5

    (D) 3.85 VIEW SOLUTION
  • Question 37
    ABCD is a Rhombus. If it is inscribed in (O, r), then ABCD is a ___________.

    (A) Square

    (B) Rectangle

    (C) Trapezium

    (D) None of the above VIEW SOLUTION
  • Question 38
    In ΔABC, m∠B = 90°, AB = 4 and BC = 3, then the radius of circle touching all three sides of triangle will be

    (A) 2.5

    (B) 2

    (C) 3.5

    (D) 3 VIEW SOLUTION
  • Question 39
    One circle touches all sides of ⧠ABCD. If AB = 5, BC = 8, CD = 6; then AD =

    (A) 3

    (B) 7

    (C) 4

    (D) 9 VIEW SOLUTION
  • Question 40
    Point P is on the outer side of (O, 15). The tangent drawn from point P touches the circle at T. If PT = 8, then OP =

    (A) 7

    (B) 13

    (C) 17

    (D) 23 VIEW SOLUTION
  • Question 41
    The cub (cubical) volume of a hemisphere, having diameter 1 cm, will be ______ cm3.

    (A) π6

    (B) π12

    (C) 2π3

    (D) 4π3 VIEW SOLUTION
  • Question 42
    If the frustum of a cone has a height of 6 cm and radius of 5 cm and 9 cm respectively; then its cubical volume will be ___________ cm3.

    (A) 320π

    (B) 151π

    (C) 302π

    (D) 98π VIEW SOLUTION
  • Question 43
    The formula for finding the total surface area of a Cylinder having cone shaped lid at both the ends, will be

    (A) πr (l + 2r)

    (B) πr (2h + r)

    (C) 2πr (h + l)

    (D) 2πr (h + 2r) VIEW SOLUTION
  • Question 44
    1 meter3 = ______ cm3

    (A) 1

    (B) 102

    (C) 103

    (D) 106 VIEW SOLUTION
  • Question 45
    The two triangles in the figure are congruent by the congruence theorem. Here, it is given OQ = OR. Which of the following condition, along with the given condition, is sufficient to prove that the two triangles are congruent to each other?


    (A) ∠P = ∠S

    (B) ∠Q = ∠R

    (C) OP = OS

    (D) PQ = SR VIEW SOLUTION
  • Question 46
    In ΔPQR, PQ1=PR2=QR3, then m∠R =
    (A) 90°

    (B) 60°

    (C) 45°

    (D) 30° VIEW SOLUTION
  • Question 47
    From P(−3, 2) the feet of a perpendicular drawn on the Y-axis is M. The co-ordinates of M are ______.

    (A) (3, 0)

    (B) (0, 2)

    (C) 32, -1

    (D) (−3, 2) VIEW SOLUTION
  • Question 48
    The distance of P(a, b) from the origin is

    (A) a2 + b2

    (B) |a – b|

    (C) |a + b|

    (D) a2+b2 VIEW SOLUTION
  • Question 49
    Which of the following group is true for ABCD?
     
     (A) ABCD is Rhombus  (a) AC and BD bisect each other.
     (B) ABCD is Parallelogram  (b) AC¯ and BD bisect at each other at an right angle.
     (C) ABCD is Rectangle  (c) AC¯ and BD are congruent and bisect each other at an right angle.
     (D) ABCD is Square  (d) AC¯ and BD are congruent and bisect each other.

    (A) 1-d, 2-a, 3-d, 4-c

    (B) 1-c, 2-d, 3-a, 4-b

    (C) 1-b, 2-a, 3-d, 4-c

    (D) 1-b, 2-c, 3-d, 4-a VIEW SOLUTION
  • Question 50
    When point A(x1, y1) and point B(x2, y2) are joined to form AB, and AB is divided in the proportion of λ : 1; the co-ordinates of the point will be

    (A) λx2+x1λ+1, λy2+y1λ+1

    (B) λx2+x1λ-1, λv2+v1λ-1

    (C) λx1+x2λ+1, λv2+v2λ+1

    (D) λx2+x1λ-1, λy2+y1λ-1 VIEW SOLUTION
  • Question 51
    Find the square root of:           
    14+65 VIEW SOLUTION
  • Question 52
    Find the quadratic equation, whose addition of zeroes is -73 and multiplication is 43. VIEW SOLUTION
  • Question 53
    In an Arithmetic Progression T7 = 18 and T18 = 7, obtain T25.        
    OR
    In an arithmetic progression 2, 7, 12, 17……, summation of how many terms will be 990? VIEW SOLUTION
  • Question 54
    In ΔPQR, m∠Q = 90° and QM  is an altitude; M∈ PR. If QM = 12, PR = 26; then find PM and RM; If PM < RM; then find PQ and QR. VIEW SOLUTION
  • Question 55
    Two concentric circles having radii 73 and 55 are given. The chord of circle having a greater radius touches the smaller circle. Find the length of this chord.       VIEW SOLUTION
  • Question 56
    Find the area of triangle ΔABC having vertices A(4, 2), B(3, 9) and C(10, 10).
    OR
    Find the co-ordinates of the points which divide the line segment joining A(−7, 5) and B(5, −1) into three congruent segments (Such points are called the points of trisection of segment). VIEW SOLUTION
  • Question 57
    In Hostel, one day reading hours of 20 students was observed, whose result is mentioned in the table below. Form the table, find the Mode.
     No. of reading hours  1 – 3 3 – 5 5 – 7 7 – 9 9 – 11
     Student’s strength in the hostel 7 2 8 2 1
    VIEW SOLUTION
  • Question 58
    A card is selected at random from a well-shuffled pack of 52 cards. Find the probability that the selected card is
    (1) a black coloured queen.
    (2) not a king VIEW SOLUTION
  • Question 59
    Prove (sinθ + cosecθ)2 + (cosθ + secθ)2 = 7 + tan2θ + cot2θ. 
    OR
    Find the value of cosec 38sec 52+23tan38 . tan60 . tan52-3 sin232+sin258 VIEW SOLUTION
  • Question 60
    The chord of a circle 84 cm in diameter subtends an angle of 60° at the centre of the circle. Find the area of the minor segment corresponding to the chord. (Take 3 = 1.73) VIEW SOLUTION
  • Question 61
    Find the solution for the following equations:
    52x+23y=7; 3x+2y=12 x0; y0 VIEW SOLUTION
  • Question 62
    Find the median of the following frequency distribution       
    Class 4 – 8 8 – 12 12 – 16 16 – 20 20 – 24 24 – 28
    Frequency 9 16 12 7 15 1
    VIEW SOLUTION
  • Question 63
    On a Hemisphere, frustum of a cone shaped shuttle-cock is used for playing Badminton. The outer radius of the frustum of cone is 5 cm and its inner radius is 2 cm. The height of the entire shuttle-cock is 7 cm. Find the outer surface area of the shuttle-cock. VIEW SOLUTION
  • Question 64
    A jet plane is at a vertical height of h. The angles of depression of two tanks on the horizontal ground are found to have measures α and β, α > β. Prove that the distance between the tanks is h tan α-tan βtan α . tan β assuming both the tanks are on the same side of the jet plane. VIEW SOLUTION
  • Question 65
    The petrol rate is increased by Rs. 5/- per litre. Now for Rs.1320/-, 2 litres less petrol can be bought as compared to the previous rate. Find the increased price of petrol per litre.
    OR
    Kailash’s age at present is 2 years less than 6 times the age of his daughter Prerna. The product of their ages 5 years later will be 330. What was the age of Kailash when his daughter Prerna was born? VIEW SOLUTION
  • Question 66
    Draw PQ, where PQ = 10 cm. Draw circle  (P, 4) and (Q, 3). Draw tangents to each circle from the centre of the other circle. Write points of construction.
    OR
    Draw ΔABC, where m∠ABC = 90°; BC = 4 cm and AC = 5 cm and then construct ΔBXY with 43 scale factor. Write points of construction. VIEW SOLUTION
  • Question 67
    Write the converse of the Pythagoras Theorem and prove it. VIEW SOLUTION
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