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Solution
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Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
If
k
∫
0
dx
2+18x2
=
π
24
 , then the value of K is
©
If
k
∫
0
dx
2+18x2
=
π
24
 , then the value of K is
©
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
The Cartesian co-ordinates of the point on the parabola y2 = -16x. whose parameter is
1
2
, are
©
The Cartesian co-ordinates of the point on the parabola y2 = -16x. whose parameter is
1
2
, are
©
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
∫
1
sinx‌cos2‌x
‌dx =
©
∫
1
sinx‌cos2‌x
‌dx =
©
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
If log10(
x3−y3
x3+y3
) = 2 then
dy
dx
 =
©
If log10(
x3−y3
x3+y3
) = 2 then
dy
dx
 =
©
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
If f : R - {2} → R is a function defined by f(x) =
x2−4
x−2
 , then its range is
©
If f : R - {2} → R is a function defined by f(x) =
x2−4
x−2
 , then its range is
©
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
If f(x) = {
x2+αfor‌x>0
2√x2+1+βfor‌x<0
) is continuous at x = 0 and f (
1
2
)= 2 then α2+β2 is
©
If f(x) = {
x2+αfor‌x>0
2√x2+1+βfor‌x<0
) is continuous at x = 0 and f (
1
2
)= 2 then α2+β2 is
©
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
If y = (tan−1x)2 then (x2+1)2
d2y
dx2
 + 2x(x2+1)
dy
dx
=
©
If y = (tan−1x)2 then (x2+1)2
d2y
dx2
 + 2x(x2+1)
dy
dx
=
©
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
The line 5x + y - 1 = 0 coincides with one of the lines given by 5x2 + xy- kx - 2y + 2 = 0 then the value of k is
©
The line 5x + y - 1 = 0 coincides with one of the lines given by 5x2 + xy- kx - 2y + 2 = 0 then the value of k is
©
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
If A = [
123
−112
124
] then (A2−5A)A−1 =
©
If A = [
123
−112
124
] then (A2−5A)A−1 =
©
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
The equation of line passing through (3, -1 ,2 ) and perpendicular to the lines
→
r
=(
^
i
+
^
j
−
^
k
) + λ (2
^
i
−2
^
j
+
^
k
) and
→
r
=(2
^
i
+
^
j
−3
^
k
) + µ (
^
i
−2
^
j
+2
^
k
) is
©
The equation of line passing through (3, -1 ,2 ) and perpendicular to the lines
→
r
=(
^
i
+
^
j
−
^
k
) + λ (2
^
i
−2
^
j
+
^
k
) and
→
r
=(2
^
i
+
^
j
−3
^
k
) + µ (
^
i
−2
^
j
+2
^
k
) is
©
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
Letters in the word HULULULU are rearranged. The Probability of all three L being together is
©
Letters in the word HULULULU are rearranged. The Probability of all three L being together is
©
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
The sum of the first 10 terms of the series 9 + 99 + 999 +...,is
©
The sum of the first 10 terms of the series 9 + 99 + 999 +...,is
©
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
If A, B, C are the angles of Δ ABC then cotA.cotB + cotB. cotC + cotC + cotA =
©
If A, B, C are the angles of Δ ABC then cotA.cotB + cotB. cotC + cotC + cotA =
©
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
If ∫
dx
√16−9x2
 = Asin−1 (Bx) + C then A+ B =
©
If ∫
dx
√16−9x2
 = Asin−1 (Bx) + C then A+ B =
©
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
∫ex[
2+sin2x
1+cos2x
]dx =
©
∫ex[
2+sin2x
1+cos2x
]dx =
©
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
A coin is tossed three times. If X denotes the absolute difference beween the number of heads and the number of tails then P(X = 1) =
©
A coin is tossed three times. If X denotes the absolute difference beween the number of heads and the number of tails then P(X = 1) =
©
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
If 2 sin (θ+
π
3
) = cos (θ−
π
6
) , then tan θ =
©
If 2 sin (θ+
π
3
) = cos (θ−
π
6
) , then tan θ =
©
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
The area of the region bounded by x2 = 4y, y = 1 , y = 4 and the y-axis lying in the first quadrant is square units.
©
The area of the region bounded by x2 = 4y, y = 1 , y = 4 and the y-axis lying in the first quadrant is square units.
©
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
If f (x) =
ex2−cosx
x2
 , for x ≠ 0 is continuous at x = 0, then value of f(0) is
©
If f (x) =
ex2−cosx
x2
 , for x ≠ 0 is continuous at x = 0, then value of f(0) is
©
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
The maximum value of 2x + y subject to 3x + 5y ≤ 26 and 5x + 3y ≤ 30, x ≥ 0, y ≥ 0 is
©
The maximum value of 2x + y subject to 3x + 5y ≤ 26 and 5x + 3y ≤ 30, x ≥ 0, y ≥ 0 is
©
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
If
→
a
,
→
b
,
→
c
 are mutually perpendicular vectors having magnitudes 1,2,3 respectively, then [
→
a
+
→
b
+
→
c
‌‌
→
b
−
→
a
‌‌
→
c
] =
©
If
→
a
,
→
b
,
→
c
 are mutually perpendicular vectors having magnitudes 1,2,3 respectively, then [
→
a
+
→
b
+
→
c
‌‌
→
b
−
→
a
‌‌
→
c
] =
©
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
If points P(4,5, x), Q(3, y, 4) and R(5, 8, 0) are collinear, then the value of x + y is
©
If points P(4,5, x), Q(3, y, 4) and R(5, 8, 0) are collinear, then the value of x + y is
©
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
If the slope of one the lines given by ax2 +2hxy + by2 = 0 is two times the other then
©
If the slope of one the lines given by ax2 +2hxy + by2 = 0 is two times the other then
©
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
The equation of the line passing through the point (3 ,1 ) and bisecting the angle between co-ordinate axes is
©
The equation of the line passing through the point (3 ,1 ) and bisecting the angle between co-ordinate axes is
©
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
The negation of the statement: “ Getting above 95% marks is necessary condition for Hema to get the admission in good college”.
©
The negation of the statement: “ Getting above 95% marks is necessary condition for Hema to get the admission in good college”.
©
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
Cos1°.Cos2°.Cos3°... Cos 179° =
©
Cos1°.Cos2°.Cos3°... Cos 179° =
©
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
If planes x - cy - bz = 0, cx - y + az = 0 and bx + ay - z = 0 pass through a straight line then a2+b2+c2 =
©
If planes x - cy - bz = 0, cx - y + az = 0 and bx + ay - z = 0 pass through a straight line then a2+b2+c2 =
©
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
The point of intersection of line represented by x2−y2 + 3 - 2 = 0 is
©
The point of intersection of line represented by x2−y2 + 3 - 2 = 0 is
©
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
A die is rolled. If X denotes the number of positive divisors of the outcome then the range of the random variable X is
©
A die is rolled. If X denotes the number of positive divisors of the outcome then the range of the random variable X is
©
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
A die is thrown four times. The probability of getting perfect square in at least one throw is
©
A die is thrown four times. The probability of getting perfect square in at least one throw is
©
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
π
4
∫
0
x.sec2xdx =
©
π
4
∫
0
x.sec2xdx =
©
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
In Δ ABC, with usual notations, if a, b, c are in A.P. Then a‌cos2(
A
2
) + c cos2(
A
2
)
©
In Δ ABC, with usual notations, if a, b, c are in A.P. Then a‌cos2(
A
2
) + c cos2(
A
2
)
©
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
If x = eθ (sinθ - cos θ) , y = eθ (sin θ + cos θ) , then
dy
dx
 at θ =
π
4
 is
©
If x = eθ (sinθ - cos θ) , y = eθ (sin θ + cos θ) , then
dy
dx
 at θ =
π
4
 is
©
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval [
π
2
,3
π
2
] is
©
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval [
π
2
,3
π
2
] is
©
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
If tan−12x + tan−1 3x =
π
4
 then x =
©
If tan−12x + tan−1 3x =
π
4
 then x =
©
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
Matrix A = [
123
115
247
] then the value of a31A31 + a32A32 + a33A33 is
©
Matrix A = [
123
115
247
] then the value of a31A31 + a32A32 + a33A33 is
©
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
The contrapositive of the statement : “If the weather is fine then my friends will come and we go for a picnic.”
©
The contrapositive of the statement : “If the weather is fine then my friends will come and we go for a picnic.”
©
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
If f(x) =
x
x2+1
 is increasing function then the value of x lies in
©
If f(x) =
x
x2+1
 is increasing function then the value of x lies in
©
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
If X = {4n - 3n - 1 : n ∊ N} and Y = {9n - 1: n ∊ N}, then X ∩ Y =
©
If X = {4n - 3n - 1 : n ∊ N} and Y = {9n - 1: n ∊ N}, then X ∩ Y =
©
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
The statement pattern P ∧ (~ p ∧ q ) is
©
The statement pattern P ∧ (~ p ∧ q ) is
©
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
If the line y = 4x - 5 touches to the curve y2=ax3 + b at the point (2, 3) then 7a + 2b =
©
If the line y = 4x - 5 touches to the curve y2=ax3 + b at the point (2, 3) then 7a + 2b =
©
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
The sides of a rectangle are given by x = ± a and y = ± b. The equation of the circle passing through the vertices of the rectangle is
The sides of a rectangle are given by x = ± a and y = ± b. The equation of the circle passing through the vertices of the rectangle is
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
The minimum value of the function f(x) = xlogx is
©
The minimum value of the function f(x) = xlogx is
©
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
If X ~ B (n,p) with n = 10, p = 0.4 then E(X2) =
©
If X ~ B (n,p) with n = 10, p = 0.4 then E(X2) =
©
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
The general solution of differential equation
dx
dy
 = cos ( x + y ) is
©
The general solution of differential equation
dx
dy
 = cos ( x + y ) is
©
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
If planes
→
r
.(p
^
i
−
^
j
+2
^
k
) + 3 = 0 and
→
r
.(2
^
i
−p
^
j
−
^
k
) - 5 = 0 include angle
π
3
 then the value of p is
©
If planes
→
r
.(p
^
i
−
^
j
+2
^
k
) + 3 = 0 and
→
r
.(2
^
i
−p
^
j
−
^
k
) - 5 = 0 include angle
π
3
 then the value of p is
©
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is
©
The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is
©
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
If lines
x−1
2
 =
y+1
3
 =
z−1
4
 and x - 3 =
y−k
2
 = z intersect then the value of k is
©
If lines
x−1
2
 =
y+1
3
 =
z−1
4
 and x - 3 =
y−k
2
 = z intersect then the value of k is
©
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
If a line makes angles 120° and 60° with the positive directions of X and Z axes respectively then the angle made by the line with positive Y-axis is
©
If a line makes angles 120° and 60° with the positive directions of X and Z axes respectively then the angle made by the line with positive Y-axis is
©
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
L and M are two points with position vectors 2
→
a
−
→
b
 and
→
a
+2
→
b
 respectively. The position vector of the point N which divides the line segment LM in the ratio 2 : 1 extenally is
©
L and M are two points with position vectors 2
→
a
−
→
b
 and
→
a
+2
→
b
 respectively. The position vector of the point N which divides the line segment LM in the ratio 2 : 1 extenally is
©
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