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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 7652. |
If bara,barb,barc,bard are unit co-planar vectors then abs((baraxxbarb)xx(barcxxbard)) = |
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Answer» 0 |
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| 7653. |
In Delta ABC,a(b cos C-c cos B)= |
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Answer» ` B^(2) - C^( 2) ` |
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| 7654. |
The total number of solutions of log_(e) |sin x| = - x^(2) + 2 x i n [0 , pi] is equal to |
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Answer» 1 |
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| 7655. |
Given thatcos ""(A)/(2) = (12)/(13), calculate without the use of tubles, the values of sin A , cos A and tan A. |
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| 7656. |
Drawthe graphof sixn xcos xtan xcoseccotxin theregion [-pi,3pi] |
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Answer» `(##AKS_NEO_CAO_MAT_XI_VIA_P02_C05_E03_001_A02##)` |
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| 7657. |
If x=X cos theta- Y sin theta, y= X sin theta+ Y cos theta and x^(2)+4xy+y^(2)=AX^(2), B^(2),"for " 0 le theta le (pi)/(2) then (A,B)= |
| Answer» ANSWER :C | |
| 7659. |
16(costheta-cos""(pi)/8)(costheta-cos""(3pi)/8)(costheta-cos""(5pi)/8)(costheta-cos""(7pi)/8)= lamda cos 4 thetathe value of lamda is |
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| 7660. |
Differentiate from first principles: 3. x^3 |
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| 7662. |
The pair of lines 6x^(2)+7xy+lambday^(2)=0(lambda ne -6)forms a rightangled triangle with x+3y+4=0 then lambda= |
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Answer» 3 |
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| 7663. |
If the angle betweenthe lines whose direction cosines are (-(2)/(sqrt(21)), (C )/(sqrt(21)), (1)/(sqrt(21))) and ((3)/(sqrt(54)), (3)/(sqrt(54)), -(6)/(sqrt(54))) is (pi)/(2), then the value of C is |
| Answer» ANSWER :A | |
| 7664. |
If (l_(1),m_(1),n_(1)) and (l_(2),m_(2),n_(2)) are the direction cosines of two lines find the direction cosines of the line which is perpendicular to both these lines. |
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| 7665. |
The sum of the digits in unit place of all the numbers formed using the digits 3,4,5,6 without repetitions, the no. of such numbers are |
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Answer» A. 432 |
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| 7666. |
Two parallel sides of a rectangle are being lenghtened at the rate of 2 cm/sec while the other two sides are shortened in such a way the area of the rectangle is 50 sq. cm The rate of change of the perimeter when the length of an increasing side 5 cm is |
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Answer» 2 cm/sec |
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| 7667. |
ABC is an acute-angled triangle incribed in a circle of radius 5 cm and centre O . The sine of angle A is equal to (3)/(5). Calculate without using tables : (i) the length of BC (ii) sin OBC (iii) sin BOC (iv) cos BOC |
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| 7668. |
Find the union of each of the following pairs of sets : A = {x : x is a natural number and 1 < x ≤ 6 } B = {x : x is a natural number and 6 < x < 10 } |
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| 7669. |
If P(sqrt(3),1,2sqrt(3)) is a pointin space, find direction cosines of vec(OP). |
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| 7670. |
f and g are real functions defined by f(x)= 2x + 1 and g(x) =4x -7. If f(x) < g(x)then x… 4 . |
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| 7671. |
If alpha = pi/19 then (sin 3 alpha - sin 23 alpha)/(sin 4 alpha + sin 16 alpha)= |
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Answer» 1 |
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| 7673. |
If the lines y=3x + 1 and 2y = x +3 are equally inclined to the line y= mx +4, find the value of m. |
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| 7674. |
Let X={a_(1), a_(2), .....a_(6)} and Y={b_1), b_(2), b_(3)}. The number of functions f from x to y such that it is onto and there are exactly three elements x in X such that f(x)=b_(1) is |
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Answer» 75 |
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| 7676. |
Given the relations R_1 = {(x,y) : x,y in N and x + y = 6} |
| Answer» SOLUTION :DOM `(R_1) = {1,2,3,4,5}, RANGE (R_1) = {5,4,3,2,1}` | |
| 7677. |
Find the sum to indicated number of terms in each of the geometric progressions in Exercises 1, - a, a^2, - a^3, .......n terms (if a ne -1) |
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| 7678. |
Find the point of intersection of the lines 17x+2y-28=0 and 7x+2y-8=0 |
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| 7679. |
In the hexagon PQRSTU, PS||PU||QT. Which sides or diagonals have negative slope |
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| 7680. |
Let f(x)=(1)/(1+|x|)+(1)/(1+|x-1|) then |
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Answer» f(X) has global MAXIMUM |
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| 7681. |
Given the quadratic equation (k-1)x^(2)-kx+1=0, (where kne1) , find k so that product of the roots is -3. |
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| 7682. |
Reflection of 3x+4y+5=0 w.t.to the ine 2+y+1=0 is |
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Answer» 2x+1=0 |
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| 7683. |
If in a Deltathe ex-reddii (r_(1) r_(2) r_(3) are in the ratio 1:2:3 then their sides are in the retio :- |
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Answer» `5:8:9` |
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| 7684. |
Given that y= (3x -1)^(2) + (2x -1)^(3), find (dy)/( dx)and the points on the curve for which (dy)/(dx)=0 |
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| 7686. |
Let bara = bari + 2barj+ 3bark , barb = -bari + 2barj+bark. " If " barc = 3bari +barj+tbark is perpendicular to (bara+barb), then find t. |
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| 7687. |
The scores of 48 children in an intelligence test are shown in the followingfrequency table . {:("Score ",71,76,79,83,86,89,92,97,101,103,107,110,114),("Frequency ",4,3,4,5,6,5,4,4,3,3,3,2,2):} Calculate sigma^(2) and find the percentage of students whose score lie between bar(x) - sigma and bar(x) + sigma |
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| 7688. |
Find the value of k , if the straight linesy-3kx+4=0 and (2k-1)x+ (8k-1) y -6=0 are perpendicular. |
| Answer» ANSWER :A | |
| 7689. |
If f is function such that f(0)=2, f(1)=3 and f(x+2)=2f(x)-f(x+1) for every real x, then f(5) is |
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Answer» 7 |
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| 7690. |
Write the negation of the following statements: Chennai is the capital of Tamil Nadu. |
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| 7691. |
For each of the following compound statements first identify the connecting words and then break it into component statements. (i) all rational numbers are real and all real numbers are not complex. (ii)square of an integer is positive or negative. (iii) the sand heats up quickly in the sun and does not cool down fast at night. (iv) x=2 and x=3 are the roots of the equation 3x^2-x-10=0 |
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Answer» <P> Solution :(i) Connecting word : AndComponent p: all rational numbers are REAL. component q: all real number are not complex (ii) Connecting word : or component p : square of an integer is POSITIVE. component q: square of an integer is negative . (iii) Connecting word : And component p : the SAND heats up quickly in the sun. component q: the sand does not cool down fast at night . (iv) Connecting word : And component p: `x=2` is a root of the equaiton `3x^2-x-10=0` component q: `x=3` is a root of the equation `3x^2-x-10=0`. |
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| 7692. |
If tan^(4)x+tan^(4)y+2cot^(2)xcot^(2)y=3+sin^(2)(x+y) then |
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Answer» `x = y = N pi pm (pi)/(6), n in Z` |
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| 7693. |
Iff(x) = {{:(|x| cos ""((1)/(x))+ 9x^(2)" , " x ne 0 ),( k " , " x= 0):} then f is continuous if the value of 'k' is |
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Answer» 9 |
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| 7694. |
A small industrial concern used three raw materials A, B and C in its manufacturing process. The price, in £ per kg, of these materials are shown below: Using 1957 as the base year, calculate for 1967. (i) a simple aggregate price index. |
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| 7695. |
There are 5 teachersand 20 students . Out of thema committee ofteachers and 3 studentsis to be formed. Find the number of ways in which this can be done.Further find in how manyof thesecommittees (a) a particularteacheris included ? (ii)a particularstudent is excluded ? |
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Answer» (II) 9690 |
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| 7696. |
Statement 1 : The period of the function f(x)=sin {x} is 1, where {.} represents fractional part function. Statement 2 : g(x)={x} has period 1. |
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Answer» STATEMENT 1 is true, statement 2 is true, statement 2 ISCORRECT explanation for statement 1. |
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| 7698. |
A committee of 7 peoples has to be formed from 9 men and 4 women . In howmanycan thisbe donewhenthen committeeconsists of (i) exactly3 women ? (ii)at least3 woman ? (iii) at most3 women ? |
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| 7699. |
The tangent function whose period is (2)/(3) is |
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Answer» `tan""(PI X)/(2)` |
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