CBSE
If g(x) = then g(x +π) equals
g(x)/g(π)
g(x) +g(π)
g (x) - g(π)
g(x). g(π)
B.
g(x) +g(π)
C.
g (x) - g(π)
Integral
To find g(x+π) in terms of g(x) of g(π)
Let ABCD be a parallelogram such that and ∠BAD be an acute angle. If is the vector that coincides with the altitude directed from the vertex B the side AD, then is given byLet ABCD be a parallelogram such that AB = q,AD = p and ∠BAD be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by (1)
D.
Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.
Statement 1: f′(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5).
Statement 1 is false, statement 2 is true
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
Statement 1 is true, statement 2 is false
C.
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
f(x) = 7 – 2x; x < 2
= 3; 2 ≤ x ≤ 5
= 2x – 7; x > 5
f(x) is constant function in [2, 5]
f is continuous in [2, 5] and differentiable in (2, 5) and f(2) = f(5)
by Rolle’s theorem f′(4) = 0
∴ Statement 2 and statement 1 both are true and statement 2 is correct explanation for statement 1.
Let be two unit vectors. If the vectors and are perpendicular to each other, then the angle between is
π/6
π/2
π/3
π/4
C.
π/3
If: R →R is a function defined by where [x] denotes the greatest integer function, then f is
continuous for every real x
discontinous only at x = 0
discontinuous only at non-zero integral values of x
continuous only at x =0
A.
continuous for every real x
If the integral then an equal to
-1
-2
1
2
D.
2
⇒ |
Let P and Q be 3 × 3 matrices with P ≠ Q. If P^{3}= Q^{3 }and P^{2}Q = Q^{2}P, then determinant of(P^{2}+ Q^{2}) is equal to
-2
1
0
-1
C.
0
P^{3}= Q^{3}
P^{3}– P^{2}Q = Q^{3}– Q^{2}P
P^{2}(P – Q) = Q^{2}(Q – P)
P^{2}(P – Q) + Q^{2}(P – Q) = O
(P^{2}+ Q^{2})(P – Q) = O
⇒ |P^{2}+ Q^{2}| = 0
The population p(t) at time t of a certain mouse species satisfies the differential equation . if p (0) = 850, then the time at which the population becomes zero is
2 log 18
log 9
log 18
A.
2 log 18
Let a, b ∈ R be such that the function f given by f(x) = ln |x| + bx
2+ ax, x ≠ 0 has extreme values at x = –1 and x = 2.
Statement 1: f has local maximum at x = –1 and at x = 2.
Statement 2:
Statement 1 is false, statement 2 is true
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
Statement 1 is true, statement 2 is false
B.
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
(i) A function f, such that f(x)= log |x| +bx^{2} +ax, x≠0
(ii) The function 'f' has extrema at x = -1 and x =2 i.e, f'(1) = f'(2) = 0 and f''(-1) ≠ 0≠f''(2)
Now, given function f is given by
f(x) = log |x| +bx^{2} +ax
Since 'f' has extrema at x = - 1 and x =2
Hence, f'(-1) = 0 =f'(2)
f'(-1) = 0
⇒ a-2b =1 ..... (i)
and f'(2) = 0
⇒ a+ 4b = -1/2
solving eq. (i) and (ii), we get
a =1/2 and b = -1/4
⇒ f'' has local maxima at both x = - 1 and x =2
Thus, a statement I is correct. Also, while solving for the statement I, we found values of a and b, which justify that statement 2 is also correct.
Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is
880
629
630
879
D.
879