M A T H E M A T I C S: Bansal Classes
M A T H E M A T I C S: Bansal Classes
M A T H E M A T I C S: Bansal Classes
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Target IIT JEE 2008 Daily Practice Problems
CLASS : XI (J-Batch) DATE : 22-23/11/2006 DPP. NO.-39
Q.1 If the lines L1 : 2x + y – 3 = 0, L2 : 5x + ky – 3 = 0 and L3 : 3x – y – 2 = 0, are concurrent, then the value
of k is
(A*) – 2 (B) 5 (C) – 3 (D) 3
2 1 3 2 0 3
[Sol. for concurrency D = 5 k 3 = 0, using C2 C2 + C1 + C3, 5 k 2 3 = 0
3 1 2 3 0 2
(k + 2)(–4 + 9) = 0 k = – 2 Ans. ] [11th J-Batch (13-11-2005)]
Q.2 The points Q = (9, 14) and R = (a, b) are symmetric w.r.t. the point (5, 3). The coordinates of the point
R are
17
(A) 7, (B) (13, 25) (C*) (1, –8) (D) none
2
[11th J-Batch (13-11-2005)]
Q.321/st.line Number of points on the straight line which joins (– 4, 11) to (16, –1) whose co-ordinates are
positive integer
(A) 1 (B) 2 (C*) 3 (D) 4
[Sol. slope = – 3/5 [12 & 13 08-01-2006]
equation of the line is 3x + 5y = 43
43 3x
5y = 43 – 3x y=
5
Hence point are (1, 8), (6, 5) , (11, 2) ]
1 2 3 5049
5050 .......
2 3 4 5050 x
Q.4 The value of x satisfying the equation = , is
1 1 1 5050
1 .......
2 3 5050
(A) 1 (B) 5049 (C*) 5050 (D) 5051
1 2 3 5049
1 1 1 1 ....... 1
[Sol. 2 3 4 5050 = x
1 1 1 5050
1 ........
2 3 5050
1 1 1 1
1 .......
2 3 4 5050 = x ; x
=1 x = 5050 Ans. ]
1 1 1 1 5050 5050
1 .......
2 3 4 5050
Q.5 If the roots of the quadratic equation ax2 + bx + c = 0 are rational and equal then the statement which
is True about the graph of y = ax2 + bx + c, is
(A) It intersects the x-axis in two distinct points.
(B) It lies entirely below the x-axis.
(C) It lies entirely above the x-axis.
(D*) It is tangent to the x-axis.
Q.6 x = logd(abc); y = logb(acd); z = logc(abd) and t = loga(bcd) then the value of
1 1 1 1
+ + + is
x 1 y 1 z 1 t 1
(Assume all logarithms to be defined)
(A) dependent on a, b, c only (B) dependent on a, b, d only
(C) dependent on all a, b, c, d (D*) independent of all a, b, c, d
[Sol. x + 1 = logd(abcd)
y + 1 = logb(abcd)
z + 1 = logc(abcd)
t + 1 = loga(abcd)
1 1 1 1
log a (abcd ) log b (abcd ) log c (abcd ) log a (abcd )
logabcd(abcd) = 1 Ans. ]
Q.7 As shown in the diagram, region R in the plane has vertices at (0, 0), (0, 5), (4, 5), (4, 1), (9, 1) and
(9, 0). There is a straight line y = mx that partitions R into two subregions of equal area. The value of m
equals to
15
(A*) (B) 1
16
5 4
(C) (D)
4 3
[Sol. By adding rectangles the total shaded area is 25.
1 25
The area of the trapezoid ABCD = (5 + 5 – 4m)(4) =
2 2
25 25 15 15
10 – 4m = 4m = 10 – = m= Ans.]
4 4 4 16
16 6 1 1 2 3 1 2 1 1
A= 9 12 1 = ·2 ·3 · 3 6 1 = 3 · 3 0 1 = 3 sq. units
26 8 1 2 2 4 1 2 0 1
III–PART:
r1 = ; r2 = ; r3 =
sa sb sc
18 ·24 18 24 30
= = 216 ; s = = 36
2 2
216 216 216
r1 = = 12 ; r2 = = 18 ; r3 = = 36 ]
36 18 36 24 36 30