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  • Question 1
    In ΔABC, D, E and F are midpoints of  AB, BC and AC  respectively. If ABC = 40 then DEF = ----- .


    (A) 10

    (B) 403

    (C) 20

    (D) 5 VIEW SOLUTION
  • Question 2
    From the given figure AD = ----



    (A) 2

    (B) 23

    (C) 32

    (D) 3 VIEW SOLUTION
  • Question 3
    In ΔABC, if m∠B = 90, & AC = 10 then length of median BM¯ = ---------.

    (A) 6

    (B) 52

    (C) 5

    (D) 8 VIEW SOLUTION
  • Question 4
    From the figure, AB = -------.


    (A) 12

    (B) 4

    (C) 8

    (D) 16 VIEW SOLUTION
  • Question 5
    From the graph OA2 = --------.


    (A) 0

    (B) a2 + b2

    (C) a2+b2

    (D) a+b VIEW SOLUTION
  • Question 6
    (1, 0), (0, 1), (1, 1) are the co-ordinates of vertices of a triangle. The triangle is ------ triangle.

    (A) Isosceles

    (B) Obtuse angled

    (C) Acute angled

    (D) Equilateral VIEW SOLUTION
  • Question 7
    In given figure, co-ordinates of foot of perpendicular P are -----------.


    (A) (5, 0)

    (B) (–5, 1)

    (C) (–1, 0)

    (D) (0, –1) VIEW SOLUTION
  • Question 8
    If O (0, 0) and P (–8, 0) then co-ordinates of its midpoint at ----------.

    (A) (–4, 0)

    (B) (4,0)

    (C) (0, –4)

    (D) (0, 0) VIEW SOLUTION
  • Question 9
    If sin2 (3x + 45) + cos2 (2x + 60) = 1 then x

    (A) 60

    (B) 30

    (C) 15

    (D) 0 VIEW SOLUTION
  • Question 10
    If tan5θ·tan 4θ = 1, then θ = ______.

    (A) 10

    (B) 3

    (C) 7

    (D) 9 VIEW SOLUTION
  • Question 11
    From given figure tan A·tan C = ____________.


    (A) 12

    (B) 2

    (C) 2

    (D) 1 VIEW SOLUTION
  • Question 12
    If cos2 45° – cos2 30° = x. cos 45°sin 45° then x = ________.

    (A) –1/2

    (B) 1/2

    (C) 2

    (D) 3/4 VIEW SOLUTION
  • Question 13
    In given figure, the minimum distance to reach from point “C” to point “A” will be _________.


    (A) a2

    (B) 2

    (C) 2

    (D) 2a VIEW SOLUTION
  • Question 14
    To find the length of a ladder making an angle θ with wall ________ trigonometric ratio is used.

    (A) tan θ

    (B) cot θ

    (C) cosec θ

    (D) none VIEW SOLUTION
  • Question 15
    If the ratio of the height of tower and the length of its shadow is 1: 3, then the angle of elevation of the sun has measure __________.

    (A) 60°

    (B) 45°

    (C) 30°

    (D) 75° VIEW SOLUTION
  • Question 16
    ___________ is true for a tangent of a circle.
    P: line intersect circle in one & only one point
    Q: line and circle must be in same plane.
    R: line passes from the centre of a circle.

    (A) Q and R

    (B) Only Q

    (C) Only P

    (D) P and Q VIEW SOLUTION
  • Question 17
    In an isosceles right angled triangle ΔABC, r = _______.


    (A) 2

    (B) 1

    (C) 1-12

    (D) 2-2 VIEW SOLUTION
  • Question 18
    In the figure, from one handkerchief from four corners, sectors P, Q, R, S each of 2 cm are cut, whose sum is P + Q + R + S = A1 and a circle of diameter 4 cm from the centre is cut whose area is A2 , then __________ is possible.


    (A) A1 ≠ A2

    (B) A1 < A2

    (C) A1 > A2

    (D) A1 = A2 VIEW SOLUTION
  • Question 19
    According to figure of clock angle θ =_______.


    (A) 150°

    (B) 20°

    (C) 120°

    (D) 100° VIEW SOLUTION
  • Question 20
    If radius of circle is decreased by 10% then there is __________ decrease in its area.

    (A) 10%

    (B) 21%

    (C) 19%

    (D) 20% VIEW SOLUTION
  • Question 21
    Formula to find area of sector is ____________.

    (A) 12rl

    (B) πrθ360

    (C) πr2θ180

    (D) πr2 VIEW SOLUTION
  • Question 22
    If the circumference of base of a hemisphere is 2π then it volume is ______________ cm3.

    (A) 2π3r3

    (B) 2π3

    (C) 8π3

    (D) π12 VIEW SOLUTION
  • Question 23
    In the given cylinder the stick of maximum length __________ can be kept inside it.


    (A) 10

    (B) 12

    (C) 13

    (D) 17 VIEW SOLUTION
  • Question 24
    Total area of the given closed figure will be ____________ square units.


    (A) 31

    (B) 45

    (C) 25

    (D) 40 VIEW SOLUTION
  • Question 25
    The ratio of the radii of two cones having equal height is 2:3 then ratio of their volume is ____________.

    (A) 3:2

    (B) 9:4

    (C) 8:27

    (D) 4:9 VIEW SOLUTION
  • Question 26
    The conjugate surd of 2-3 is __________.

    (A) -2+3

    (B) 2--3

    (C) 3+2 

    (D) 12-3 VIEW SOLUTION
  • Question 27
    To get the terminating decimal expansion of a rational number pq. If q = 2m 5n then m and n must belong to __________.

    (A) Z

    (B) N U {0}

    (C) N

    (D) R VIEW SOLUTION
  • Question 28
    For polynomial p(x) = x2 – 4x + 3, α + β = _______.

    (A) Positive fraction

    (B) Negative integer

    (C) Positive integer

    (D) Zero VIEW SOLUTION
  • Question 29
    The graph of polynomial P(x) = ax – b, where a ≠ 0; a, b ∈ R intersect

    (A) ba, 0

    (B) 0, ba

    (C) -ba, 0

    (D) -ab, 0 VIEW SOLUTION
  • Question 30
    The graph of p(x) = 5x + 3, x ∈ R is __________.

    (A) ray

    (B) parabola

    (C) line segment

    (D) line VIEW SOLUTION
  • Question 31
    For the zeroes α & β of polynomial P(x) = ax2 + bx + c, 1α+1β = ____________.

    (A) -bc

    (B) -ba

    (C) ca

    (D) none VIEW SOLUTION
  • Question 32
    The probability of complement event of impossible event is ___________.

    (A) 0.5

    (B) 0

    (C) 1

    (D) 0.46 VIEW SOLUTION
  • Question 33
    Find the probability of having 5 Sundays in the month of February in leap year 2004.

    (A) 2/7

    (B) 0

    (C) 1/7

    (D) 1 VIEW SOLUTION
  • Question 34
    Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
    Frequancy 5 15 13 17 10

    For the information given above, n2-cf will be = ____________.
    (A) 10

    (B) 20

    (C) 30

    (D) 25 VIEW SOLUTION
  • Question 35
    For the measures of central tendency, __________ of the following is not true.

    (A) Z=3M  2x

    (B) 2x+Z=3M

    (C) 2x -3M=-Z

    (D) 2x=Z-3M VIEW SOLUTION
  • Question 36
    If x-Z=3 and x+Z=45, then M = ________.

    (A) 26

    (B) 22

    (C) 24

    (D) 23 VIEW SOLUTION
  • Question 37
    If before three years sum of ages of father and son was 59 years then before five years the sum of their ages would have been __________.

    (A) 55

    (B) 61

    (C) 69

    (D) 57 VIEW SOLUTION
  • Question 38
    To eliminate x from equations x + y + 3x = 12 → ① & 8x + 3y = 17 → ②, equation ② is to be multiplied by ______________.

    (A) 8

    (B) -12

    (C) 12

    (D) 3 VIEW SOLUTION
  • Question 39
    Equation x3-y2=1  can be written in standard form as _______.

    (A) 3x – 2y – 6 = 0

    (B) 2x – 3y – 6 = 0

    (C) 2x – 3y = 6

    (D) 2x – 3y = 1 VIEW SOLUTION
  • Question 40
    In a two digit number, if number in unit place is 8 and number in tens place is y then that number is ____________.

    (A) y + 8

    (B) y + 80

    (C) 10y + 8

    (D) 80 y VIEW SOLUTION
  • Question 41
    The factors of quadratic polynomial P(x) = x2 + 4x – 5 are ____________.

    (A) (x + 5) (x – 1)

    (B) (x + 5) (x + 1)

    (C) (x + 1) (x – 5)

    (D) (x – 1) (x – 5) VIEW SOLUTION
  • Question 42
    ______________ is true for discriminate of quadratic equation x2 + x + 1= 0.

    (A) D = 0

    (B) D < 0

    (C) D > 0

    (D) D is a perfect square VIEW SOLUTION
  • Question 43
    If one of the roots of the equation kx2 – 7x + 3 = 0 is 3, then k = ___________.

    (A) –3

    (B) 3

    (C) –2

    (D) 2 VIEW SOLUTION
  • Question 44
    ______________ cannot be the sum of a non zero number and its reciprocal.

    (A) 0

    (B) 2

    (C) x+1x

    (D) 52 VIEW SOLUTION
  • Question 45
    For a quadratic equation, if discriminate D = 0, then _____________ is not possible for its roots α + β.

    (A) α = β

    (B) α – β = 0

    (C) α + β = 2α

    (D) α + β = 0 VIEW SOLUTION
  • Question 46
    _____________ can be one of the term in Arithmetic progression 4, 7, 10, ------.

    (A) 103

    (B) 123

    (C) 171

    (D) 99 VIEW SOLUTION
  • Question 47
    (n – 2)th term of an arithmetic progression will be ___________.

    (A) a + (n – 1)d

    (B) a + (n – 3)d

    (C) a + (n – 2)d

    (D) none VIEW SOLUTION
  • Question 48
    In the AP, 5, 7, 9, 11, 13, ------ the sixth term which is prime is __________.

    (A) 15

    (B) 19

    (C) 17

    (D) 23 VIEW SOLUTION
  • Question 49
    From the given BD = __________.



    (A) x + y

    (B) xy

    (C) xy

    (D) x+y VIEW SOLUTION
  • Question 50
    For ΔABC & ΔPQR, if m∠A = m∠R and m∠C = m∠Q, then ABC ↔ ___________ is a similarity.

    (A) RQP

    (B) PQR

    (C) RPQ

    (D) QP VIEW SOLUTION
  • Question 51
    If 7 is prime, then prove that 7 is irrational. VIEW SOLUTION
  • Question 52
    For polynomial P(x) = 6x3 + 29x2 + 44x + 21 find P (–2). VIEW SOLUTION
  • Question 53
    Find the solution of given pair of linear equation by elimination method. 
    3x + 4y = – 17 → ①

    5x + 2y = – 19 → ② VIEW SOLUTION
  • Question 54
    For an AP, 13, 43, 73, 103 ......., Find T18
     
    OR
     
    For an AP, 3, 9, 15, 21......., Find S10     VIEW SOLUTION
  • Question 55
    Write statement of Pythagoras theorem and show that 6, 8, and 10 are Pythagorean triplets.  VIEW SOLUTION
  • Question 56
    If X(3, 1), Y(4, 5) and Z(–2, –1) are co-ordinates of vertices of  ΔXYZ then find area of ΔXYZ.   VIEW SOLUTION
  • Question 57
    If sin θ = a then find the value of cot θ + sec θ.    
                     
                             OR

    For ΔABC, prove that tan A+C2=cotB2. VIEW SOLUTION
  • Question 58
    Find mode given data: 
     
    Class 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69
    Frequency 15 20 50 30 10
    VIEW SOLUTION
  • Question 59
    Write standard form of quadratic equation and find the roots of the equation 3x2+52x+2=0 using general formula.  VIEW SOLUTION
  • Question 60
    From top of a tower the angle of depression of top and bottom of a multistoreyed building are 30° and 60° respectively. If the height of the building is 100 m. find the height of a tower.  VIEW SOLUTION
  • Question 61
    The mean of the following frequency distribution of 100 observations is 148. Find missing frequencies F1 and F2.  
     
    Class 0 – 49 50 – 99 100 – 149 150 – 199 200 – 249 250 – 299 300 – 349
    Frequency 10 15 F1 20 15 F2 2

    OR

    The median of 230 observations is 46. Find a and b.

    Class 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70
    Frequency 12 30 a 65 b 25
    VIEW SOLUTION
  • Question 62
    A box contains 100 cards marked with numbers 1 to 100. If one card is drawn randomly from the box. Find the probability that it bears. 

    (1) Even prime number.

    (2) A number divisible by 7.

    (3) The number at unit place is 9. VIEW SOLUTION
  • Question 63
    Prove that, tangents drawn to the end points of diameter of the circle are parallel to each other.      VIEW SOLUTION
  • Question 64
    A cylindrical container having diameter 16 cm and height 40 cm is full of ice cream. The ice-cream is to be filled into cones of height 12 cm and diameter 4 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.     
    OR

    A cylinder has hemispherical ends having radius 7 cm and total height of solid is104 cm. If its outer surface is to be polished & cost of polish is Rs 100 per sq. mtr. find the total cost of polish. VIEW SOLUTION
  • Question 65
    The length of a side of a square field is 20 mtr. A cow is tied at the corner by means of a 7 mtr long rope. Find the area of the field which cow can graze. If the length of rope is doubled then find the increase in the grazing area.  VIEW SOLUTION
  • Question 66
    Divide a given line segment in ratio of 3:5 and write steps of construction.   VIEW SOLUTION
  • Question 67
    If for acuted angled ΔABC and ΔPQR ABC ↔ PQR is similarity then prove that AABCAPQR=AB2PQ2=BC2QR2=AC2PR2 

    OR

    Write converse of Pythagoras theorem and prove it. VIEW SOLUTION
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