Saturday, May 9, 2020

Class 9th Chapter-1(Number System, Sankhya paddhati[in Hindi]) Ex 1.6 I ...

Tuesday, August 4, 2015

Basic Mathematics

Basic Mathematics

Q-1 Angle always measure in --------
(a) Radian (b) Steradion
(c) A&B (d) None

Q-2 1 right angle = -----------
(a) 400 grade (b) 100 grade
(c) 300 grade (d)) None

Q-3 1 rad= --------
(a) 56×570 (b) 57×270
(c) 630 (d) None

Q-4 1min= ----------
(a) 60² (b) 70²
(c) 80² (d) None

Q-5 Cot (900-f)=?
(a) Sec f (b) Tan f
(c) Cot f (d) None

Q-6 Cot (1800-f) = -x , find x
(a) Cot f (b) Secf
(c) Tan f (d) None

Q-7 In 1st quadrant all T- ratio are
(a) + ive (b) -ive
(c) 0 (d) None

Q-8 Sec f = 1/?
(a) Cos f (b) Sec f
(c) Tan f (d) None

Q-9 In θ = l/r , l and r are
(a) Arc and radius (b) Arcs
(c) Ratio (d) None

Q-10 (Newton)0 = ?
(a) Newton (b) 1
(c) 2 (d) None

Q-11 log¥1=?
(a) 0 (b) 1 (c) 3 (d) None

Q-12 Sin 1200=?
(a) Ö5/2 (b) Ö3/2 (c) 2 (d) None

Q-13 Tan 900/Cot 900
(a) ¥ (b) 0 (c) 2¥ (d) None

Q-14 2×718 is value of -------
(a) 2e (b) e (c) 8e (d) None

Q-15 If base of log is e then it is
(a) Neperian log (b) Common log
(c) A & B (d) None

Q-16 log 1050 is
(a) Natural logarithm (b) Common logarithm
(c) A & B (d) None

Q-17 log (14×7) = log 7×log ……..
(a) 7 (b) 14
(c) 8 (d) 9

Q-18 In 1975 characteristic is …..
(a) 3 (b) 2
(c) 4 (d) 8

Q-19 Log7=?
(a) 1×567 (b) 0×8451
(c) 2×871 (d) 4×8451

Q-20 Antilog 0 would be….
(a) 1 (b) 2
(c) 3 (d) 9

Q-21 7, 70,700 have mantissa….
(a) 0 (b) 1
(c) 2 (d) 3

Q-22 d/dx(x15)
(a) 15x143 (b) 15x14
(c) 15x (d) None

Q-23 By d/dt we mean that
(a) Diff. w. r t t (b) Diff w.r.t x
(c) Diff. w. r. t h (d) None

Q-24 d/dx (Cosx) = ……..
(a) -Sin x (b) Cos x
(c) Tanx (d) None

Q-25 d/dx (2009) = ?
(a) 0 (b) 2
(c) 8 (d) 9



ANSWER and REASONS:-


1 (a) Radian
2 (b) 100 grade
3 (a) 56×570
4 (a) 60²
5 (b) Tan f
6 (a) Cot f
7 (a) +ive
8 (a) Cos f
9 (a) Arc and radius
10 (b) 1
11 (a) 0 = Log 1 =0
12 (b) Ö3/2
13 (a) ¥
14 (b) e
15 (a) Neperian log
16 (b) Common logarithm
17 (b) 14
18 (a) 3 =4-1=3
19 (b) 0×8451
20 (a) 1
21 (a) 0
22 (b) 15x14
23 (a) Diff. w. r .t t
24 (a) -Sin x
25 (a) 0

Thursday, April 23, 2015

Mathematics 4

Mathematics 

Q-1 If A is a rectangular matrix of order 3 × 4, then rank of a matrix is
(a) Less than equal to 3
(b) > 3
(c) 4
(d) None

Q-2 If characteristics eq. of a matrix of order 3 × 3 is cubic and it have different three root, then the minimal eq. will be of degree.
(a) 2
(b) 3
(c) 4
(d) 1

Q-3 In A3 – 7I = 0, Here we use I with 7, what is the reason behind it.
(a) To make it matrix
(b) To make it equal to A2
(c) To make it equal to A3
(d) None

Q-4 If in a Square Matrix, a row is zero, then it is
(a) Singular matrix
(b) Non singular matrix
(c) Hermition
(d) None

Q-5 If a matrix of order 3 have three non zero row, then ranks of A is
(a) 2
(b) 3
(c) 4
(d) 9

Q-6 What is the condition for the matrix to be Involuntary ?
(a) A3 = I
(b) A2 = I
(c) A = I
(d) None

Q-7 For upper triangular matrix
(a)aij = 0, i = j
(b) aij, i>j
(c) aij = 0, i no. of variable
(c) a and b
(d) None


Q-20 2x + 6y = 0 have
(a) Unique solution
(b) Infinite many solution
(c) No solution
(d) None


Q-21 If A2 = A, then it is
(a) Idempotent matrix
(b) Nilpotent matrix
(c) Involuntary matrix
(d) None


Q-22 (A + B)1 =?
(a) A1 – B1
(b) B1 – A1
(c) A1 + B1
(d) (B1)1


Q-23 If 2, 3, 4 are eigen value of A, then eigen value of A2 is
(a) (4, 9, 6)
(b) 4, 9, 16
(c) 5, 9, 16
(d) None


Q-24 If the upper triangular matrix have diagonal elements 2, 4, 8 then eigen value of this upper triangular matrix is
(a) 2, 4, 8
(b) 2, 4, 6
(c) 7, 5, 6
(d) 9, 10, 4


Q-25 If A is matrix of order 5 then its rank is
(a) 4
(b) 5
(c) 9
(d) 6

Answers

1(a) Less than equal to 3
2(b) 3
3(a) To make it matrix
4(a) Singular matrix
5(b) 3
6(b) A2 = I
7(b) aij, i > j

8(b) Characteristic eq.
9(c) 2
10(b) 3
11(a) 4
12(b) No
13(c) A1
14(a) Symmetric
15(b) Trivial Solution is x = y = z = 0
16(a) 4
17(b) Skew-Hermition
18(a) 4
19(a) Rank of A < no. of variable
20(b) Infinite many solution
21(a) Idempotent matrix
22(c) A1 + B1
23(b) 4, 9, 16
24(a) 2, 4, 8
25(c) 9

Reason

2 If roots are different then degree of characteristics eq. & minimal eq. is same
4 If any row of matrix is zero, then its A = 0, therefore it is singular matrix
11 For this A ¹ 0
Rank of A = 4
20 For 2x + 6y = 0 but y = K
2x + 6K = 0
2x = –6k , x = – 3k
x = – 3k, y = k,
k have so many value

Mathematics

Mathematics 

Q-1 The radius of 5 (x2 + y2) – 5 (x + y) + 10 = 0 is
(a) Ö6/7
(b) Ö5/2
(c) Ö7/9
(d) Ö9/16

Q-2 The radical plane of x2 + y2 + 2x + 6y + 9 = 0 & x2 + y2 + 6x + 9y – 8 = 0 is
(a) 4x + 5y – 18 = 0
(b) 4x + 5y – 17 = 0
(c) 4x + 8y + 19 = 0
(d) None

Q-3 The center of circle x2 + y2 + 2u1 x + 2v1 y + d = 0 is
(a) (u1 , v1)
(b) ( – u1, – v)
(c) (– u1/2, – v1/2)
(d) None

Q-4 In y2 = 2x, the vertex is
(a) (0, 1)
(b) (0, 2)
(c) (0, 0)
(d) None

Q-5 In ( x – 5)2 + ( y – 3)2 = 5
Find the center & radius of a circle.
(a) (5, 3) & Ö5
(b) (5, 4), 5
(c) (5, 2), 6
(d) None

Q-6 In eq. of circle coefficient of x2 is equal to y2 & it should be equal to
(a) 2
(b) 1
(c) 3
(d) 4

Q-7 The eq. of tangent to the circle x2 + y2 = 5 at (5, 3) is
(a) 5x + 9y = 10
(b) 5x + 3y = 5
(c) 5x + 9y = 4
(d) None

Q-8 In the circle x2 + y2 + 2xy + 5z + c = 0, the centre is
(a) (0, 0)
(b) (1, 1)
(c) It is not a circle
(d) (4, 3)

Q-9 In order to find pt. of intersection two line should be
(a) Intersecting
(b) Parallel
(c) a and b
(c) None

Q-10 When distance between centre of two circle is equal to sum of their radius, then in this case two circle touch each other
(a) Internally
(b) Externally
(c) Not touch
(d) None

Q-11 The eq. of circle with end pt. of diameter is (5, 2) & (1, 5) is
(a) x2 + y2 – 6x + 7y – 10 = 0
(b) x2 + y2 – 6x – 7y + 10 = 0
(c) x2 + y2 + 6x + 7y – 11 = 0
(d) x2 + y2 – 6x + 7y – 11 = 0

Q-12 If we want to find radical plane, then how many circle we held
(a) 2
(b) 3
(c) 5
(d) 9

Q-13 If in a equation Ax2 + By2 + 2Hxy + 2Gx + 2Fy + c = 0
B2 – AB = 0, Then is a
(a) Ellipse
(b) Parabola
(c) Hyperbola
(d) None

Q-14 In x2/a2 + y2/b2 = 1, then value of major axis is
(a) 2a
(b) 2b
(c) 2d
(d) None

Q-15 In x2/a2 + y2/b2 = 1, then value of minor axis is
(a) 2a
(b) 2b
(c) 2e
(d) None

Q-16 In x2/25 + y2/16 = 1, the latus rectum is
(a) 32/5
(b) 16/14
(c) 16/9
(d) None

Q-17 In y2 = 4ax, the eq. of axis is
(a) x = 0
(b) y = 0
(c) x = y= 0
(d) None

Q-18 If Ratio of distance of any pt. on conic to focus & directrix is 1, then it is
(a) Parabola
(b) Ellipse
(c) Hyperbola
(d) None

Q-19 If a = b in x2/a2 – y2/b2 = 1, then it is
(a) Rectangle hyperbola
(b) Hyperbola
(c) Ellipse
(d) None

Q-20 For rectangle hyperbola, the value of l is
(a) Ö2
(b) Ö3
(c) Ö14
(d) Ö5

Q-21 What is parametric form of x2 + y2 = r 2 ?
(a) x = r cos Ө, y = r sin Ө
(b) x = cos Ө, y = sin
(c) x = r2 cos Ө, y = r2 sin Ө
(d) None

Q-22 Find the eq. of axis of (x + 1)2/52 + (y + 1)2 /32 = 1
(a) y = 0
(b) y = 1
(c) y = 3
(d) y = 5

Q-23 What is the focus of parabola y2 = 8x ?
(a) (2,0)
(b) (3,0)
(c) (4,0)
(d) (5,1)

Q-24 What is the focus of a parabola ?
Y2 = – 36x
(a) (0, – 9)
(b) (0,9)
(c) (0,5)
(d) (0,4)

Q-25 What is focus of a parabola x2 = 36y ?
(a) (0,4)
(b)(0,9)
(c)(0,5)
(d) None

Answers:

1(b) Ö5/2
2(b) 4x + 5y – 17 = 0
3(b) ( – u1, – v1)
4(c) (0, 0)
5(a) (5, 3) & Ö5
6(b) 1
7(b) 5x + 3y = 5
8(c) It is not a circle
9(a) Intersecting
10(b) Externally
11(b) x2 + y2 – 6x – 7y + 10 = 0
12(a) 2
13 (b)Parabola
14(a) 2a
15(b) 2b
16(a) 32/5
17(b) y = 0
18(a) Parabola
19(a) Rectangle hyperbola
20(a) Ö2
21(a) x = r cos Ө, y = r sin Ө
22(a) y = 0
23(a) (2,0)
24(a)(0, – 9)
25(b)(0,9)

Reason:

1 (x2 + y2) – 5 (x + y) + 10 = 0
First of all divide it by 5 because coefficient of x2 & y2 should be 1
(x2 + y2) – x – y – 2 = 0
( ½, 1/2), d = – 2
radius = Ö(1/2)2 + (1/2)2 + 2
Ö1/4 + ¼ +2
Ö2/4 + 2
Ö1/2 + 2 = Ö 5/2
2 Let S1 = x2 + y2 + 2x + 6y + 9 = 0
S2 = x2 + y2 + 6x + 6y + 9 = 0
Eq. of radical plane is
S1 – S2 = 0
– 4x – 5y + 17 = 0
4x + 5y – 17 = 0
7 Equation of Tangent at (x1, y1)
xy1 + yy1 = 5
But at pt. (5, 3) it is
x(5) + y(3) = 5
5x + 3y = 5
8 It is not a circle because in circle there is not any term which contain xy etc
11 Equation of circle in diameter form is
(x – x1) (x – x2) + (y – y1) (y – y2) = 0
(x – 5) (x – 1) + (y – 2) (y – 5) = 0
x2 – x – 5x +5 + y2 – 5y – 2y + 5 = 0
x2 – 6x + 5 + y2 – 7y + 5 = 0
x2 + y2 – 6x – 7y + 10 = 0
16 Latus rectum is 2b2/a
By x2/25 + y2/16 = 1
a2 = 25, b2 = 16, a = 5, b = 4
Latus rectum = 2b2/a = 2(16)/5 = 32/5
22 For x2/a2 + y2/b2 = 1, the eq. of axis in y = 0
23 Compare y2 = 8x
With y2 = –4ax
4a = 8, a = 2
F (a, 0), i.e F (2, 0)
24 Compare y2 = – 36x
With y2 = –4ax
4ax = 36, a = 9
F (–a, 0) , F (–9, 0)

Mathematics Numbers

Mathematics Numbers

Q-1 Which prime of the following is smallest even Prime number?
(a) 4 (b) 2 (c) 8 (d) 10

Q-2 HCF of 7/4, 21/4, 28/12 is
(a) 7/100 (b) 7/24 (c) 7/25 (d) None

Q-3 LCM of 12/9, 24/18, 36/27 is
(a) 7 (b) 8 (c) 11 (d) None

Q-4 x/y=2/5, y/z = 8 , find x/z=?
(a) 4/24 (b) 4/25 (c) 4/58 (d) None

Q-5 12/13x-41/26x=11, find x
(a) 26× 11/17 (b) 26 ×12/9 (c) 26× 18/11 (d) None

Q-6 How many prime no. are there between 10 to 30?
(a) 7 (b) 6 (c) 8 (d) 9

Q-7 1/ (n-n)! =?
(a) 2 (b) 1 (c) 3 (d) 5

Q-8 If Manoj’s age 5 years ago was 23 years, then what will be its present age?
(a) 25 (b) 18 (c) 19 (d) 28

Q-9  25% of 50 of 3/35 %of 25 of 4=?
(a) 14/11 (b) 15/14 (c) 19/13 (d) None

Q-10  5 x +7/7x +8 = 9/11, find x
(a) 5/6 (b) 5/11 (c) 5/8 (d) None

Q-11 1+2+3+4+ --------- 12 = ?
(a) 72 (b) 78 (c) 79 (d) 80

Q-12 10 +11+12+ ---------- 15= ?
(a) 175 (b) 75 (c) 68 (d) None

Q-13 (2n) 2 -(2n+2)2 is always divisible by which value?
(a) 5 (b) n (c) 6 (d) None

Q-14 X2 + 11x+30 =0 find the value of x
(a) - 5, -6 (b) 5, 6 (c) 15/9 (d) None

Q-15 Find the digit at unit place of 313× 41× 152 ×161
(a) 3 (b) 6 (c) 4 (d) 5

Q-16 Find the value of x in 53x4, if it is divisible by4
(a) 4 (b) 3 (c) 5 (d) 7

Q-17 If x +y = 11 and x2+y2=12, find the value of x y
(a) 67 (b) 66 (c) 68 (d) 29

Q-18 Find H.C.F of 34 × 46× 78, 33× 47× 79
(a) 34 × 46 ×78 (b) 34 × 46 (c) A&B (d) None

Q-19 99× 99 × 99
(a) 1000 300 - 30001 (b) 100001 (c) 1001 (d) None

Q-20 Find the number which have large of divisor?
(a) 11 (b) 17 (c) 21 (d) 29

Q-21 (X/13) (X/13) = 4, find x
(a) 27 (b) 26 (c) 28 (d) None

Q-22 ( 703 + 503)/ (70)2 + 502 - (70) (50)
(a) 130 (b) 120 (c) 180 (d) None

Q-23 If 10 year after the age of Nirmal is 38 year then presently her age will be
(a) 28 (b) 38 (c) 48 (d) None

Q-24 Find LCM of 2, 8, 16, 32
(a) 16 (b) 32 (c) 2 (d) 8

Q-25 H.C.F of (4, 16, 32)
(a) 8 (b) 4 (c) 8 (d) None


ANSWERS:-


1 (b) 2
2 (b) 7/24
3 (b) 8
4 (b) 4/25
5 (a) 26× 11/17
6 (b) 6
7 (b) 1
8 (d) 28
9 (b) 15/14
10 (c) 5/8
11 (b) 78
12 (b) 75
13 (b) n
14 (a) - 5, -6
15 (b) 6
16 (a) 4
17 (b) 66
18 (a) 34 × 46 ×78
19 (a) 1000 300 - 30001
20 (c) 21
21 (b) 26
22 (b) 120
23 (a) 28
24 (b) 32
25 (b) 4


REASONS:-



2 (b) HCF=HCF of 7,21,28/LCM of 4,8,12=7/24
3 (b) LCM= LCM12,24,36/1CF 9,18,27
= 72/9 = 8
4 (b) x/y × y/2 = x/2
=2/5×4/18 =4/45
5 (a) (24 -41) x /26 =11
= 17/26x=11
x=11×26/17
6 (b) 11, 13, 17,19,23,29
7 (b) 1/01
=1=1/1=1
9 (b) 25/100×50×3/35/100×25×4
= 150/35×4
=150/140=15/14
10 (c) 11(5x+7) =9(7x+8)
=55x+77 = 63x+72
= 5 = 8x
5/8 =x
11 (b) 1+2+3----------- +12
= 12(12+1)/2
= 12(13)/2 =78
12 (b) (1+ 2+3+--------+9) + (10+-------- +15) -(1+2+-------+9)
= å 15-åa

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