X : Maths: Chapter: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
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Type- 1
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1. The pair 2x=3y-5 and 2y= 5x-4 of linear equations represents two lines which are
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Ans(c)
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(a) Parallel (b) coincident (c) intersecting (d) either parallel or coincident
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2. The pair x=p and y=q of the linear equations in two variables x and y graphically represents two lines which are
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Ans(c)
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(a) Parallel (b) coincident (c) intersecting at(p,q) (d) intersecting at(q,p)
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3. If the lines represented by the pair of linear equations 2x+5y=3 and (k+1)x +2(k+2)y=2k are coincident, then the value of k is
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Ans(b)
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(a) -3 (b) 3 (c) 1(d) -2
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4. If the pair of linear equations (3k+1)x+3y-2=0 and (k2+1 )x+(k-2)y-5=0 inconsistent, then the value of k is
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Ans(b)
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(a) 1 (b) -1 (c) 2 (d)-2
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5. If the pair of linear equations 2x+3y=11 and 2px+(p+q)y=p+5q has infinitely many solution then (a) p=2q (b)q=2p (c)p=-2q (d) q= -2p
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Ans(b)
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X : Maths: Chapter: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
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Type- II
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1. Find the value of k for which the given system of equations has unique solution:
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2x+3y-5=0, kx-6y-8=0
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[Ans k≠ -4]
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2. For what value of k will the following system of linear equations have infinite number of solution? 2x+3y-5=2; (k+2)x+(2k+1)y=2(k-1)
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[Ans k=4]
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3. Find two numbers whose sum is 18 and difference is 6.
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[Ans 12,6]
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4. Solve for x and y. X+6/y=6, 3x-8/y=5.
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[Ans x=3, y=2]
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5. The sum of the numerator and the denominator of a fraction is 20 if we subtract 5 from the numerator and 5 from denominator, then the ratio of the numerator and the denominator will be 1:4 .Find the fraction.
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[Ans: 7/13]
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X : Maths: Chapter: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
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Type- III
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1 Solve the following system of equations by using the method of elimination
by equating the coefficient x/10+y/5+1=15, x/8+y/6=15.
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[Ans x=80, y=30]
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2. If two digit number is four times the sum of its digits and twice the product of digits. Find the number.
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Ans: 36
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3. Solve the following system of equations.
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bx/a- ay/b +a +b=0 bx –ay +2ab=0
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Ans x= -3a, y= -b
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4. Solve graphically the system of linear equations.
4x-3y+4=0, 4x +3y=20 also find the area of the region bounded by the lines and x-axis.
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Ans x=2, y=4, Area=12 sq. unit]
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5. The sum of two natural’s number is 8 and sum of their reciprocals is 8/15. Find the numbers
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[Ans 5 and 3]
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X : Maths: Chapter: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
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Type- IV
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1. Solve for x and y:
2/2x+y – 1/x-2y +5/9 =0 9/2x+y – 6/x-2y +4 =0
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Ans x=2 , y=1/2
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2. Draw the graph the following equations: 2x+3y-12=0 and 7x-3y-15=0.Determine the coordinates of the vertices of the triangle formed by the lines and the y-axis
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(0,4),(3,2),(0,-5)
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3. The sum of the digits of a two- digit number is 12 the number obtained by interchanging the two digits exceed the given number by 18. Find the number.
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Ans: 57
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4. Abdul traveled 300km by train and 200km by taxi, it took him 5 hours 30 minutes. But if he travels 260 km by train and 240 km by bus he takes 6 minutes longer. Find the speed of the train and of the taxi
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Ans 100 km/hr., 80 km/hr.
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5. Solve the following pairs of equation for x and y.
15/x-y +22/x+y=5, 40/x-y + 55/x+y =13.
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Ans x=8, y=3
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6. Find the value of ‘p’ if (-3, p) lies on 7x+2y=14.
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SELF
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7. Solve the following system of linear equations using the method of cross-multiplication:
ax +by =1 and bx +ay = (a+b)2 / a2+b2 =1
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SELF
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8. Solve for x and y. bx +ay = a+b. and ax[1/a-b -1/a+b]+ by [1/b-a
-1/b+a]=2 |
SELF
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CBSE X Mathematics: Linear Equations in two Variables
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Linear Equations in two Variables MCQ’ Test -1
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Linear Equations in two Variables Test paper-2
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Linear Equations in two Variables Test paper-3
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Linear Equations in two Variables Test paper-4
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Linear Equations in two Variables Test paper-5
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Linear Equations in two Variables Test paper-6
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Linear Equations in two Variables MCQ's -7
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Here is the simple definition about linear equation,We can call a linear equation is a type of algebraic equation in which each term can be a constant or can be product of the constant and its the first order equation.graph linear equations
ReplyDeleteIn a unit-test the no. of hose that passed and the no. of these that failed were in the ratio 3:1. Had
ReplyDelete8 more appeared and 6 less passed, the ratio of passes to failures would have been 2:1. Find
how many appeared?
Let, appeared = x and Passed = y Then, failed = x - y
Deletey/(x - y) = 3 ---- (i)
If, appeared = x + 8 then Passed = y - 6 and Failed = x + 8 - (y - 6) = x - y + 14
Then, (y - 6)/(x - y + 14) = 2
y - 6 = 2(x - y + 14)
y - 6 = 2x - 2y + 28
3y = 2x + 34 --- (ii)
Now let's solve the two simultaneous equations:
From (i):
y = 3(x - y)
y = 3x - 3y
3x = 4y
x = 4y/3 --- (iii)
Substitute it in (ii):
3y = 2(4y/3) + 34
9y = 8y + 102
y = 102.
Substitute value of y in (iii)
x = 4(102)/3 = 136.
So, the total number of candidates that appeared on the test = 136.
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ReplyDeletethe distance b/w school nd metro station is 300m . kartikay started running frm school 2wards metrostation , while. ashu started running frm metro station to school. they meet after 4 minute had kartikay doubled his speed or ashu reduced his speed to third of the original they would hv met one minute earlier. find the speeds.?
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