In an examination, a candidate has to pass in each of the five subjects. In how many ways can he fail?
- ✓$31$
- B$10$
- C$21$
- D$5$
Answer: A.
View full solution →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→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
9 Q→05Case study (4 Marks)
3 Q→065 Marks Questions
6 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:
- ✓$n a^{ n -1}$
- B$1$
- C$na^n$
- D$na$
Answer: A.
View full solution →$\sin 18^{\circ}=?$
- A$\frac{(\sqrt{3}+1)}{2}$
- B$\frac{(\sqrt{3}-1)}{2}$
- C$\frac{(\sqrt{5}+1)}{4}$
- D$\frac{(\sqrt{5}-1)}{4}$
Which of the following is a null set?
- A$C =\phi$
- B$B=\{x: x+3=3\}$
- C$D=\{0\}$
- D
Solve the system of inequalities $(x+5)-7(x-2) \geq 4 x+9,2(x-3)-7(x+5) \leq 3 x-9$
- ✓$\frac{-9}{4} \leq x \leq 1$
- B$-4 \leq x \leq 1$
- C$-1 \leq x \leq 1$
- D$-4 \leq x \leq 4$
Answer: A.
View full solution →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.
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.
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 $(-3, -2).$
View full solution →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 →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 $10$ ?
View full solution →One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be a black card (i.e., a club or, a spade).
Differentiate the function with respect to $x:\left(3 x^2-x+1\right)^4$.
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
View full solution →$i.$ 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
Find a $G.P.$ for which sum of the first two term is $-4$ and the fifth term is $4$ times the third term.
View full solution →If the $p^{\text {th }}$ and $q^{\text {th }}$ terms of a $GP$ are $q$ and $p$ respectively, then show that $(p+q)^{\text {th }}$ term is $\left(\frac{q^p}{p^f}\right)^{\frac{1}{p-q}}$.
View full solution →Find the derivative of function $\frac{a x+b}{c x+d} ($it is to be understood that $a , b , c , d , p , q , r$ and $s$ are fixed non$-$zero constants and $m$ and $n$ are integers$).$
View full solution →Differentiate $\frac{x^2-1}{x}$ from first principle.
View full solution →Consider 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 $Z. (2)$
Four friends Dinesh, Yuvraj, Sonu, and Rajeev are playing cards. Dinesh, shuffling a cards and told to Rajeev choose any four cards.
$i$. What is the probability that Rajeev getting all face card. $(1)$
$ii$. What is the probability that Rajeev getting two red cards and two black card. $(1)$
$iii$. What is the probability that Rajeev getting one card from each suit. $(2)$
OR
What is the probability that Rajeev getting two king and two Jack cards. $(2)$
View full solution →$i$. What is the probability that Rajeev getting all face card. $(1)$
$ii$. What is the probability that Rajeev getting two red cards and two black card. $(1)$
$iii$. What is the probability that Rajeev getting one card from each suit. $(2)$
OR
What is the probability that Rajeev getting two king and two Jack cards. $(2)$
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)
Prove that: $\cos ^3 x \sin 3 x+\sin ^3 x \cos 3 x=\frac{3}{4} \sin 4 x$.
View full solution →Prove that: $\cos 10^{\circ} \cos 30^{\circ} \cos 50^{\circ} \cos 70^{\circ}=\frac{3}{16}$.
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 →Find the equation of the parabola whose focus is $(1, -1)$ and whose vertex is $(2, 1)$. Also find its axis and latus rectum.
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.
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