$\cos 40^{\circ}+\cos 80^{\circ}+\cos 160^{\circ}+\cos 240^{\circ}=$
- A$\frac{1}{2}$
- B$\frac{-1}{2}$
- C1
- D$0$
Question types
Model Paper 2 question types
45 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
45
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
18 Q→022 Marks Questions
7 Q→033 Marks Question
9 Q→045 Marks Questions
6 Q→05Assertion (A) & Reason (B) MCQ
2 Q→06Case study (4 Marks)
3 Q→Sample Questions
Model Paper 2 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\lim _{x \rightarrow a} \frac{x^n-a^n}{x-a}$ is equal to:
- A$n a^{ n -1}$
- B1
- C$na^n$
- Dna
The lines $8 x+4 y=1,8 x+4 y=5,4 x+8 y=3,4 x+8 y=7$ form a
- ATrapezium
- BRhombus
- CRectangle
- DSquare
$(\sqrt{5}+1)^4+(\sqrt{5}-1)^4$ is
- Aan irrational number
- Ba negative real number
- Ca rational number
- Da negative integer
In an examination, a candidate has to pass in each of the five subjects. In how many ways can he fail?
- A31
- B10
- C21
- D5
An integer is chosen at random from the numbers ranging from 1 to 50. What is the probability that the integer chosen is a multiple of 2 or 3 or 10?
f, g and h are three functions defined from R to R as follows:
i. $f(x)=x^2$
ii. $g(x)=x^2+1$
iii. $h(x)=\sin x$
Then, find the range of each function.
View full solution →i. $f(x)=x^2$
ii. $g(x)=x^2+1$
iii. $h(x)=\sin x$
Then, find the range of each function.
Find the domain and range of the function $f(x)=1-|x-2|$
View full solution →In what ratio is the line joining the points (2, 3) and (4, -5) divided by the line passing through the points (6, 8) and (-3, -2).
If $A=\{a, b, c, d, e\}, B=\{a, c, e, g\}$ and $C=\{b, e, f, g\}$, verify that: $(A \cap B) \cap C=A \cap(B \cap C)$
View full solution →Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science, 4 in English and Science, 4 in all the three. Find how many passed
i. in English and Mathematics but not in Science
ii. in Mathematics and Science but not in English
iii. in Mathematics only
iv. in more than one subject only
i. in English and Mathematics but not in Science
ii. in Mathematics and Science but not in English
iii. in Mathematics only
iv. in more than one subject only
Differentiate $\frac{x^2-1}{x}$ from first principle.
View full solution →Show that the coefficient of the middle term in the expansion of $(1+ x )^{2 n }$ is equal to the sum of the coefficients of middle terms in the expansion of $(1+x)^{2 n -1}$.
View full solution →The letters of the word SURITI are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word SURITI.
Find a G.P. for which sum of the first two term is -4 and the fifth term is 4 times the third term.
Prove that: $\cos ^3 x \sin 3 x+\sin ^3 x \cos 3 x=\frac{3}{4} \sin 4 x$.
View full solution →Draw the shape of the ellipse $4 x^2+9 y^2=36$ and find its major axis, minor axis, value of $c$, vertices, directrices, foci, eccentricity and length of latusrectum.
View full solution →Solve the following system of linear inequalities
$-2-\frac{x}{4} \geq \frac{1+x}{3}$ and $3-x<4(x-3)$
View full solution →$-2-\frac{x}{4} \geq \frac{1+x}{3}$ and $3-x<4(x-3)$
Find the equation of the parabola whose focus is (1, -1) and whose vertex is (2, 1). Also find its axis and latus rectum.
Prove that: $\cos 10^{\circ} \cos 30^{\circ} \cos 50^{\circ} \cos 70^{\circ}=\frac{3}{16}$.
View full solution →Assertion (A): Let $A =\{1,2,3\}$ and $B =\{1,2,3,4\}$. Then, $A \subset B$.
Reason (R): If every element of $X$ is also an element of $Y$, then $X$ is a subset of $Y$.
Reason (R): If every element of $X$ is also an element of $Y$, then $X$ is a subset of $Y$.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Assertion (A): The sum of infinite terms of a geometric progression is given by $S_{\infty}=\frac{a}{1-r}$, provided $|r|<1$.
Reason (R): The sum of n terms of Geometric progression is $S _{ n }=\frac{a\left(r^n-1\right)}{r-1}$.
Reason (R): The sum of n terms of Geometric progression is $S _{ n }=\frac{a\left(r^n-1\right)}{r-1}$.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
iConsider the complex number Z = 2 - 2i.
Complex Number in Polar Form
i. Find the principal argument of Z. (1)
ii. Find the value of $z \overline { Z }$ ? (1)
iii. Find the value of $| Z |$. (2)
OR
Find the real part of Z. (2)
View full solution →Complex Number in Polar Form
i. Find the principal argument of Z. (1)
ii. Find the value of $z \overline { Z }$ ? (1)
iii. Find the value of $| Z |$. (2)
OR
Find the real part of Z. (2)
Consider the graphs of the functions f(x), h(x) and g(x).
i. Find the range of h(x). (1)
ii. Find the domain of f(x). (1)
iii. Find the value of f(10). (2)
OR
Find the range of g(x). (2)
i. Find the range of h(x). (1)
ii. Find the domain of f(x). (1)
iii. Find the value of f(10). (2)
OR
Find the range of g(x). (2)
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