Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 - KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS HYD – 32 REVISION TEST - 02 FOR CLASS XII BOARD EXAM 2021 Sample Answers Max. marks: 40 Time Allowed: 1½ hr SECTION – A (1 MARK EACH) 1. Let A be any non-empty set and P(A) be the power set of A. A relation R defined on P(A) by X R Y X ∩ Y = X, X, Y ∈ P(A). Examine whether R is symmetric. 2. Write the principal values of sec –1 (–2). 3. If matrix A = [1 2 3] then find AA′, where A′ is the transpose of matrix A. 4. Given a square matrix A of order 3 × 3, such that | A| = 12, find the value of | A . adj A|. 5. Find dy dx , if x 2 + y 2 = 5 SECTION – B (2 MARKS EACH) 6. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one. Given f : {1, 2, 3} ⟶ {4,5,6,7} as f={(1,4),(2,5),(3,6)}. We have f(1) = 4, f(2) = 5, f(3) = 6. We notice x1 ≠ x2 then f(x1) ≠ f(x2). Hence, f is one-one. 7. Write cot –1 2 1 1 x , |x| > 1 in the simplest form.
Transcript
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -
KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS HYD – 32 REVISION TEST - 02 FOR CLASS XII BOARD EXAM 2021
Sample Answers Max. marks: 40 Time Allowed: 1½ hr
SECTION – A (1 MARK EACH)
1. Let A be any non-empty set and P(A) be the power set of A. A relation R defined on P(A) by X
R Y X ∩ Y = X, X, Y ∈ P(A). Examine whether R is symmetric.
2. Write the principal values of sec–1(–2).
3. If matrix A = [1 2 3] then find AA′, where A′ is the transpose of matrix A.
4. Given a square matrix A of order 3 × 3, such that |A| = 12, find the value of |A . adj A|.
5. Find dydx
, if x2 + y2 = 5
SECTION – B (2 MARKS EACH)
6. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one. Given f : {1, 2, 3} ⟶ {4,5,6,7} as f={(1,4),(2,5),(3,6)}. We have f(1) = 4, f(2) = 5, f(3) = 6. We notice x1 ≠ x2 then f(x1) ≠ f(x2). Hence, f is one-one.
7. Write cot–12
11x
, |x| > 1 in the simplest form.
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2 -
8. If 1 2 3 1 7 113 4 2 5 23k
, then write the value of k.
9. If x ∈ N and 3 2
8,3 2
xx x
then find the value of x.
10. Discuss the continuity of the function f(x) at x = 1, defined by
f(x) =
13 1,22
3 , 123 , 1 22
if xx
if x
x if x
11. Prove that the tangents to the curve y = x3 + 6 at the points (–1, 5) and (1, 7) are parallel.
SECTION – C (3 MARKS EACH) 12. Show that the relation S in the set R of real numbers, defined as
S = {(a, b) : a, b ∈ R and a ≤ b3} is neither reflexive, nor symmetric, nor transitive.
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 3 -
13. If A = 1 2 22 1 22 2 1
, verify that A2 – 4A – 5I = O.
14. Find the intervals in which the function f(x) = x4 – 4x3 – 45x2 + 51 is (i) strictly increasing (ii) strictly decreasing.
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 4 -
SECTION – D (5 MARKS EACH)
15. If A = 2 3 53 2 41 1 2
, find A–1. Using A–1 solve the following system of equations:
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 5 -
CASE STUDY-BASED QUESTIONS (Each sub-question carries 1 mark)
17. A farmer wants to construct a small tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. The cost of building tank is Rs. 70 per sq metre for the base and Rs. 45 per sq metre for sides.
Based on the above information, answer the following questions: (Attempt any four)
(i) Find a function that models the cost of the box.
(ii) Find the length and breadth of the box for which the cost of the box is minimum.
Length = 2 m and Breadth = 2 m.
(iii) Find the cost of least expensive tank. Rs. 1000
(iv) If the volume is doubled, then find the increased cost of tank. Following the above steps, we get x = y = 2 2 C = 560 + 180 (2 2 +2 2 ) = 560 + 720 2 = 560 + 720 x 1.414 = 1578.08 Increased cost = Rs. 578.08
(v) If the top is closed and the rate is same as for the base, then find the cost of least expensive tank. Rs. 1280
